From 23650be6350636356a817e0253dc639b830e1979 Mon Sep 17 00:00:00 2001
From: onur <onur@rpi.local>
Date: Sun, 26 Jul 2026 01:59:08 +0300
Subject: [PATCH] feat(gps): split Doppler paths for ESKF and PPS

---
 README.md                                     |  40 +-
 soc/software/fusion/README.md                 |  35 +-
 .../gps_measurement_python/.gitignore         |   3 +
 soc/software/gps_measurement_python/README.md | 226 ++++++
 .../gps_measurement_python/__init__.py        |   1 +
 .../analyze_doppler_eskf.py                   | 428 ++++++++++++
 .../analyze_measurement_scenarios.py          | 425 +++++++++++
 .../code_smoothing_model.py                   | 132 ++++
 .../doppler_eskf_model.py                     | 657 ++++++++++++++++++
 .../firmware_wls_model.py                     | 353 ++++++++++
 .../measurement_scenarios.py                  | 368 ++++++++++
 .../output/01_position_3d_rms.png             | Bin 0 -> 88002 bytes
 .../output/02_solution_availability.png       | Bin 0 -> 93875 bytes
 .../output/03_noise_burst_transition.png      | Bin 0 -> 217925 bytes
 .../output/04_code_smoothing_cfo.png          | Bin 0 -> 41999 bytes
 .../output/05_doppler_eskf_velocity_rms.png   | Bin 0 -> 85959 bytes
 .../output/06_airliner_maneuver_trace.png     | Bin 0 -> 180062 bytes
 .../output/07_outlier_wls_nis.png             | Bin 0 -> 188184 bytes
 .../output/08_low_cn0_wls_vs_eskf.png         | Bin 0 -> 360934 bytes
 .../gps_measurement_python/output/ANALYSIS.md |  94 +++
 .../output/DOPPLER_ESKF_ANALYSIS.md           |  65 ++
 .../output/doppler_eskf_summary.csv           |  33 +
 .../output/scenario_summary.csv               |  51 ++
 .../gps_measurement_python/requirements.txt   |   2 +
 .../gps_measurement_python/rtl_dll_model.py   | 200 ++++++
 .../test_doppler_eskf_model.py                | 148 ++++
 .../test_measurement_model.py                 | 182 +++++
 soc/software/gps_system/README.md             |  96 ++-
 .../gps_system/header/gps/NavEquations.h      |   6 +
 .../header/gps/gps_tracking_measurement.h     |  23 +
 .../gps_system/src/adapters/gps_system_uart.c |   3 +-
 .../src/gps/gps_interrupt_handlers.c          |   8 +-
 soc/software/gps_system/src/gps/gps_ip.c      |  70 +-
 .../src/gps/gps_tracking_measurement.c        | 229 +++++-
 .../tests/test_gps_tracking_measurement.c     |  88 +++
 35 files changed, 3884 insertions(+), 82 deletions(-)
 create mode 100644 soc/software/gps_measurement_python/.gitignore
 create mode 100644 soc/software/gps_measurement_python/README.md
 create mode 100644 soc/software/gps_measurement_python/__init__.py
 create mode 100644 soc/software/gps_measurement_python/analyze_doppler_eskf.py
 create mode 100644 soc/software/gps_measurement_python/analyze_measurement_scenarios.py
 create mode 100644 soc/software/gps_measurement_python/code_smoothing_model.py
 create mode 100644 soc/software/gps_measurement_python/doppler_eskf_model.py
 create mode 100644 soc/software/gps_measurement_python/firmware_wls_model.py
 create mode 100644 soc/software/gps_measurement_python/measurement_scenarios.py
 create mode 100644 soc/software/gps_measurement_python/output/01_position_3d_rms.png
 create mode 100644 soc/software/gps_measurement_python/output/02_solution_availability.png
 create mode 100644 soc/software/gps_measurement_python/output/03_noise_burst_transition.png
 create mode 100644 soc/software/gps_measurement_python/output/04_code_smoothing_cfo.png
 create mode 100644 soc/software/gps_measurement_python/output/05_doppler_eskf_velocity_rms.png
 create mode 100644 soc/software/gps_measurement_python/output/06_airliner_maneuver_trace.png
 create mode 100644 soc/software/gps_measurement_python/output/07_outlier_wls_nis.png
 create mode 100644 soc/software/gps_measurement_python/output/08_low_cn0_wls_vs_eskf.png
 create mode 100644 soc/software/gps_measurement_python/output/ANALYSIS.md
 create mode 100644 soc/software/gps_measurement_python/output/DOPPLER_ESKF_ANALYSIS.md
 create mode 100644 soc/software/gps_measurement_python/output/doppler_eskf_summary.csv
 create mode 100644 soc/software/gps_measurement_python/output/scenario_summary.csv
 create mode 100644 soc/software/gps_measurement_python/requirements.txt
 create mode 100644 soc/software/gps_measurement_python/rtl_dll_model.py
 create mode 100644 soc/software/gps_measurement_python/test_doppler_eskf_model.py
 create mode 100644 soc/software/gps_measurement_python/test_measurement_model.py

diff --git a/README.md b/README.md
index 023aedc..64fd25a 100644
--- a/README.md
+++ b/README.md
@@ -136,7 +136,7 @@ tracking loop, her 20 ms:
       -> sabit tracking snapshot
       -> synchronizer + APB-domain atomik register + interrupt
       -> C/N0 ve Doppler/range-rate donusumu
-      -> satellite velocity/clock-drift duzeltmeli C/N0-weighted velocity WLS
+      -> ham Doppler + tek-kanal FDE ile C/N0-weighted velocity WLS
       -> ECEF velocity + 3x3 covariance + receiver clock drift
       -> ECEF->ENU adapter
       -> ayri velocity NIS gate
@@ -145,14 +145,42 @@ tracking loop, her 20 ms:
 ```
 
 RTL Doppler veya C/N0 uzerinde IIR yapmaz; ham ve 20 ms sabit snapshot'i
-software'e verir. Software ayni PRN icin C/N0'yi `alpha=0.2`, Doppler'i
-`alpha=0.05` ile yumusatir. L1 range-rate
-`-doppler_hz * c / 1575420000` ile hesaplanir. En az dort uyduyla cozulmus
-velocity WLS state'i `[vx, vy, vz, receiver_clock_drift_mps]`'dir; uydu LOS
-hizi ve broadcast satellite clock drift observation'dan ayrilir. C/N0,
+software'e verir. Software ayni PRN icin C/N0'yi `alpha=0.2` ile yumusatir;
+Doppler'in hem ham de `alpha=0.05` IIR sonucu korunur. L1 range-rate
+`-doppler_hz * c / 1575420000` ile hesaplanir. Ham yol tek-kanal
+leave-one-out FDE'li velocity WLS'ten ESKF'ye, filtreli yol ayri velocity
+WLS'ten yalniz PPS clock-bias drift predictor'una gider. PPS'in ana faz/zaman
+olcumu position WLS `clock_bias_m` sonucudur; Doppler yalniz 200 ms epoch'lar
+arasindaki turev prediction'ina ve kalite siniflandirmasina yardim eder. Her
+iki velocity WLS state'i `[vx, vy, vz, receiver_clock_drift_mps]`'dir; uydu
+LOS hizi ve broadcast satellite clock drift observation'dan ayrilir. C/N0,
 range-rate agirligini belirler; post-fit residual gerekirse formal
 covariance'i yalniz buyutur.
 
+Klasik mutlak-pseudorange GNSS modelinde receiver zaman hatasi
+`delta_t_r(t)` ise:
+
+```text
+code WLS 4. state:     b_r     = c * delta_t_r             [metre]
+Doppler WLS 4. state:  bdot_r  = c * d(delta_t_r)/dt       [metre/saniye]
+b_r(t + dt) ~= b_r(t) + bdot_r * dt
+```
+
+Burada `bdot_r`, receiver oscillator frequency error'inin range-rate
+birimindeki ortak etkisidir. Ornegin `0.1 ppm` yaklasik `29.98 m/s` eder;
+Doppler WLS bu ortak terimi uydu yonune gore degisen gercek `vx/vy/vz`
+hareketinden ayirir.
+
+Bu projede onemli bir datum farki vardir: position WLS'e verilen capture
+zamanlarindan ortak receiver zamani cikarilir ve `STARTOFFSET` eklenir. Bu
+nedenle `solution.clock_bias_m`, saf `c*delta_t_r` degil, yaklasik
+`c*STARTOFFSET - reference_range` olan referans-uyduya bagli goreli
+datumdur. Doppler WLS'nin dorduncu bilinmeyeni yine uydulara ortak receiver
+clock/frequency drift'tir; fakat iki fit arasinda
+`clock_bias_m(t+dt)=clock_bias_m(t)+clock_drift_mps*dt` kisiti kurulmaz.
+Fit'ler ayri measurement/normal-equation kullanir. Doppler WLS, LOS
+vektorleri icin position WLS'nin guncel receiver konumuna baglidir.
+
 ESKF; ENU position/velocity, quaternion attitude, accel bias ve gyro bias
 iceren 15 hata durumlu filtredir. Her timestamp'li IMU ornegi prediction'a
 girer. Gecikmis GPS position ve Doppler velocity olcumleri kendi capture
diff --git a/soc/software/fusion/README.md b/soc/software/fusion/README.md
index a1bfc32..6648307 100644
--- a/soc/software/fusion/README.md
+++ b/soc/software/fusion/README.md
@@ -98,14 +98,17 @@ TDK veya ST IMU -> imu_sensor ----/
    kontrol eder. Carrier değeri için
    `doppler_hz = carrier_q7/128 - 4092000`, L1 pseudorange-rate için
    `range_rate = -doppler_hz*c/1575420000` kullanılır.
-3. Aynı PRN'in 50 Hz snapshot'larında C/N0 `alpha=0.2`, Doppler `alpha=0.05`
-   software IIR ile yumuşatılır. RTL ham ölçümü korur; hardware Doppler IIR
-   içermez.
-4. En az dört uyduyla C/N0-weighted velocity WLS
+3. Aynı PRN'in 50 Hz snapshot'larında C/N0 `alpha=0.2` ile yumuşatılır.
+   Doppler'in ham değeri ile `alpha=0.05` software-IIR değeri ayrı tutulur;
+   RTL hardware Doppler IIR içermez.
+4. Ham Doppler, en az dört uyduyla C/N0-weighted velocity WLS
    `[receiver_vx, receiver_vy, receiver_vz, receiver_clock_drift_mps]`
    state'ini çözer. Her observation'dan satellite LOS velocity çıkarılır,
    broadcast satellite clock drift eklenir. Inverse normal matrix ve post-fit
-   residual ECEF velocity covariance'ini üretir.
+   residual ECEF velocity covariance'ini üretir. En az altı kullanılabilir
+   uyduda `3.5 sigma` normalized-residual gate açılırsa bütün tek-kanal
+   leave-one-out adayları denenir ve en düşük weighted residual'lı aday ESKF
+   yolu için seçilir.
 5. GPS adapter velocity ve 3x3 covariance'i ECEF'ten ENU'ya döndürür,
    kart ölçümüne dayalı minimum `2/2/3 m/s` standard-deviation floor'larını
    uygular ve position ile aynı capture timestamp'ini korur.
@@ -114,6 +117,28 @@ TDK veya ST IMU -> imu_sensor ----/
    velocity reject aynı epoch'taki kabul edilmiş position update'ini bozmaz.
    Sonra daha yeni IMU history current-time horizon'a kadar replay edilir.
 
+Filtreli Doppler ikinci bir velocity WLS'e girer; bu sonuç fusion/ESKF'ye
+yayınlanmaz. Yalnız PPS yazılım filtresinde position-WLS referans datumunun
+clock-bias drift predictor'u ve PPS kalite metriği olarak kullanılır. PPS'in
+ana ölçümü position WLS `clock_bias_m` değeridir. Doppler WLS'nin dördüncü
+`receiver_clock_drift_mps` state'i PPS'e doğrudan verilmez; filtreli receiver
+velocity ve referans uydu ephemeris hızıyla datum türevi ayrıca hesaplanır.
+
+Klasik mutlak-pseudorange modelinde receiver clock bias
+`c*delta_t_r`, Doppler clock drift ise bunun türevi
+`c*d(delta_t_r)/dt`'dir. Doppler WLS carrier pseudorange-rate'ten
+`[vx,vy,vz,receiver_clock_drift]` çözer. `0.1 ppm` receiver oscillator
+error'i yaklaşık `29.98 m/s` ortak Doppler drift'idir; dördüncü state
+çözülmezse bunun bir bölümü platform hızı sanılır.
+
+Bu projedeki position WLS bias'i ise capture'lar ortak receiver zamanına göre
+farklandığı ve `STARTOFFSET` eklendiği için saf receiver clock bias'i değil,
+referans-uyduya bağlı göreli bir datumdur. Bu yüzden position
+`clock_bias_m` ile Doppler `clock_drift_mps` arasında doğrudan türev kısıtı
+kurulmaz. Doppler WLS ayrı bir normal equation kullanır fakat LOS vektörleri
+için güncel position WLS receiver konumuna, uydu konum/hız/clock drift'i için
+broadcast ephemerise bağlıdır.
+
 Bu zincirin RTL/register ayrıntısı
 `hardware/external/gps/rtl/trck_src/README.md`, bare-metal WLS ve kart
 doğrulaması `soc/software/gps_system/README.md` içindedir.
diff --git a/soc/software/gps_measurement_python/.gitignore b/soc/software/gps_measurement_python/.gitignore
new file mode 100644
index 0000000..98dbeb4
--- /dev/null
+++ b/soc/software/gps_measurement_python/.gitignore
@@ -0,0 +1,3 @@
+__pycache__/
+*.py[cod]
+.venv/
diff --git a/soc/software/gps_measurement_python/README.md b/soc/software/gps_measurement_python/README.md
new file mode 100644
index 0000000..09f85e0
--- /dev/null
+++ b/soc/software/gps_measurement_python/README.md
@@ -0,0 +1,226 @@
+# GPS code measurement ve DLL kalite modeli
+
+Bu dizin, mevcut firmware/RTL ölçüm yolunu değiştirmeden önce code-phase
+hassasiyeti, DLL jitter telemetrisi, dinamik WLS sigma ve carrier/Doppler
+smoothing seçeneklerini aynı sentetik veri üzerinde karşılaştırır.
+
+Bu genel amaçlı bir RF/GNSS simülatörü değildir. Projeye özgü executable
+tasarım modelidir.
+
+Dizin iki ayrı kararı inceler:
+
+1. Position WLS için C/N0'ın açıklamadığı DLL jitter/variance telemetrisi.
+2. Velocity WLS ve ESKF öncesindeki sabit Doppler IIR'in gürültü-gecikme
+   etkisi.
+
+## Modellenen mevcut mimari
+
+| Proje davranışı | Model |
+|---|---|
+| Normalized early-minus-late DLL discriminator | `rtl_dll_model.rtl_discriminator()` |
+| Signed Q2.13 discriminator quantization | `rtl_dll_model.py` |
+| `LF_code.sv` C1=`21.25`, C2=`0.05712890625` ve Q20 çıkış | `CodeLoopFilterRtl` |
+| 20 adet 1 ms DLL örneği/NAV bit | `synthesize_dll_window()` |
+| Firmware C/N0 IIR, alpha=`0.2` | `ChannelQuality.update()` |
+| URA/elevation/C/N0 position sigma | `firmware_sigma_m(CURRENT)` |
+| ECEF x/y/z + common clock-bias WLS | `firmware_wls()` |
+| 99% chi-square ve en az 7 uyduda leave-one-out FDE | `firmware_wls()` |
+| Position solve periyodu 200 ms | `measurement_scenarios.py` |
+| Doppler IIR alpha=`0.05`, 50 Hz | `doppler_eskf_model.py` |
+| ECEF velocity + common clock-drift WLS | `velocity_wls()` |
+| Velocity WLS periyodu 200 ms | `doppler_eskf_model.py` |
+| TDK 100 Hz IMU process-noise profili | `VelocityBiasEskf` |
+| Velocity 3-DOF `%99.9`, NIS=`16.266236` | `VelocityBiasEskf.update_velocity()` |
+
+Kaynak eşlemeleri:
+
+- `hardware/external/gps/rtl/trck_src/code_loop_discriminator.sv`
+- `hardware/external/gps/rtl/trck_src/LF_code.sv`
+- `hardware/external/gps/rtl/trck_src/NCO_code.sv`
+- `hardware/external/gps/rtl/trck_src/tracking_measurement.sv`
+- `hardware/external/gps/rtl/common/definitions.sv`
+- `soc/software/gps_system/src/gps/gps_tracking_measurement.c`
+- `soc/software/gps_system/src/gps/gps_interrupt_handlers.c`
+- `soc/software/gps_system/src/gps/NavEquations.c`
+
+`REM_CODE_PHASE`, DLL discriminator residual'ı olarak modellenmez. RTL'de bu
+değer code NCO'nun epoch taşma remainder'ıdır. Yeni kalite metriğinin girdisi
+RTL içindeki gerçek signed `dll_error` örnekleridir.
+
+## Karşılaştırılan sigma politikaları
+
+- `current_cn0`: mevcut URA + elevation + C/N0 modeli.
+- `naive_add_dll`: DLL variance'ı bağımsızmış gibi ekler. Nominal durumda aynı
+  thermal jitter'ı iki kere saydığı için negatif kontrol olarak bulunur.
+- `dll_excess`: yalnız ölçülen DLL variance'ın C/N0'dan beklenen variance'ı aşan
+  bölümünü code sigma'ya ekler.
+- `dll_excess_guard`: excess variance'a ek olarak sürekli discriminator mean
+  stress'inde ağırlığı azaltır.
+- `oracle_variance`: sentetik gerçek jitter çarpanını bilir. Ulaşılabilir üst
+  sınırı gösterir; firmware algoritması değildir.
+
+Dinamik model:
+
+```text
+sigma_base^2 = sigma_URA^2 + sigma_elevation^2 + sigma_CN0^2
+ratio = EWMA(measured_DLL_variance / expected_DLL_variance(C/N0))
+
+sigma_dynamic^2 =
+    sigma_URA^2
+  + sigma_elevation^2
+  + sigma_CN0^2 * max(1, ratio)
+```
+
+Bu form C/N0 ile DLL thermal jitter'ını iki kere toplamaz. Yalnızca C/N0
+modelinin açıklayamadığı kanal-bağımlı excess jitter'ı şişirir.
+
+## Senaryolar
+
+- Temiz açık gökyüzü
+- Bütün kanallarda düşük C/N0
+- C/N0'da görünmeyen tek-kanal DLL jitter
+- Bütün kanallarda ortak, C/N0'da görünmeyen DLL jitter
+- Gürültü burst ve recovery
+- Re-lock sırasında DLL mean/jitter stress
+- Düşük-variance stable multipath bias
+- Bias + excess jitter
+- Kötü geometri + gizli jitter
+- İlk başta düşük, sonra iyileşen C/N0
+
+Ayrı 1D model ham code, kör scalar IIR ve Doppler-predicted code smoothing'i
+range-rate adımları ve residual carrier CFO altında karşılaştırır. Carrier
+ölçümleri RTL cadence'i olan 50 Hz'de üretilir ve 200 ms WLS epoch'una kadar
+entegre edilir. Hem raw carrier-rate hem de mevcut firmware'deki
+`GPS_TRACK_DOPPLER_SMOOTH_ALPHA=0.05` çıkışı denenir. Bu ayrım önemlidir:
+PPS datum-drift predictor'u için yararlı olan yavaş Doppler filtresi, ESKF
+velocity veya hızlı code-aiding prediction'ında dinamik lag üretebilir.
+
+## Doppler pre-IIR ve ESKF modeli
+
+`doppler_eskf_model.py`, aynı truth, tracking gürültüsü ve IMU örnekleriyle şu
+dört yolu karşılaştırır:
+
+- Önceki: 50 Hz `alpha=0.05` IIR -> 5 Hz velocity WLS -> ESKF.
+- Ham Doppler -> 5 Hz velocity WLS -> ESKF.
+- C/N0 + düşük-geçiren navigation acceleration ile adaptif IIR -> WLS -> ESKF.
+- Ham Doppler -> RAIM-benzeri leave-one-out robust WLS -> ESKF.
+
+Mevcut `alpha=0.05` tek-kutuplu IIR için 50 Hz'de eşdeğer cutoff yaklaşık
+`0.408 Hz`, zaman sabiti `0.390 s`, DC group delay ise yaklaşık `380 ms`'dir.
+Bu gecikme constant velocity'de görünmez; acceleration sırasında velocity
+measurement innovation'ına doğrudan girer.
+
+ESKF modeli bu karar için gerekli `[velocity, accel-bias]` alt sistemidir.
+Firmware'deki TDK process acceleration noise density `0.025
+m/s2/sqrt(Hz)`, accelerometer bias random walk `0.0015 m/s2/sqrt(s)`, WLS'nin
+gerçek 3x3 covariance'ı, fusion adapter'ın `2/2/3 m/s` ENU velocity sigma
+tabanları ve velocity NIS kapısı kullanılır. Position, attitude, lever-arm ve
+tam 15-state cross-covariance bu modelin kapsamında değildir.
+
+Senaryo matrisi sabit uçuş, airliner/aggressive manevra, düşük C/N0, tek-kanal
+Doppler burst, common receiver clock-drift step, 15 saniye GPS kesintisi ve
+birleşik arıza koşullarını içerir.
+
+20-seed sentetik sonuçların özeti:
+
+- ESKF ham WLS gürültüsünü nominalde yaklaşık `0.416 m/s` 3D RMS'ten `0.190
+  m/s` seviyesine indirir; temporal filtreleme zaten ESKF'de gerçekleşir.
+- Sabit pre-IIR sakin uçuşta `0.182 m/s`, ham yol `0.190 m/s` verir. Airliner
+  manevrasında sabit IIR gecikmesi sonucu `0.416 m/s`, ham yol `0.190 m/s`;
+  aggressive manevrada sırasıyla `0.942 m/s` ve `0.190 m/s` oluşur. Adapter
+  sigma tabanları iki yolu da NIS içinde tutsa bile dinamik lag kalır.
+- Düşük C/N0 manevrasında adaptif taslak en iyi gürültü/gecikme uzlaşmasını
+  verir; eşikleri firmware'e taşımadan önce kart loguyla kalibre etmek gerekir.
+- ESKF yalnız aggregate 3D velocity gördüğünden tek uydu burst'ünün kaynağını
+  ayıramaz. Kanal outlier/FDE işlemi velocity WLS öncesinde yapılmalıdır.
+- Common receiver clock-frequency hatası WLS'nin dördüncü clock-drift state'i
+  tarafından hızdan ayrılır.
+
+Bu sonuçlarla firmware'de ESKF için ham Doppler -> kanal validity/FDE ->
+velocity WLS + covariance -> ESKF yolu uygulanmıştır. Ayrı yavaş-filtered
+Doppler velocity yalnız PPS position-WLS clock-bias datumunun drift predictor'u
+ve PPS kalite metriği için tutulur. Ayrıntılı tablo ve sınırlar
+`output/DOPPLER_ESKF_ANALYSIS.md` içindedir.
+
+## Kurulum ve çalıştırma
+
+Repo içindeki `soc/software` dizininden:
+
+```bash
+python3 -m venv gps_measurement_python/.venv
+gps_measurement_python/.venv/bin/pip install \
+  -r gps_measurement_python/requirements.txt
+gps_measurement_python/.venv/bin/python -m unittest \
+  gps_measurement_python/test_measurement_model.py \
+  gps_measurement_python/test_doppler_eskf_model.py
+gps_measurement_python/.venv/bin/python \
+  -m gps_measurement_python.analyze_measurement_scenarios \
+  --seeds 12 --jobs 4
+gps_measurement_python/.venv/bin/python \
+  -m gps_measurement_python.analyze_doppler_eskf \
+  --seeds 20 --jobs 4
+```
+
+Sistem Python'unda `venv` paketi yoksa bağımlılıklar izole bir target dizinine
+de kurulabilir:
+
+```bash
+python3 -m pip install --target /tmp/gps-measurement-deps \
+  -r gps_measurement_python/requirements.txt
+PYTHONPATH=/tmp/gps-measurement-deps:. python3 \
+  -m unittest gps_measurement_python/test_measurement_model.py
+PYTHONPATH=/tmp/gps-measurement-deps:. python3 \
+  -m gps_measurement_python.analyze_measurement_scenarios \
+  --seeds 12 --jobs 4
+```
+
+Çıktılar `gps_measurement_python/output/` altındadır:
+
+- `scenario_summary.csv`
+- `ANALYSIS.md`
+- `01_position_3d_rms.png`
+- `02_solution_availability.png`
+- `03_noise_burst_transition.png`
+- `04_code_smoothing_cfo.png`
+- `doppler_eskf_summary.csv`
+- `DOPPLER_ESKF_ANALYSIS.md`
+- `05_doppler_eskf_velocity_rms.png`
+- `06_airliner_maneuver_trace.png`
+- `07_outlier_wls_nis.png`
+- `08_low_cn0_wls_vs_eskf.png`
+
+## Kalibrasyon sınırı
+
+Modelde C/N0'dan beklenen normalized discriminator standard deviation'ı
+45 dB-Hz için `0.020` kabul edilir ve firmware ile aynı 20 dB amplitude yasası
+ile ölçeklenir. Bu sayı karttan alınmış bir kalibrasyon değildir.
+
+Karar vermeden önce karttan her kanal için en az şu 50 Hz kayıt alınmalıdır:
+
+```text
+sequence, PRN, C/N0,
+DLL mean, DLL variance, DLL sample count,
+code NCO correction, carrier frequency,
+ABS_SAMPLE, REM_CODE_PHASE, lock
+```
+
+Kayıtlarla `expected_DLL_variance(C/N0)` eğrisi çıkarılmalı; temperature,
+elevation ve lock yaşına göre ayrıştırılmalıdır. Stable multipath, DLL yeni
+denge noktasına oturduğunda düşük variance bırakabilir. Bu durum tek başına
+DLL variance ile çözülemez; ek correlator tap'leri veya correlation-shape
+metriği gerekir.
+
+RTL için en düşük maliyetli keşif arayüzü, her 20 ms NAV-bit penceresinde
+`dll_error` üzerinden aşağıdaki ham istatistikleri biriktirmektir:
+
+```text
+signed sum(error)       : 15 + ceil(log2(20)) = 20 bit
+unsigned sum(error^2)   : 30 + ceil(log2(20)) = 35 bit
+valid sample count      : 5 bit
+```
+
+35-bit kare toplamı APB'de iki 32-bit register ile taşınabilir. Ortalama,
+sample variance, C/N0 expectation ratio ve hysteresis yazılımda hesaplanır.
+Bölme ve square-root RTL'ye konmaz. Bu tuple mevcut measurement sequence,
+C/N0, carrier frequency, `ABS_SAMPLE` ve `REM_CODE_PHASE` ile aynı 20 ms
+snapshot'ta tutulmalıdır.
diff --git a/soc/software/gps_measurement_python/__init__.py b/soc/software/gps_measurement_python/__init__.py
new file mode 100644
index 0000000..57dd220
--- /dev/null
+++ b/soc/software/gps_measurement_python/__init__.py
@@ -0,0 +1 @@
+"""Project-specific GPS code-measurement and WLS analysis model."""
diff --git a/soc/software/gps_measurement_python/analyze_doppler_eskf.py b/soc/software/gps_measurement_python/analyze_doppler_eskf.py
new file mode 100644
index 0000000..126189f
--- /dev/null
+++ b/soc/software/gps_measurement_python/analyze_doppler_eskf.py
@@ -0,0 +1,428 @@
+"""Monte Carlo comparison of Doppler prefilter choices before velocity ESKF."""
+
+from __future__ import annotations
+
+import argparse
+import csv
+import math
+from concurrent.futures import ProcessPoolExecutor
+from dataclasses import dataclass
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+from .doppler_eskf_model import (
+    DopplerEskfTrace,
+    DopplerPath,
+    PATH_ORDER,
+    VELOCITY_NIS_GATE,
+    flight_scenarios,
+    run_doppler_eskf_scenario,
+)
+
+
+PATH_LABEL = {
+    DopplerPath.FIXED_IIR: "Önceki sabit IIR",
+    DopplerPath.RAW: "Ham Doppler + ESKF",
+    DopplerPath.ADAPTIVE_IIR: "Adaptif IIR + ESKF",
+    DopplerPath.RAW_ROBUST: "Ham + robust WLS + ESKF",
+}
+
+
+@dataclass(frozen=True)
+class TrialMetrics:
+    scenario: str
+    path: DopplerPath
+    fused_rms_mps: float
+    fused_p95_mps: float
+    quiet_rms_mps: float
+    dynamic_rms_mps: float
+    wls_rms_mps: float
+    wls_p95_mps: float
+    clock_drift_rms_mps: float
+    velocity_accept_percent: float
+    nis_reject_percent: float
+    fused_95_coverage_percent: float
+    excluded_epoch_percent: float
+    mean_covariance_scale: float
+    mean_alpha: float
+
+
+@dataclass(frozen=True)
+class Summary:
+    scenario: str
+    path: DopplerPath
+    seeds: int
+    fused_rms_mps: float
+    fused_rms_seed_std_mps: float
+    fused_p95_mps: float
+    quiet_rms_mps: float
+    dynamic_rms_mps: float
+    wls_rms_mps: float
+    wls_p95_mps: float
+    clock_drift_rms_mps: float
+    velocity_accept_percent: float
+    nis_reject_percent: float
+    fused_95_coverage_percent: float
+    excluded_epoch_percent: float
+    mean_covariance_scale: float
+    mean_alpha: float
+
+
+def _rms(values: np.ndarray) -> float:
+    return float(np.sqrt(np.mean(np.square(values)))) if len(values) else math.nan
+
+
+def _truth_at_wls(trace: DopplerEskfTrace) -> np.ndarray:
+    return np.column_stack(
+        [
+            np.interp(
+                trace.wls_time_s,
+                trace.time_s,
+                trace.truth_velocity_mps[:, axis],
+            )
+            for axis in range(3)
+        ]
+    )
+
+
+def trial_metrics(scenario_index: int, trace: DopplerEskfTrace) -> TrialMetrics:
+    scenario = flight_scenarios()[scenario_index]
+    burn_in = trace.time_s >= 5.0
+    fused_vector_error = trace.fused_velocity_mps - trace.truth_velocity_mps
+    fused_error = np.linalg.norm(fused_vector_error, axis=1)
+    dynamic = burn_in & (np.linalg.norm(trace.acceleration_mps2, axis=1) > 0.25)
+    quiet = burn_in & ~dynamic
+
+    fused_nees = []
+    for sample in np.flatnonzero(burn_in):
+        covariance = trace.fused_velocity_covariance_mps2[sample]
+        error = fused_vector_error[sample]
+        fused_nees.append(float(error @ np.linalg.inv(covariance) @ error))
+    fused_nees_array = np.asarray(fused_nees)
+
+    wls_error = np.linalg.norm(trace.wls_velocity_mps - _truth_at_wls(trace), axis=1)
+    true_clock_drift = np.asarray(
+        [scenario.receiver_clock_drift_mps(float(time)) for time in trace.wls_time_s]
+    )
+    clock_error = trace.wls_clock_drift_mps - true_clock_drift
+    valid_nis = trace.wls_nis[np.isfinite(trace.wls_nis)]
+
+    return TrialMetrics(
+        scenario=trace.scenario,
+        path=trace.path,
+        fused_rms_mps=_rms(fused_error[burn_in]),
+        fused_p95_mps=float(np.percentile(fused_error[burn_in], 95.0)),
+        quiet_rms_mps=_rms(fused_error[quiet]),
+        dynamic_rms_mps=_rms(fused_error[dynamic]),
+        wls_rms_mps=_rms(wls_error),
+        wls_p95_mps=float(np.percentile(wls_error, 95.0)),
+        clock_drift_rms_mps=_rms(clock_error),
+        velocity_accept_percent=100.0 * float(np.mean(trace.wls_accepted)),
+        nis_reject_percent=100.0 * float(np.mean(valid_nis > VELOCITY_NIS_GATE)),
+        # 7.8147 is the 95-percent chi-square threshold for three states.
+        fused_95_coverage_percent=100.0 * float(np.mean(fused_nees_array <= 7.8147279)),
+        excluded_epoch_percent=100.0
+        * float(np.mean(trace.excluded_satellites >= 0)),
+        mean_covariance_scale=float(np.mean(trace.wls_covariance_scale)),
+        mean_alpha=float(np.mean(trace.adaptive_alpha)),
+    )
+
+
+def _worker(task: tuple[int, int]) -> tuple[int, int, list[TrialMetrics]]:
+    scenario_index, seed = task
+    scenario = flight_scenarios()[scenario_index]
+    traces = run_doppler_eskf_scenario(scenario, seed)
+    return (
+        scenario_index,
+        seed,
+        [trial_metrics(scenario_index, traces[path]) for path in PATH_ORDER],
+    )
+
+
+def summarize(items: list[TrialMetrics]) -> Summary:
+    if not items:
+        raise ValueError("cannot summarize an empty trial list")
+
+    def average(field_name: str) -> float:
+        values = np.asarray([getattr(item, field_name) for item in items], dtype=float)
+        finite = values[np.isfinite(values)]
+        return float(np.mean(finite)) if len(finite) else math.nan
+
+    fused_rms = np.asarray([item.fused_rms_mps for item in items])
+    return Summary(
+        scenario=items[0].scenario,
+        path=items[0].path,
+        seeds=len(items),
+        fused_rms_mps=average("fused_rms_mps"),
+        fused_rms_seed_std_mps=float(np.std(fused_rms)),
+        fused_p95_mps=average("fused_p95_mps"),
+        quiet_rms_mps=average("quiet_rms_mps"),
+        dynamic_rms_mps=average("dynamic_rms_mps"),
+        wls_rms_mps=average("wls_rms_mps"),
+        wls_p95_mps=average("wls_p95_mps"),
+        clock_drift_rms_mps=average("clock_drift_rms_mps"),
+        velocity_accept_percent=average("velocity_accept_percent"),
+        nis_reject_percent=average("nis_reject_percent"),
+        fused_95_coverage_percent=average("fused_95_coverage_percent"),
+        excluded_epoch_percent=average("excluded_epoch_percent"),
+        mean_covariance_scale=average("mean_covariance_scale"),
+        mean_alpha=average("mean_alpha"),
+    )
+
+
+def write_csv(path: Path, summaries: list[Summary]) -> None:
+    with path.open("w", newline="", encoding="utf-8") as output:
+        writer = csv.DictWriter(output, fieldnames=list(Summary.__dataclass_fields__))
+        writer.writeheader()
+        for item in summaries:
+            row = dict(item.__dict__)
+            row["path"] = item.path.value
+            writer.writerow(row)
+
+
+def _summary_plot(path: Path, summaries: list[Summary]) -> None:
+    scenarios = flight_scenarios()
+    x = np.arange(len(scenarios))
+    width = 0.19
+    figure, axis = plt.subplots(figsize=(15, 6.3))
+    for path_index, doppler_path in enumerate(PATH_ORDER):
+        values = [
+            next(
+                item.fused_rms_mps
+                for item in summaries
+                if item.scenario == scenario.name and item.path == doppler_path
+            )
+            for scenario in scenarios
+        ]
+        axis.bar(
+            x + (path_index - 1.5) * width,
+            values,
+            width,
+            label=PATH_LABEL[doppler_path],
+        )
+    axis.set_ylabel("ESKF 3D velocity RMS (m/s)")
+    axis.set_yscale("log")
+    axis.set_xticks(x)
+    axis.set_xticklabels([item.name for item in scenarios], rotation=25, ha="right")
+    axis.grid(axis="y", alpha=0.25)
+    axis.legend(ncol=2)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def _maneuver_trace_plot(path: Path, trace_set: dict[DopplerPath, DopplerEskfTrace]) -> None:
+    reference = trace_set[DopplerPath.FIXED_IIR]
+    figure, axes = plt.subplots(3, 1, figsize=(13, 8.5), sharex=True)
+    for doppler_path in PATH_ORDER:
+        trace = trace_set[doppler_path]
+        error = np.linalg.norm(trace.fused_velocity_mps - trace.truth_velocity_mps, axis=1)
+        axes[0].plot(trace.time_s, error, label=PATH_LABEL[doppler_path], linewidth=1.0)
+    axes[1].plot(
+        reference.time_s,
+        np.linalg.norm(reference.acceleration_mps2, axis=1),
+        color="black",
+        linewidth=1.2,
+        label="True |acceleration|",
+    )
+    adaptive = trace_set[DopplerPath.ADAPTIVE_IIR]
+    axes[2].step(
+        adaptive.wls_time_s,
+        adaptive.adaptive_alpha,
+        where="post",
+        color="tab:green",
+    )
+    axes[0].set_ylabel("3D velocity error (m/s)")
+    axes[1].set_ylabel("Acceleration (m/s²)")
+    axes[2].set_ylabel("Adaptive alpha")
+    axes[2].set_xlabel("Time (s)")
+    axes[0].set_ylim(bottom=0.0)
+    axes[0].legend(ncol=2)
+    for axis in axes:
+        axis.grid(alpha=0.25)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def _outlier_plot(path: Path, trace_set: dict[DopplerPath, DopplerEskfTrace]) -> None:
+    figure, axes = plt.subplots(2, 1, figsize=(13, 7), sharex=True)
+    for doppler_path in PATH_ORDER:
+        trace = trace_set[doppler_path]
+        error = np.linalg.norm(trace.wls_velocity_mps - _truth_at_wls(trace), axis=1)
+        axes[0].plot(trace.wls_time_s, error, label=PATH_LABEL[doppler_path], linewidth=1.0)
+        axes[1].plot(trace.wls_time_s, trace.wls_nis, label=PATH_LABEL[doppler_path], linewidth=0.9)
+    axes[1].axhline(VELOCITY_NIS_GATE, color="black", linestyle="--", linewidth=1.0)
+    for start, stop in ((30.0, 31.0), (56.0, 57.0), (72.0, 72.6)):
+        for axis in axes:
+            axis.axvspan(start, stop, color="tab:red", alpha=0.10)
+    axes[0].set_ylabel("WLS velocity error (m/s)")
+    axes[1].set_ylabel("Velocity NIS")
+    axes[1].set_xlabel("Time (s)")
+    axes[0].legend(ncol=2)
+    for axis in axes:
+        axis.grid(alpha=0.25)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def _filtering_plot(path: Path, trace_set: dict[DopplerPath, DopplerEskfTrace]) -> None:
+    figure, axes = plt.subplots(2, 1, figsize=(13, 7), sharex=True)
+    for doppler_path in (DopplerPath.FIXED_IIR, DopplerPath.RAW, DopplerPath.ADAPTIVE_IIR):
+        trace = trace_set[doppler_path]
+        wls_error = np.linalg.norm(trace.wls_velocity_mps - _truth_at_wls(trace), axis=1)
+        fused_error = np.linalg.norm(trace.fused_velocity_mps - trace.truth_velocity_mps, axis=1)
+        axes[0].plot(trace.wls_time_s, wls_error, label=PATH_LABEL[doppler_path], linewidth=0.9)
+        axes[1].plot(trace.time_s, fused_error, label=PATH_LABEL[doppler_path], linewidth=0.9)
+    axes[0].set_ylabel("WLS 3D error (m/s)")
+    axes[1].set_ylabel("ESKF 3D error (m/s)")
+    axes[1].set_xlabel("Time (s)")
+    axes[0].legend(ncol=2)
+    for axis in axes:
+        axis.grid(alpha=0.25)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def _lookup(
+    summaries: list[Summary], scenario: str, doppler_path: DopplerPath
+) -> Summary:
+    return next(
+        item
+        for item in summaries
+        if item.scenario == scenario and item.path == doppler_path
+    )
+
+
+def write_report(path: Path, summaries: list[Summary], seed_count: int) -> None:
+    lines = [
+        "# Doppler WLS -> ESKF model sonuçları",
+        "",
+        f"Monte Carlo seed sayısı: `{seed_count}`; ilk 5 saniye RMS metriklerinden çıkarıldı.",
+        "50 Hz tracking, önceki `alpha=0.05` Doppler IIR, 5 Hz dört-state velocity WLS, fusion adapter'ın `2/2/3 m/s` ENU sigma tabanları, TDK profiliyle 100 Hz IMU propagation ve 3-DOF `%99.9` NIS kapısı modellenmiştir.",
+        "",
+        "## Sonuç tablosu",
+        "",
+        "| Senaryo | Yol | ESKF RMS (m/s) | Dynamic RMS | WLS RMS | Accept (%) | 95% cov. (%) | Exclude (%) |",
+        "|---|---|---:|---:|---:|---:|---:|---:|",
+    ]
+    for scenario in flight_scenarios():
+        for doppler_path in PATH_ORDER:
+            item = _lookup(summaries, scenario.name, doppler_path)
+            dynamic = "-" if not np.isfinite(item.dynamic_rms_mps) else f"{item.dynamic_rms_mps:.3f}"
+            lines.append(
+                f"| {scenario.name} | {PATH_LABEL[doppler_path]} | "
+                f"{item.fused_rms_mps:.3f} | {dynamic} | {item.wls_rms_mps:.3f} | "
+                f"{item.velocity_accept_percent:.1f} | {item.fused_95_coverage_percent:.1f} | "
+                f"{item.excluded_epoch_percent:.1f} |"
+            )
+
+    steady_fixed = _lookup(summaries, "steady_cruise", DopplerPath.FIXED_IIR)
+    steady_raw = _lookup(summaries, "steady_cruise", DopplerPath.RAW)
+    air_fixed = _lookup(summaries, "airliner_maneuver", DopplerPath.FIXED_IIR)
+    air_raw = _lookup(summaries, "airliner_maneuver", DopplerPath.RAW)
+    weak_fixed = _lookup(summaries, "low_cn0_airliner", DopplerPath.FIXED_IIR)
+    weak_raw = _lookup(summaries, "low_cn0_airliner", DopplerPath.RAW)
+    weak_adaptive = _lookup(summaries, "low_cn0_airliner", DopplerPath.ADAPTIVE_IIR)
+    outlier_raw = _lookup(summaries, "single_satellite_outliers", DopplerPath.RAW)
+    outlier_robust = _lookup(summaries, "single_satellite_outliers", DopplerPath.RAW_ROBUST)
+    clock_raw = _lookup(summaries, "clock_drift_steps", DopplerPath.RAW)
+
+    lines.extend(
+        [
+            "",
+            "## Bulgular",
+            "",
+            f"- Sabit hızda pre-IIR ESKF RMS'i `{steady_fixed.fused_rms_mps:.3f}` m/s, ham yol `{steady_raw.fused_rms_mps:.3f}` m/s. Yani pre-IIR sakin durumda daha düzgün çıktı veriyor; ESKF ham gürültüyü zaten `{steady_raw.wls_rms_mps:.3f}` m/s WLS RMS'ten bu seviyeye indiriyor.",
+            f"- Airliner manevrasında sabit IIR `{air_fixed.fused_rms_mps:.3f}` m/s ve `%{air_fixed.nis_reject_percent:.1f}` NIS ret oranı verirken ham yol `{air_raw.fused_rms_mps:.3f}` m/s ve `%{air_raw.nis_reject_percent:.1f}` ret verdi. Konservatif adapter tabanları rejection'ı sınırlasa bile covariance'ın temsil etmediği IIR gecikmesi fused velocity'de dinamik hata bırakır.",
+            f"- Düşük C/N0 manevrasında sabit/ham/adaptif RMS sırasıyla `{weak_fixed.fused_rms_mps:.3f}`, `{weak_raw.fused_rms_mps:.3f}`, `{weak_adaptive.fused_rms_mps:.3f}` m/s oldu. Adaptif yol bu sentetik koşulda gürültü/gecikme uzlaşmasını sağladı; gerçek eşikler kart verisi ister.",
+            f"- Tek uydu burst'ünde raw WLS RMS `{outlier_raw.wls_rms_mps:.3f}` m/s, robust leave-one-out ile `{outlier_robust.wls_rms_mps:.3f}` m/s. ESKF son RMS farkı daha küçük; çünkü mevcut residual covariance inflation aggregate hatayı zaten zayıflatıyor. Robust kapı yine de hatalı kanalı bütün epoch'u reddetmeden ayırır.",
+            f"- Common clock-drift step raw velocity RMS'ini bozmadı; clock-drift state RMS'i `{clock_raw.clock_drift_rms_mps:.3f}` m/s. Dördüncü WLS bilinmeyeni ortak frekans hatasını üç hız bileşeninden ayırıyor.",
+            "",
+            "## Mimari kararı",
+            "",
+            "- ESKF açıkken uygulanan ana yol: 20 ms ham Doppler snapshot -> kanal validity/outlier kontrolü -> 5 Hz robust velocity WLS + gerçek covariance -> adapter tabanları -> ESKF. Sabit `alpha=0.05` temporal IIR yalnız PPS drift-predictor yolunda kalır.",
+            "- ESKF yalnız 3D aggregate velocity gördüğü için tek uydu hatasını sonradan teşhis edemez. Per-satellite robust gate/FDE WLS öncesinde kalmalıdır.",
+            "- Standalone GPS speed, PPS aiding veya ESKF kapalı build için ayrı, yavaş filtrelenmiş Doppler çıktısı tutulabilir. Aynı filtered değeri hem code aiding hem ESKF velocity için kullanmak uygun değildir.",
+            "- Adaptif IIR mümkündür; modelde C/N0 sakin-state alpha'sını, düşük geçiren IMU navigation acceleration ise dynamic alpha'yı seçer. Ancak ESKF'li ana yol için ham ölçüm daha sade ve gecikmesizdir.",
+            "",
+            "## Model sınırları",
+            "",
+            "- Sonuçlar sentetik hata büyüklüklerine koşulludur; kartta yüzde kazanç iddiası değildir.",
+            "- Uydu geometrisi sabit sekiz-kanal local LOS modelidir. Satellite velocity/clock düzeltmelerinin doğru yapıldığı varsayılmıştır.",
+            "- ESKF, bu soruya etki eden `[velocity, accel-bias]` alt sistemine indirgenmiştir; attitude, lever-arm ve tam position cross-covariance modellenmemiştir.",
+            "- Tam firmware'deki position update'in velocity/accel-bias cross-covariance üzerinden sağlayabileceği kısmi recovery bu azaltılmış modelde yoktur. Bu nedenle uzun NIS-ret zincirinin mutlak büyüklüğü değil, pre-IIR'in gecikme ve ret mekanizması karar girdisidir.",
+            "- Carrier loop gürültüsü C/N0 sigma yasasıyla üretilmiştir. Gerçek correlation, oscillator phase noise ve cycle slip dağılımları kart loguyla kalibre edilmelidir.",
+            "- Robust WLS'nin `3.5 sigma`, en az altı uydu ve bütün tek-kanal leave-one-out seçimi C implementasyonuyla aynıdır. RTL değişmez; raw/filtered ayrımı firmware'dedir.",
+            "",
+        ]
+    )
+    path.write_text("\n".join(lines), encoding="utf-8")
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--seeds", type=int, default=20)
+    parser.add_argument("--jobs", type=int, default=4)
+    parser.add_argument(
+        "--output",
+        type=Path,
+        default=Path(__file__).resolve().parent / "output",
+    )
+    arguments = parser.parse_args()
+    arguments.output.mkdir(parents=True, exist_ok=True)
+
+    scenarios = flight_scenarios()
+    tasks = [
+        (scenario_index, seed)
+        for scenario_index in range(len(scenarios))
+        for seed in range(1, arguments.seeds + 1)
+    ]
+    grouped: dict[tuple[int, DopplerPath], list[TrialMetrics]] = {
+        (scenario_index, doppler_path): []
+        for scenario_index in range(len(scenarios))
+        for doppler_path in PATH_ORDER
+    }
+    with ProcessPoolExecutor(max_workers=max(1, arguments.jobs)) as executor:
+        for scenario_index, seed, metrics in executor.map(_worker, tasks):
+            for item in metrics:
+                grouped[(scenario_index, item.path)].append(item)
+            print(f"completed {scenarios[scenario_index].name} seed={seed}", flush=True)
+
+    summaries = [
+        summarize(grouped[(scenario_index, doppler_path)])
+        for scenario_index in range(len(scenarios))
+        for doppler_path in PATH_ORDER
+    ]
+    write_csv(arguments.output / "doppler_eskf_summary.csv", summaries)
+    write_report(
+        arguments.output / "DOPPLER_ESKF_ANALYSIS.md",
+        summaries,
+        arguments.seeds,
+    )
+    _summary_plot(arguments.output / "05_doppler_eskf_velocity_rms.png", summaries)
+
+    airliner = run_doppler_eskf_scenario(
+        next(item for item in scenarios if item.name == "airliner_maneuver"), 1
+    )
+    _maneuver_trace_plot(arguments.output / "06_airliner_maneuver_trace.png", airliner)
+    outlier = run_doppler_eskf_scenario(
+        next(item for item in scenarios if item.name == "single_satellite_outliers"), 1
+    )
+    _outlier_plot(arguments.output / "07_outlier_wls_nis.png", outlier)
+    weak = run_doppler_eskf_scenario(
+        next(item for item in scenarios if item.name == "low_cn0_airliner"), 1
+    )
+    _filtering_plot(arguments.output / "08_low_cn0_wls_vs_eskf.png", weak)
+    print(f"wrote Doppler/ESKF analysis to {arguments.output}", flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/soc/software/gps_measurement_python/analyze_measurement_scenarios.py b/soc/software/gps_measurement_python/analyze_measurement_scenarios.py
new file mode 100644
index 0000000..ff3b617
--- /dev/null
+++ b/soc/software/gps_measurement_python/analyze_measurement_scenarios.py
@@ -0,0 +1,425 @@
+"""Run the complete DLL-quality/WLS and code-smoothing comparison."""
+
+from __future__ import annotations
+
+import argparse
+import csv
+import math
+from concurrent.futures import ProcessPoolExecutor
+from dataclasses import dataclass
+from pathlib import Path
+
+import matplotlib
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+from .code_smoothing_model import run_smoothing_trial
+from .firmware_wls_model import SigmaMethod
+from .measurement_scenarios import EpochSample, run_scenario, scenario_matrix
+
+
+METHOD_ORDER = (
+    SigmaMethod.CURRENT,
+    SigmaMethod.NAIVE_ADD_DLL,
+    SigmaMethod.DLL_EXCESS,
+    SigmaMethod.DLL_EXCESS_GUARD,
+    SigmaMethod.ORACLE,
+)
+METHOD_LABEL = {
+    SigmaMethod.CURRENT: "Mevcut C/N0",
+    SigmaMethod.NAIVE_ADD_DLL: "Naif DLL ekle",
+    SigmaMethod.DLL_EXCESS: "DLL excess",
+    SigmaMethod.DLL_EXCESS_GUARD: "DLL excess+mean",
+    SigmaMethod.ORACLE: "Oracle variance",
+}
+
+
+@dataclass(frozen=True)
+class Summary:
+    scenario: str
+    method: SigmaMethod
+    epochs: int
+    horizontal_rms_m: float
+    position_3d_rms_m: float
+    position_3d_p95_m: float
+    valid_percent: float
+    valid_3d_rms_m: float
+    horizontal_2sigma_coverage_percent: float
+    false_valid_over_25m_percent: float
+    fde_percent: float
+    mean_measurement_sigma_m: float
+
+
+def _worker(task: tuple[int, int]) -> tuple[int, int, list[EpochSample]]:
+    scenario_index, seed = task
+    scenario = scenario_matrix()[scenario_index]
+    return scenario_index, seed, run_scenario(scenario, seed, METHOD_ORDER)
+
+
+def _rms(values: np.ndarray) -> float:
+    return float(np.sqrt(np.mean(np.square(values)))) if len(values) else math.nan
+
+
+def summarize(scenario_name: str, method: SigmaMethod, samples: list[EpochSample]) -> Summary:
+    selected = [
+        item
+        for item in samples
+        if item.method == method and item.time_s >= 5.0
+    ]
+    horizontal = np.asarray([item.horizontal_error_m for item in selected])
+    error_3d = np.asarray([item.position_error_3d_m for item in selected])
+    valid = np.asarray([item.valid for item in selected], dtype=bool)
+    horizontal_sigma = np.asarray([item.horizontal_sigma_m for item in selected])
+    fde = np.asarray([item.fde_applied for item in selected], dtype=bool)
+    mean_sigma = np.asarray([item.mean_measurement_sigma_m for item in selected])
+    false_valid = valid & (error_3d > 25.0)
+    return Summary(
+        scenario=scenario_name,
+        method=method,
+        epochs=len(selected),
+        horizontal_rms_m=_rms(horizontal),
+        position_3d_rms_m=_rms(error_3d),
+        position_3d_p95_m=float(np.percentile(error_3d, 95.0)),
+        valid_percent=100.0 * float(np.mean(valid)),
+        valid_3d_rms_m=_rms(error_3d[valid]),
+        horizontal_2sigma_coverage_percent=100.0
+        * float(np.mean(horizontal <= 2.0 * horizontal_sigma)),
+        false_valid_over_25m_percent=100.0 * float(np.mean(false_valid)),
+        fde_percent=100.0 * float(np.mean(fde)),
+        mean_measurement_sigma_m=float(np.mean(mean_sigma)),
+    )
+
+
+def write_csv(path: Path, summaries: list[Summary]) -> None:
+    with path.open("w", newline="", encoding="utf-8") as output:
+        writer = csv.DictWriter(output, fieldnames=list(Summary.__dataclass_fields__))
+        writer.writeheader()
+        for item in summaries:
+            row = dict(item.__dict__)
+            row["method"] = item.method.value
+            writer.writerow(row)
+
+
+def _comparison_plot(
+    path: Path,
+    summaries: list[Summary],
+    field: str,
+    ylabel: str,
+    *,
+    logarithmic: bool = False,
+) -> None:
+    scenarios = scenario_matrix()
+    x = np.arange(len(scenarios))
+    width = 0.16
+    figure, axis = plt.subplots(figsize=(15, 6.5))
+    for method_index, method in enumerate(METHOD_ORDER):
+        values = [
+            getattr(
+                next(
+                    item
+                    for item in summaries
+                    if item.scenario == scenario.name and item.method == method
+                ),
+                field,
+            )
+            for scenario in scenarios
+        ]
+        axis.bar(
+            x + (method_index - 2) * width,
+            values,
+            width,
+            label=METHOD_LABEL[method],
+        )
+    axis.set_ylabel(ylabel)
+    if logarithmic:
+        axis.set_yscale("log")
+    axis.set_xticks(x)
+    axis.set_xticklabels([item.name for item in scenarios], rotation=28, ha="right")
+    axis.grid(axis="y", alpha=0.25)
+    axis.legend(ncol=3)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def _transition_plot(path: Path, samples: list[EpochSample]) -> None:
+    figure, axes = plt.subplots(2, 1, figsize=(12, 7), sharex=True)
+    for method in (
+        SigmaMethod.CURRENT,
+        SigmaMethod.DLL_EXCESS,
+        SigmaMethod.DLL_EXCESS_GUARD,
+    ):
+        selected = [item for item in samples if item.method == method]
+        axes[0].plot(
+            [item.time_s for item in selected],
+            [item.position_error_3d_m for item in selected],
+            label=METHOD_LABEL[method],
+            linewidth=1.2,
+        )
+    reference = [item for item in samples if item.method == SigmaMethod.CURRENT]
+    axes[1].plot(
+        [item.time_s for item in reference],
+        [item.maximum_dll_ratio for item in reference],
+        color="tab:red",
+    )
+    axes[0].axvspan(22.0, 45.0, color="tab:orange", alpha=0.15)
+    axes[1].axvspan(22.0, 45.0, color="tab:orange", alpha=0.15)
+    axes[0].set_ylabel("3D konum hatası (m)")
+    axes[1].set_ylabel("Maks. DLL variance ratio")
+    axes[1].set_xlabel("Zaman (s)")
+    axes[0].legend()
+    for axis in axes:
+        axis.grid(alpha=0.25)
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def smoothing_summary(seed_count: int) -> dict[str, dict[str, float]]:
+    result: dict[str, dict[str, float]] = {}
+    for label, cfo_mps in (
+        ("cfo_compensated", 0.0),
+        ("cfo_residual_0p5_mps", 0.5),
+        ("cfo_residual_3_mps", 3.0),
+    ):
+        trials = [
+            run_smoothing_trial(seed, doppler_cfo_mps=cfo_mps)
+            for seed in range(1, seed_count + 1)
+        ]
+        result[label] = {
+            field: float(np.mean([getattr(item, field) for item in trials]))
+            for field in trials[0].__dataclass_fields__
+        }
+    return result
+
+
+def _smoothing_plot(path: Path, smoothing: dict[str, dict[str, float]]) -> None:
+    labels = list(smoothing)
+    x = np.arange(len(labels))
+    width = 0.20
+    figure, axis = plt.subplots(figsize=(10, 5.5))
+    for offset, (field, title) in enumerate(
+        (
+            ("raw_rmse_m", "Ham code"),
+            ("scalar_iir_rmse_m", "Kör IIR"),
+            ("doppler_smoothed_rmse_m", "Raw Doppler-predicted"),
+            (
+                "firmware_iir_doppler_smoothed_rmse_m",
+                "FW-IIR Doppler-predicted",
+            ),
+        )
+    ):
+        axis.bar(
+            x + (offset - 1.5) * width,
+            [smoothing[label][field] for label in labels],
+            width,
+            label=title,
+        )
+    axis.set_xticks(x)
+    axis.set_xticklabels(labels)
+    axis.set_ylabel("Range RMSE (m)")
+    axis.set_yscale("log")
+    axis.grid(axis="y", alpha=0.25)
+    axis.legend()
+    figure.tight_layout()
+    figure.savefig(path, dpi=150)
+    plt.close(figure)
+
+
+def write_report(
+    path: Path,
+    summaries: list[Summary],
+    focused_rms: dict[str, dict[SigmaMethod, float]],
+    smoothing: dict[str, dict[str, float]],
+    seed_count: int,
+) -> None:
+    current = {
+        item.scenario: item
+        for item in summaries
+        if item.method == SigmaMethod.CURRENT
+    }
+    lines = [
+        "# GPS code measurement model sonuçları",
+        "",
+        f"Monte Carlo seed sayısı: `{seed_count}`. İlk 5 saniye metriklere alınmadı.",
+        "",
+        "## Yöntem karşılaştırması",
+        "",
+        "| Senaryo | Yöntem | 3D RMS (m) | Mevcuda göre | P95 (m) | Valid (%) | >25 m false-valid (%) |",
+        "|---|---|---:|---:|---:|---:|---:|",
+    ]
+    for scenario in scenario_matrix():
+        baseline = current[scenario.name].position_3d_rms_m
+        for method in METHOD_ORDER:
+            item = next(
+                value
+                for value in summaries
+                if value.scenario == scenario.name and value.method == method
+            )
+            improvement = 100.0 * (baseline - item.position_3d_rms_m) / baseline
+            lines.append(
+                f"| {scenario.name} | {METHOD_LABEL[method]} | "
+                f"{item.position_3d_rms_m:.2f} | {improvement:+.1f}% | "
+                f"{item.position_3d_p95_m:.2f} | {item.valid_percent:.1f} | "
+                f"{item.false_valid_over_25m_percent:.2f} |"
+            )
+
+    lines.extend(
+        [
+            "",
+            "## Modelden çıkan karar özeti",
+            "",
+            "- C/N0 ile uyumlu nominal DLL jitter'da `dll_excess`, mevcut çözümü değiştirmemelidir.",
+            "- Bütün measurement sigmaları aynı sabitle çarpılırsa WLS konum noktası değişmez; yalnız covariance/integrity değişir. Fakat ortak DLL jitter çarpanı, C/N0/elevation bileşimi kanaldan kanala farklı olduğu için toplam sigmaları eşit oranda büyütmez.",
+            "- Kanal-bağımlı ve C/N0'da görünmeyen excess jitter varsa dinamik sigma o kanalı down-weight ederek konumu iyileştirebilir.",
+            "- Stable multipath bias düşük DLL variance bırakabildiği için variance-only yöntem çözüm değildir.",
+            "- 50 Hz'de DLL ratio alpha=0.10 yaklaşık 0.19 s zaman sabiti ve 0.57 s yüzde-95 geçiş verir.",
+            "- Aşağıdaki yüzdeler seçilen sentetik hata büyüklüklerine koşulludur; kart için kazanç tahmini değildir.",
+            "",
+            "## Bozulma penceresi odaklı 3D RMS",
+            "",
+            "| Senaryo/pencere | Mevcut (m) | DLL excess (m) | DLL excess+mean (m) | Oracle variance (m) |",
+            "|---|---:|---:|---:|---:|",
+        ]
+    )
+    for label, values in focused_rms.items():
+        lines.append(
+            f"| {label} | {values[SigmaMethod.CURRENT]:.2f} | "
+            f"{values[SigmaMethod.DLL_EXCESS]:.2f} | "
+            f"{values[SigmaMethod.DLL_EXCESS_GUARD]:.2f} | "
+            f"{values[SigmaMethod.ORACLE]:.2f} |"
+        )
+    lines.extend(
+        [
+            "",
+            "## Code smoothing ve carrier CFO",
+            "",
+            "| Carrier-rate koşulu | Ham RMSE (m) | Kör IIR RMSE (m) | Raw Doppler RMSE (m) | FW-IIR Doppler RMSE (m) | Kör IIR peak (m) | Raw Doppler peak (m) | FW-IIR Doppler peak (m) |",
+            "|---|---:|---:|---:|---:|---:|---:|---:|",
+        ]
+    )
+    for label, values in smoothing.items():
+        lines.append(
+            f"| {label} | {values['raw_rmse_m']:.2f} | "
+            f"{values['scalar_iir_rmse_m']:.2f} | "
+            f"{values['doppler_smoothed_rmse_m']:.2f} | "
+            f"{values['firmware_iir_doppler_smoothed_rmse_m']:.2f} | "
+            f"{values['scalar_iir_peak_dynamic_error_m']:.2f} | "
+            f"{values['doppler_peak_dynamic_error_m']:.2f} | "
+            f"{values['firmware_iir_doppler_peak_dynamic_error_m']:.2f} |"
+        )
+
+    lines.extend(
+        [
+            "",
+            "## Yorum sınırları",
+            "",
+            "- `current_cn0`, firmware'deki URA/elevation/C/N0 sigma modelidir.",
+            "- `naive_add_dll`, aynı thermal jitter'ı iki kere saymanın negatif kontrolüdür.",
+            "- `dll_excess`, yalnız ölçülen DLL variance'ın C/N0 beklentisini aşan kısmını code variance'a ekler.",
+            "- `dll_excess_guard`, variance'a ek olarak sürekli discriminator mean stress'ini kullanır.",
+            "- `oracle_variance`, sentetik gerçek jitter çarpanını bilir; yalnız variance kaynakları için erişilebilir üst sınırdır, bias'ı bilmez.",
+            "- Stable multipath DLL'nin yeni denge noktasında düşük residual variance bırakabilir. Bu nedenle variance-only yönteminin onu çözmesi beklenmez.",
+            "- Discriminator gürültü ölçeği kart correlator kayıtları gelene kadar kalibrasyon varsayımıdır; oran tabanlı yöntem mutlak ölçeğe göre daha az hassastır.",
+            "- Sonuçlar bitstream veya firmware değişikliği değildir; karar öncesi executable tasarım keşfidir.",
+            "",
+        ]
+    )
+    path.write_text("\n".join(lines), encoding="utf-8")
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--seeds", type=int, default=12)
+    parser.add_argument("--jobs", type=int, default=4)
+    parser.add_argument(
+        "--output",
+        type=Path,
+        default=Path(__file__).resolve().parent / "output",
+    )
+    arguments = parser.parse_args()
+    arguments.output.mkdir(parents=True, exist_ok=True)
+
+    scenarios = scenario_matrix()
+    tasks = [
+        (scenario_index, seed)
+        for scenario_index in range(len(scenarios))
+        for seed in range(1, arguments.seeds + 1)
+    ]
+    grouped: dict[int, list[EpochSample]] = {
+        index: [] for index in range(len(scenarios))
+    }
+    transition_samples: list[EpochSample] = []
+    with ProcessPoolExecutor(max_workers=max(1, arguments.jobs)) as executor:
+        for scenario_index, seed, samples in executor.map(_worker, tasks):
+            grouped[scenario_index].extend(samples)
+            if scenarios[scenario_index].name == "noise_burst_recovery" and seed == 1:
+                transition_samples = samples
+            print(
+                f"completed {scenarios[scenario_index].name} seed={seed}",
+                flush=True,
+            )
+
+    summaries = [
+        summarize(scenario.name, method, grouped[index])
+        for index, scenario in enumerate(scenarios)
+        for method in METHOD_ORDER
+    ]
+    focused_windows = {
+        "noise_burst_recovery [22,45) s": ("noise_burst_recovery", 22.0, 45.0),
+        "dll_transient_stress [25,34) s": ("dll_transient_stress", 25.0, 34.0),
+        "cn0_step_recovery [5,30) s": ("cn0_step_recovery", 5.0, 30.0),
+    }
+    focused_rms: dict[str, dict[SigmaMethod, float]] = {}
+    for label, (scenario_name, start_s, stop_s) in focused_windows.items():
+        scenario_index = next(
+            index
+            for index, scenario in enumerate(scenarios)
+            if scenario.name == scenario_name
+        )
+        focused_rms[label] = {}
+        for method in METHOD_ORDER:
+            values = np.asarray(
+                [
+                    item.position_error_3d_m
+                    for item in grouped[scenario_index]
+                    if item.method == method
+                    and start_s <= item.time_s < stop_s
+                ]
+            )
+            focused_rms[label][method] = _rms(values)
+    smoothing = smoothing_summary(max(arguments.seeds, 20))
+
+    write_csv(arguments.output / "scenario_summary.csv", summaries)
+    write_report(
+        arguments.output / "ANALYSIS.md",
+        summaries,
+        focused_rms,
+        smoothing,
+        arguments.seeds,
+    )
+    _comparison_plot(
+        arguments.output / "01_position_3d_rms.png",
+        summaries,
+        "position_3d_rms_m",
+        "3D RMS (m)",
+        logarithmic=True,
+    )
+    _comparison_plot(
+        arguments.output / "02_solution_availability.png",
+        summaries,
+        "valid_percent",
+        "Integrity-valid çözüm (%)",
+    )
+    _transition_plot(
+        arguments.output / "03_noise_burst_transition.png",
+        transition_samples,
+    )
+    _smoothing_plot(arguments.output / "04_code_smoothing_cfo.png", smoothing)
+    print(f"wrote analysis to {arguments.output}", flush=True)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/soc/software/gps_measurement_python/code_smoothing_model.py b/soc/software/gps_measurement_python/code_smoothing_model.py
new file mode 100644
index 0000000..83b56d4
--- /dev/null
+++ b/soc/software/gps_measurement_python/code_smoothing_model.py
@@ -0,0 +1,132 @@
+"""One-dimensional code smoothing study with carrier/Doppler aiding."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+
+@dataclass(frozen=True)
+class SmoothingResult:
+    raw_rmse_m: float
+    scalar_iir_rmse_m: float
+    doppler_smoothed_rmse_m: float
+    firmware_iir_doppler_smoothed_rmse_m: float
+    scalar_iir_peak_dynamic_error_m: float
+    doppler_peak_dynamic_error_m: float
+    firmware_iir_doppler_peak_dynamic_error_m: float
+
+
+def run_smoothing_trial(
+    seed: int,
+    *,
+    duration_s: float = 80.0,
+    tracking_dt_s: float = 0.020,
+    wls_dt_s: float = 0.200,
+    code_sigma_m: float = 4.0,
+    doppler_sigma_mps: float = 0.25,
+    doppler_cfo_mps: float = 0.0,
+    alpha: float = 0.10,
+    firmware_doppler_alpha: float = 0.05,
+) -> SmoothingResult:
+    """Compare raw code, blind IIR and Doppler-propagated code smoothing.
+
+    The truth includes a range-rate step so a visually smooth but lagging
+    scalar IIR is penalized.  ``doppler_cfo_mps`` represents residual receiver
+    carrier frequency offset after the nominal IF subtraction.
+    """
+
+    if abs(round(wls_dt_s / tracking_dt_s) - wls_dt_s / tracking_dt_s) > 1.0e-12:
+        raise ValueError("WLS period must be an integer number of tracking periods")
+    rng = np.random.default_rng(seed)
+    tracking_time_s = np.arange(0.0, duration_s, tracking_dt_s)
+    true_rate_tracking = np.where(
+        tracking_time_s < 20.0,
+        -120.0,
+        np.where(tracking_time_s < 45.0, 230.0, -40.0),
+    )
+    true_range_tracking = np.empty_like(tracking_time_s)
+    true_range_tracking[0] = 21_000_000.0
+    true_range_tracking[1:] = (
+        true_range_tracking[0]
+        + np.cumsum(true_rate_tracking[:-1] * tracking_dt_s)
+    )
+    measured_rate_tracking = (
+        true_rate_tracking
+        + doppler_cfo_mps
+        + rng.normal(0.0, doppler_sigma_mps, len(tracking_time_s))
+    )
+    filtered_rate_tracking = np.empty_like(measured_rate_tracking)
+    filtered_rate_tracking[0] = measured_rate_tracking[0]
+    for index in range(1, len(filtered_rate_tracking)):
+        filtered_rate_tracking[index] = (
+            firmware_doppler_alpha * measured_rate_tracking[index]
+            + (1.0 - firmware_doppler_alpha) * filtered_rate_tracking[index - 1]
+        )
+
+    tracking_per_wls = int(round(wls_dt_s / tracking_dt_s))
+    wls_indices = np.arange(0, len(tracking_time_s), tracking_per_wls)
+    time_s = tracking_time_s[wls_indices]
+    true_range = true_range_tracking[wls_indices]
+    raw_code = true_range + rng.normal(0.0, code_sigma_m, len(time_s))
+
+    scalar = np.empty_like(raw_code)
+    doppler_smoothed = np.empty_like(raw_code)
+    firmware_iir_doppler_smoothed = np.empty_like(raw_code)
+    scalar[0] = raw_code[0]
+    doppler_smoothed[0] = raw_code[0]
+    firmware_iir_doppler_smoothed[0] = raw_code[0]
+    for index in range(1, len(time_s)):
+        scalar[index] = alpha * raw_code[index] + (1.0 - alpha) * scalar[index - 1]
+        start = wls_indices[index - 1]
+        stop = wls_indices[index]
+        raw_range_delta = (
+            float(np.sum(measured_rate_tracking[start:stop]))
+            * tracking_dt_s
+        )
+        filtered_range_delta = (
+            float(np.sum(filtered_rate_tracking[start:stop]))
+            * tracking_dt_s
+        )
+        prediction = doppler_smoothed[index - 1] + raw_range_delta
+        doppler_smoothed[index] = (
+            prediction + alpha * (raw_code[index] - prediction)
+        )
+        filtered_prediction = (
+            firmware_iir_doppler_smoothed[index - 1]
+            + filtered_range_delta
+        )
+        firmware_iir_doppler_smoothed[index] = (
+            filtered_prediction
+            + alpha * (raw_code[index] - filtered_prediction)
+        )
+
+    warm = time_s >= 5.0
+    dynamic = ((time_s >= 20.0) & (time_s < 25.0)) | (
+        (time_s >= 45.0) & (time_s < 50.0)
+    )
+    rmse = lambda error, mask: float(np.sqrt(np.mean(np.square(error[mask]))))
+    return SmoothingResult(
+        raw_rmse_m=rmse(raw_code - true_range, warm),
+        scalar_iir_rmse_m=rmse(scalar - true_range, warm),
+        doppler_smoothed_rmse_m=rmse(doppler_smoothed - true_range, warm),
+        firmware_iir_doppler_smoothed_rmse_m=rmse(
+            firmware_iir_doppler_smoothed - true_range,
+            warm,
+        ),
+        scalar_iir_peak_dynamic_error_m=float(
+            np.max(np.abs(scalar[dynamic] - true_range[dynamic]))
+        ),
+        doppler_peak_dynamic_error_m=float(
+            np.max(np.abs(doppler_smoothed[dynamic] - true_range[dynamic]))
+        ),
+        firmware_iir_doppler_peak_dynamic_error_m=float(
+            np.max(
+                np.abs(
+                    firmware_iir_doppler_smoothed[dynamic]
+                    - true_range[dynamic]
+                )
+            )
+        ),
+    )
diff --git a/soc/software/gps_measurement_python/doppler_eskf_model.py b/soc/software/gps_measurement_python/doppler_eskf_model.py
new file mode 100644
index 0000000..54849fd
--- /dev/null
+++ b/soc/software/gps_measurement_python/doppler_eskf_model.py
@@ -0,0 +1,657 @@
+"""Project-specific Doppler WLS to ESKF timing/noise model.
+
+The model compares four paths using one shared 50 Hz tracking stream and one
+shared 100 Hz IMU stream:
+
+* the legacy fixed-alpha Doppler IIR before 5 Hz velocity WLS;
+* raw Doppler into WLS, leaving temporal filtering to the ESKF;
+* a global IMU-driven adaptive-alpha IIR;
+* raw Doppler with the per-satellite robust WLS gate used before the ESKF.
+
+The ESKF is reduced to the velocity and accelerometer-bias error states that
+matter to this experiment.  Its process noise, 3-D measurement covariance and
+99.9-percent velocity NIS gate mirror the project firmware.  Attitude and
+position are intentionally outside this model's scope.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+from enum import Enum
+from typing import Callable
+
+import numpy as np
+
+
+IMU_HZ = 100.0
+TRACKING_HZ = 50.0
+VELOCITY_WLS_HZ = 5.0
+IMU_DT_S = 1.0 / IMU_HZ
+TRACKING_STEPS = int(round(IMU_HZ / TRACKING_HZ))
+WLS_STEPS = int(round(IMU_HZ / VELOCITY_WLS_HZ))
+FIXED_DOPPLER_ALPHA = 0.05
+CN0_ALPHA = 0.20
+VELOCITY_NIS_GATE = 16.26623619623813
+PROCESS_ACCEL_NOISE_DENSITY = 0.025
+ACCEL_BIAS_RANDOM_WALK = 0.0015
+MINIMUM_HORIZONTAL_VELOCITY_STD_MPS = 2.0
+MINIMUM_VERTICAL_VELOCITY_STD_MPS = 3.0
+
+
+class DopplerPath(str, Enum):
+    FIXED_IIR = "fixed_iir_wls_eskf"
+    RAW = "raw_wls_eskf"
+    ADAPTIVE_IIR = "adaptive_iir_wls_eskf"
+    RAW_ROBUST = "raw_robust_wls_eskf"
+
+
+PATH_ORDER = (
+    DopplerPath.FIXED_IIR,
+    DopplerPath.RAW,
+    DopplerPath.ADAPTIVE_IIR,
+    DopplerPath.RAW_ROBUST,
+)
+
+
+@dataclass(frozen=True)
+class FlightScenario:
+    name: str
+    description: str
+    duration_s: float
+    initial_velocity_mps: np.ndarray
+    acceleration: Callable[[float], np.ndarray]
+    cn0_offset: Callable[[float], float]
+    noise_multiplier: Callable[[float, int], float]
+    outlier_mps: Callable[[float, int], float]
+    receiver_clock_drift_mps: Callable[[float], float]
+    gps_gaps: tuple[tuple[float, float], ...] = ()
+
+
+@dataclass(frozen=True)
+class VelocityWlsResult:
+    velocity_mps: np.ndarray
+    clock_drift_mps: float
+    covariance_mps2: np.ndarray
+    residual_mps: np.ndarray
+    residual_rms_mps: float
+    covariance_scale: float
+    excluded_satellite: int | None
+
+
+@dataclass
+class AdaptiveAlpha:
+    alpha: float = FIXED_DOPPLER_ALPHA
+    hold_samples: int = 0
+    filtered_acceleration_mps2: np.ndarray = field(
+        default_factory=lambda: np.zeros(3, dtype=float)
+    )
+
+    def update(
+        self,
+        measured_acceleration_mps2: np.ndarray,
+        median_cn0_dbhz: float,
+    ) -> float:
+        # A raw 100 Hz accelerometer sample is too noisy for coefficient
+        # switching.  This 50 Hz vector EWMA has an approximately 0.16 s time
+        # constant and, unlike smoothing |a|, does not retain the positive
+        # magnitude bias of zero-mean sensor noise.
+        motion_alpha = 0.12
+        self.filtered_acceleration_mps2 += motion_alpha * (
+            measured_acceleration_mps2 - self.filtered_acceleration_mps2
+        )
+        magnitude = float(np.linalg.norm(self.filtered_acceleration_mps2))
+
+        if median_cn0_dbhz >= 46.0:
+            quiet_alpha = 0.08
+        elif median_cn0_dbhz >= 37.0:
+            quiet_alpha = FIXED_DOPPLER_ALPHA
+        else:
+            quiet_alpha = 0.03
+
+        if magnitude >= 2.5:
+            self.alpha = 0.40
+            self.hold_samples = 25
+        elif magnitude >= 0.55:
+            self.alpha = 0.20
+            self.hold_samples = 25
+        elif self.hold_samples > 0:
+            self.hold_samples -= 1
+        else:
+            self.alpha = quiet_alpha
+        return self.alpha
+
+
+@dataclass
+class VelocityBiasEskf:
+    velocity_mps: np.ndarray
+    accel_bias_mps2: np.ndarray
+    covariance: np.ndarray
+    accepted: int = 0
+    rejected_nis: int = 0
+    last_nis: float = float("nan")
+
+    @classmethod
+    def initialize(
+        cls,
+        initial_velocity_mps: np.ndarray,
+        initial_velocity_error_mps: np.ndarray,
+    ) -> "VelocityBiasEskf":
+        covariance = np.zeros((6, 6), dtype=float)
+        covariance[:3, :3] = np.eye(3)
+        covariance[3:, 3:] = np.eye(3) * 0.1**2
+        return cls(
+            velocity_mps=initial_velocity_mps + initial_velocity_error_mps,
+            accel_bias_mps2=np.zeros(3),
+            covariance=covariance,
+        )
+
+    def propagate(self, measured_acceleration_mps2: np.ndarray, dt_s: float) -> None:
+        self.velocity_mps += (
+            measured_acceleration_mps2 - self.accel_bias_mps2
+        ) * dt_s
+
+        transition = np.eye(6)
+        transition[:3, 3:] = -np.eye(3) * dt_s
+        accel_variance = PROCESS_ACCEL_NOISE_DENSITY**2
+        bias_variance = ACCEL_BIAS_RANDOM_WALK**2
+        process = np.zeros((6, 6), dtype=float)
+        # Match eskf.c's first-order discrete injection: velocity and bias
+        # driving noise are added after F P F^T, without exact-discretization
+        # dt^2/dt^3 cross terms.
+        process[:3, :3] = np.eye(3) * accel_variance * dt_s
+        process[3:, 3:] = np.eye(3) * bias_variance * dt_s
+        self.covariance = (
+            transition @ self.covariance @ transition.T + process
+        )
+        self.covariance = 0.5 * (self.covariance + self.covariance.T)
+
+    def update_velocity(
+        self,
+        measurement_mps: np.ndarray,
+        covariance_mps2: np.ndarray,
+    ) -> bool:
+        innovation = measurement_mps - self.velocity_mps
+        innovation_covariance = self.covariance[:3, :3] + covariance_mps2
+        inverse = np.linalg.inv(innovation_covariance)
+        nis = float(innovation @ inverse @ innovation)
+        self.last_nis = nis
+        if not np.isfinite(nis) or nis > VELOCITY_NIS_GATE:
+            self.rejected_nis += 1
+            return False
+
+        measurement_matrix = np.zeros((3, 6), dtype=float)
+        measurement_matrix[:, :3] = np.eye(3)
+        gain = self.covariance @ measurement_matrix.T @ inverse
+        correction = gain @ innovation
+        self.velocity_mps += correction[:3]
+        self.accel_bias_mps2 += correction[3:]
+        identity = np.eye(6)
+        residual_transform = identity - gain @ measurement_matrix
+        self.covariance = (
+            residual_transform
+            @ self.covariance
+            @ residual_transform.T
+            + gain @ covariance_mps2 @ gain.T
+        )
+        self.covariance = 0.5 * (self.covariance + self.covariance.T)
+        self.accepted += 1
+        return True
+
+
+@dataclass(frozen=True)
+class DopplerEskfTrace:
+    scenario: str
+    path: DopplerPath
+    time_s: np.ndarray
+    truth_velocity_mps: np.ndarray
+    fused_velocity_mps: np.ndarray
+    fused_velocity_covariance_mps2: np.ndarray
+    acceleration_mps2: np.ndarray
+    wls_time_s: np.ndarray
+    wls_velocity_mps: np.ndarray
+    wls_clock_drift_mps: np.ndarray
+    wls_covariance_mps2: np.ndarray
+    wls_covariance_scale: np.ndarray
+    wls_nis: np.ndarray
+    wls_accepted: np.ndarray
+    adaptive_alpha: np.ndarray
+    excluded_satellites: np.ndarray
+
+
+def _zero_acceleration(_time_s: float) -> np.ndarray:
+    return np.zeros(3)
+
+
+def _airliner_acceleration(time_s: float) -> np.ndarray:
+    if 15.0 <= time_s < 25.0:
+        return np.asarray([2.0, 0.0, 0.0])
+    if 38.0 <= time_s < 52.0:
+        return np.asarray([0.0, 1.5, 0.25])
+    if 68.0 <= time_s < 76.0:
+        return np.asarray([-2.5, 0.0, -0.15])
+    return np.zeros(3)
+
+
+def _aggressive_acceleration(time_s: float) -> np.ndarray:
+    if 10.0 <= time_s < 16.0:
+        return np.asarray([6.0, 0.0, 1.0])
+    if 26.0 <= time_s < 33.0:
+        return np.asarray([0.0, 7.0, 0.0])
+    if 46.0 <= time_s < 52.0:
+        return np.asarray([-5.0, -4.0, -1.0])
+    if 64.0 <= time_s < 76.0:
+        phase = 2.0 * np.pi * (time_s - 64.0) / 3.0
+        return np.asarray([3.0 * np.sin(phase), 4.0 * np.cos(phase), 0.5 * np.sin(phase)])
+    return np.zeros(3)
+
+
+def _constant_zero(_time_s: float) -> float:
+    return 0.0
+
+
+def _constant_one(_time_s: float, _satellite: int) -> float:
+    return 1.0
+
+
+def _no_outlier(_time_s: float, _satellite: int) -> float:
+    return 0.0
+
+
+def flight_scenarios() -> tuple[FlightScenario, ...]:
+    return (
+        FlightScenario(
+            "steady_cruise",
+            "Constant aircraft velocity with nominal open-sky Doppler noise.",
+            90.0,
+            np.asarray([180.0, 20.0, 0.0]),
+            _zero_acceleration,
+            _constant_zero,
+            _constant_one,
+            _no_outlier,
+            _constant_zero,
+        ),
+        FlightScenario(
+            "airliner_maneuver",
+            "Moderate longitudinal, turn and climb-rate accelerations.",
+            90.0,
+            np.asarray([120.0, 0.0, 0.0]),
+            _airliner_acceleration,
+            _constant_zero,
+            _constant_one,
+            _no_outlier,
+            _constant_zero,
+        ),
+        FlightScenario(
+            "aggressive_maneuver",
+            "High acceleration and oscillatory manoeuvre segments.",
+            90.0,
+            np.asarray([80.0, 0.0, 0.0]),
+            _aggressive_acceleration,
+            _constant_zero,
+            _constant_one,
+            _no_outlier,
+            _constant_zero,
+        ),
+        FlightScenario(
+            "low_cn0_airliner",
+            "Airliner manoeuvre with a 10 dB signal-quality loss.",
+            90.0,
+            np.asarray([120.0, 0.0, 0.0]),
+            _airliner_acceleration,
+            lambda _time_s: -10.0,
+            _constant_one,
+            _no_outlier,
+            _constant_zero,
+        ),
+        FlightScenario(
+            "single_satellite_outliers",
+            "One channel has repeatable 12 m/s Doppler bursts.",
+            90.0,
+            np.asarray([120.0, 0.0, 0.0]),
+            _airliner_acceleration,
+            _constant_zero,
+            _constant_one,
+            lambda time_s, satellite: (
+                12.0
+                if satellite == 2
+                and (
+                    30.0 <= time_s < 31.0
+                    or 56.0 <= time_s < 57.0
+                    or 72.0 <= time_s < 72.6
+                )
+                else 0.0
+            ),
+            _constant_zero,
+        ),
+        FlightScenario(
+            "clock_drift_steps",
+            "Common receiver clock-frequency steps coexist with manoeuvres.",
+            90.0,
+            np.asarray([120.0, 0.0, 0.0]),
+            _airliner_acceleration,
+            _constant_zero,
+            _constant_one,
+            _no_outlier,
+            lambda time_s: (
+                18.0 if 28.0 <= time_s < 55.0 else (-9.0 if time_s >= 55.0 else 0.0)
+            ),
+        ),
+        FlightScenario(
+            "gps_gap_recovery",
+            "Fifteen-second GNSS gap during an aircraft manoeuvre.",
+            90.0,
+            np.asarray([120.0, 0.0, 0.0]),
+            _airliner_acceleration,
+            _constant_zero,
+            _constant_one,
+            _no_outlier,
+            _constant_zero,
+            gps_gaps=((42.0, 57.0),),
+        ),
+        FlightScenario(
+            "mixed_flight_faults",
+            "Aggressive motion, temporary weak signal, channel bursts and clock step.",
+            90.0,
+            np.asarray([80.0, 0.0, 0.0]),
+            _aggressive_acceleration,
+            lambda time_s: -9.0 if 34.0 <= time_s < 60.0 else 0.0,
+            lambda time_s, satellite: (
+                2.5 if 34.0 <= time_s < 60.0 and satellite in (1, 6) else 1.0
+            ),
+            lambda time_s, satellite: (
+                -10.0 if satellite == 4 and 54.0 <= time_s < 55.0 else 0.0
+            ),
+            lambda time_s: 12.0 if time_s >= 48.0 else 0.0,
+            gps_gaps=((78.0, 83.0),),
+        ),
+    )
+
+
+def local_los_matrix() -> np.ndarray:
+    azimuth_deg = np.asarray([8.0, 55.0, 104.0, 151.0, 205.0, 253.0, 301.0, 342.0])
+    elevation_deg = np.asarray([73.0, 48.0, 31.0, 18.0, 64.0, 39.0, 24.0, 14.0])
+    azimuth = np.deg2rad(azimuth_deg)
+    elevation = np.deg2rad(elevation_deg)
+    return np.column_stack(
+        [
+            np.cos(elevation) * np.sin(azimuth),
+            np.cos(elevation) * np.cos(azimuth),
+            np.sin(elevation),
+        ]
+    )
+
+
+def velocity_sigma_mps(cn0_dbhz: np.ndarray) -> np.ndarray:
+    return np.clip(30.0 * np.power(10.0, -cn0_dbhz / 20.0), 0.05, 5.0)
+
+
+def _solve_velocity_candidate(
+    design: np.ndarray,
+    observations_mps: np.ndarray,
+    sigma_mps: np.ndarray,
+    indices: np.ndarray,
+) -> VelocityWlsResult:
+    selected_design = design[indices]
+    selected_observations = observations_mps[indices]
+    selected_sigma = sigma_mps[indices]
+    weights = 1.0 / np.square(selected_sigma)
+    normal = selected_design.T @ (weights[:, None] * selected_design)
+    inverse = np.linalg.inv(normal)
+    solution = inverse @ (selected_design.T @ (weights * selected_observations))
+    residual = selected_observations - selected_design @ solution
+    weighted_residual_square_sum = float(np.sum(weights * np.square(residual)))
+    degrees_of_freedom = len(indices) - 4
+    covariance_scale = (
+        max(1.0, weighted_residual_square_sum / degrees_of_freedom)
+        if degrees_of_freedom > 0
+        else 1.0
+    )
+    return VelocityWlsResult(
+        velocity_mps=solution[:3].copy(),
+        clock_drift_mps=float(solution[3]),
+        covariance_mps2=covariance_scale * inverse[:3, :3],
+        residual_mps=residual,
+        residual_rms_mps=float(np.sqrt(np.mean(np.square(residual)))),
+        covariance_scale=covariance_scale,
+        excluded_satellite=None,
+    )
+
+
+def velocity_wls(
+    observations_mps: np.ndarray,
+    cn0_dbhz: np.ndarray,
+    *,
+    robust: bool = False,
+) -> VelocityWlsResult:
+    los = local_los_matrix()
+    design = np.column_stack([-los, np.ones(len(los))])
+    sigma = velocity_sigma_mps(cn0_dbhz)
+    indices = np.arange(len(observations_mps), dtype=int)
+    full = _solve_velocity_candidate(design, observations_mps, sigma, indices)
+    if not robust or len(indices) < 6:
+        return full
+
+    normalized = np.abs(full.residual_mps) / sigma
+    if float(np.max(normalized)) <= 3.5:
+        return full
+
+    # The largest full-fit residual is not necessarily the bad satellite:
+    # WLS leverage can distribute one channel's error over the other rows.
+    # Compare every leave-one-out hypothesis and use the one with the lowest
+    # normalized post-fit residual energy.  The firmware robust velocity WLS
+    # uses the same trigger and candidate selection.
+    candidates: list[tuple[float, int, VelocityWlsResult]] = []
+    for excluded in indices:
+        used = indices[indices != excluded]
+        candidate = _solve_velocity_candidate(design, observations_mps, sigma, used)
+        score = float(
+            np.sum(np.square(candidate.residual_mps / sigma[used]))
+        )
+        candidates.append((score, int(excluded), candidate))
+    _score, excluded, candidate = min(candidates, key=lambda item: item[0])
+    return VelocityWlsResult(
+        **{
+            **candidate.__dict__,
+            "excluded_satellite": excluded,
+        }
+    )
+
+
+def fusion_velocity_covariance(covariance_mps2: np.ndarray) -> np.ndarray:
+    """Apply fusion_gps_adapter.c's ENU velocity covariance sanitizer floors."""
+
+    output = np.asarray(covariance_mps2, dtype=float).copy()
+    variance_floor = np.square(
+        np.asarray(
+            [
+                MINIMUM_HORIZONTAL_VELOCITY_STD_MPS,
+                MINIMUM_HORIZONTAL_VELOCITY_STD_MPS,
+                MINIMUM_VERTICAL_VELOCITY_STD_MPS,
+            ]
+        )
+    )
+    for axis in range(3):
+        output[axis, axis] = max(output[axis, axis], variance_floor[axis])
+    for row in range(3):
+        for column in range(row + 1, 3):
+            covariance = 0.5 * (output[row, column] + output[column, row])
+            limit = 0.95 * np.sqrt(output[row, row] * output[column, column])
+            covariance = float(np.clip(covariance, -limit, limit))
+            output[row, column] = covariance
+            output[column, row] = covariance
+    return output
+
+
+def _in_gap(scenario: FlightScenario, time_s: float) -> bool:
+    return any(start <= time_s < stop for start, stop in scenario.gps_gaps)
+
+
+def _truth_trajectory(scenario: FlightScenario) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    time_s = np.arange(0.0, scenario.duration_s, IMU_DT_S)
+    acceleration = np.asarray([scenario.acceleration(float(time)) for time in time_s])
+    velocity = np.empty((len(time_s), 3), dtype=float)
+    velocity[0] = scenario.initial_velocity_mps
+    velocity[1:] = velocity[0] + np.cumsum(acceleration[:-1] * IMU_DT_S, axis=0)
+    return time_s, acceleration, velocity
+
+
+def run_doppler_eskf_scenario(
+    scenario: FlightScenario,
+    seed: int,
+    paths: tuple[DopplerPath, ...] = PATH_ORDER,
+) -> dict[DopplerPath, DopplerEskfTrace]:
+    rng = np.random.default_rng(seed)
+    time_s, truth_acceleration, truth_velocity = _truth_trajectory(scenario)
+    satellite_count = len(local_los_matrix())
+    baseline_cn0 = np.asarray([47.0, 45.0, 43.0, 38.0, 46.0, 42.0, 40.0, 36.0])
+    filtered_cn0 = baseline_cn0.copy()
+    fixed_measurement: np.ndarray | None = None
+    adaptive_measurement: np.ndarray | None = None
+    latest_raw: np.ndarray | None = None
+    alpha_selector = AdaptiveAlpha()
+    latest_alpha = FIXED_DOPPLER_ALPHA
+
+    initial_error = rng.normal(0.0, 0.8, 3)
+    filters = {
+        path: VelocityBiasEskf.initialize(
+            scenario.initial_velocity_mps,
+            initial_error,
+        )
+        for path in paths
+    }
+    fused_history = {
+        path: np.empty((len(time_s), 3), dtype=float)
+        for path in paths
+    }
+    fused_covariance_history = {
+        path: np.empty((len(time_s), 3, 3), dtype=float)
+        for path in paths
+    }
+    wls_times = {path: [] for path in paths}
+    wls_velocity = {path: [] for path in paths}
+    wls_clock_drift = {path: [] for path in paths}
+    wls_covariance = {path: [] for path in paths}
+    wls_covariance_scale = {path: [] for path in paths}
+    wls_nis = {path: [] for path in paths}
+    wls_accepted = {path: [] for path in paths}
+    wls_alpha = {path: [] for path in paths}
+    excluded = {path: [] for path in paths}
+
+    true_accel_bias = rng.normal(0.0, 0.04, 3)
+    latest_acceleration_measurement = truth_acceleration[0] + true_accel_bias
+    los = local_los_matrix()
+
+    for sample in range(len(time_s)):
+        if sample > 0:
+            true_accel_bias += rng.normal(
+                0.0,
+                ACCEL_BIAS_RANDOM_WALK * np.sqrt(IMU_DT_S),
+                3,
+            )
+            imu_noise_std = PROCESS_ACCEL_NOISE_DENSITY / np.sqrt(IMU_DT_S)
+            latest_acceleration_measurement = (
+                truth_acceleration[sample - 1]
+                + true_accel_bias
+                + rng.normal(0.0, imu_noise_std, 3)
+            )
+            for path in paths:
+                filters[path].propagate(latest_acceleration_measurement, IMU_DT_S)
+
+        if sample % TRACKING_STEPS == 0:
+            current_time = float(time_s[sample])
+            true_cn0 = baseline_cn0 + scenario.cn0_offset(current_time)
+            raw_cn0 = np.clip(true_cn0 + rng.normal(0.0, 1.2, satellite_count), 10.0, 60.0)
+            filtered_cn0 = CN0_ALPHA * raw_cn0 + (1.0 - CN0_ALPHA) * filtered_cn0
+            nominal_sigma = velocity_sigma_mps(true_cn0)
+            actual_sigma = nominal_sigma * np.asarray(
+                [
+                    scenario.noise_multiplier(current_time, satellite)
+                    for satellite in range(satellite_count)
+                ]
+            )
+            raw = (
+                -los @ truth_velocity[sample]
+                + scenario.receiver_clock_drift_mps(current_time)
+                + rng.normal(0.0, actual_sigma)
+                + np.asarray(
+                    [
+                        scenario.outlier_mps(current_time, satellite)
+                        for satellite in range(satellite_count)
+                    ]
+                )
+            )
+            if fixed_measurement is None:
+                fixed_measurement = raw.copy()
+                adaptive_measurement = raw.copy()
+            else:
+                fixed_measurement += FIXED_DOPPLER_ALPHA * (raw - fixed_measurement)
+                latest_alpha = alpha_selector.update(
+                    latest_acceleration_measurement,
+                    float(np.median(filtered_cn0)),
+                )
+                adaptive_measurement += latest_alpha * (raw - adaptive_measurement)
+            latest_raw = raw
+
+        if (
+            sample > 0
+            and sample % WLS_STEPS == 0
+            and latest_raw is not None
+            and not _in_gap(scenario, float(time_s[sample]))
+        ):
+            for path in paths:
+                if path == DopplerPath.FIXED_IIR:
+                    observations = fixed_measurement
+                elif path == DopplerPath.ADAPTIVE_IIR:
+                    observations = adaptive_measurement
+                else:
+                    observations = latest_raw
+                result = velocity_wls(
+                    np.asarray(observations),
+                    filtered_cn0,
+                    robust=(path == DopplerPath.RAW_ROBUST),
+                )
+                accepted = filters[path].update_velocity(
+                    result.velocity_mps,
+                    fusion_velocity_covariance(result.covariance_mps2),
+                )
+                wls_times[path].append(float(time_s[sample]))
+                wls_velocity[path].append(result.velocity_mps)
+                wls_clock_drift[path].append(result.clock_drift_mps)
+                wls_covariance[path].append(result.covariance_mps2)
+                wls_covariance_scale[path].append(result.covariance_scale)
+                wls_nis[path].append(filters[path].last_nis)
+                wls_accepted[path].append(accepted)
+                wls_alpha[path].append(
+                    latest_alpha
+                    if path == DopplerPath.ADAPTIVE_IIR
+                    else (FIXED_DOPPLER_ALPHA if path == DopplerPath.FIXED_IIR else 1.0)
+                )
+                excluded[path].append(
+                    -1 if result.excluded_satellite is None else result.excluded_satellite
+                )
+
+        for path in paths:
+            fused_history[path][sample] = filters[path].velocity_mps
+            fused_covariance_history[path][sample] = filters[path].covariance[:3, :3]
+
+    return {
+        path: DopplerEskfTrace(
+            scenario=scenario.name,
+            path=path,
+            time_s=time_s,
+            truth_velocity_mps=truth_velocity,
+            fused_velocity_mps=fused_history[path],
+            fused_velocity_covariance_mps2=fused_covariance_history[path],
+            acceleration_mps2=truth_acceleration,
+            wls_time_s=np.asarray(wls_times[path]),
+            wls_velocity_mps=np.asarray(wls_velocity[path]),
+            wls_clock_drift_mps=np.asarray(wls_clock_drift[path]),
+            wls_covariance_mps2=np.asarray(wls_covariance[path]),
+            wls_covariance_scale=np.asarray(wls_covariance_scale[path]),
+            wls_nis=np.asarray(wls_nis[path]),
+            wls_accepted=np.asarray(wls_accepted[path], dtype=bool),
+            adaptive_alpha=np.asarray(wls_alpha[path]),
+            excluded_satellites=np.asarray(excluded[path], dtype=int),
+        )
+        for path in paths
+    }
diff --git a/soc/software/gps_measurement_python/firmware_wls_model.py b/soc/software/gps_measurement_python/firmware_wls_model.py
new file mode 100644
index 0000000..2beb8a0
--- /dev/null
+++ b/soc/software/gps_measurement_python/firmware_wls_model.py
@@ -0,0 +1,353 @@
+"""Python mirror of the firmware's code-measurement WLS policy.
+
+The model copies the receiver-specific parts of NavEquations.c:
+
+* four states: ECEF x/y/z and common receiver clock bias in metres;
+* URA + elevation + C/N0 variance model;
+* normalized weights for the numerical solve and absolute weights for
+  covariance/integrity;
+* the 99-percent chi-square table;
+* single-satellite leave-one-out FDE only when at least seven measurements
+  are available.
+
+Atmospheric and satellite-clock corrections are represented as already
+corrected measurement errors.  That keeps this study focused on tracking
+quality rather than duplicating the existing PPS orbit/atmosphere model.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from enum import Enum
+
+import numpy as np
+
+
+URA_SIGMA_M = np.asarray(
+    [
+        2.4,
+        3.4,
+        4.85,
+        6.85,
+        9.65,
+        13.65,
+        24.0,
+        48.0,
+        96.0,
+        192.0,
+        384.0,
+        768.0,
+        1536.0,
+        3072.0,
+        6144.0,
+    ],
+    dtype=float,
+)
+CHI_SQUARE_99 = np.asarray(
+    [0.0, 6.634896601, 9.210340372, 11.34486673, 13.27670414, 15.08627247],
+    dtype=float,
+)
+
+
+class SigmaMethod(str, Enum):
+    CURRENT = "current_cn0"
+    NAIVE_ADD_DLL = "naive_add_dll"
+    DLL_EXCESS = "dll_excess"
+    DLL_EXCESS_GUARD = "dll_excess_guard"
+    ORACLE = "oracle_variance"
+
+
+@dataclass(frozen=True)
+class SigmaInputs:
+    ura_index: np.ndarray
+    elevation_deg: np.ndarray
+    cn0_dbhz: np.ndarray
+    dll_variance_ratio: np.ndarray
+    dll_mean_z: np.ndarray
+    actual_jitter_multiplier: np.ndarray
+
+
+@dataclass(frozen=True)
+class WlsSolution:
+    position_ecef_m: np.ndarray
+    clock_bias_m: float
+    residual_m: np.ndarray
+    sigma_m: np.ndarray
+    covariance: np.ndarray
+    chi_square: float
+    chi_square_ratio: float
+    chi_square_pass: bool
+    valid: bool
+    used_indices: np.ndarray
+    excluded_index: int | None
+
+
+def cn0_code_sigma_m(cn0_dbhz: np.ndarray | float) -> np.ndarray:
+    sigma = 3.0 * np.power(10.0, (45.0 - np.asarray(cn0_dbhz)) / 20.0)
+    return np.clip(sigma, 0.5, 30.0)
+
+
+def elevation_sigma_m(elevation_deg: np.ndarray | float) -> np.ndarray:
+    bounded = np.clip(np.asarray(elevation_deg), 10.0, 90.0)
+    return 3.0 / np.sin(np.deg2rad(bounded))
+
+
+def firmware_sigma_m(
+    inputs: SigmaInputs,
+    method: SigmaMethod,
+) -> np.ndarray:
+    ura = URA_SIGMA_M[np.asarray(inputs.ura_index, dtype=int)]
+    elevation = elevation_sigma_m(inputs.elevation_deg)
+    code = cn0_code_sigma_m(inputs.cn0_dbhz)
+    ratio = np.clip(np.asarray(inputs.dll_variance_ratio), 0.05, 25.0)
+
+    if method == SigmaMethod.CURRENT:
+        code_variance_factor = np.ones_like(code)
+    elif method == SigmaMethod.NAIVE_ADD_DLL:
+        # Deliberately included as a negative control: at ratio=1 this counts
+        # the C/N0-predicted thermal jitter twice.
+        code_variance_factor = 1.0 + ratio
+    elif method == SigmaMethod.DLL_EXCESS:
+        # Only the measured excess over the C/N0 expectation is added.
+        code_variance_factor = np.maximum(1.0, ratio)
+    elif method == SigmaMethod.DLL_EXCESS_GUARD:
+        mean_factor = np.square(
+            np.maximum(1.0, np.asarray(inputs.dll_mean_z) / 3.0)
+        )
+        code_variance_factor = np.maximum.reduce(
+            [np.ones_like(code), ratio, mean_factor]
+        )
+    elif method == SigmaMethod.ORACLE:
+        code_variance_factor = np.square(
+            np.maximum(0.05, np.asarray(inputs.actual_jitter_multiplier))
+        )
+    else:
+        raise ValueError(f"unsupported sigma method: {method}")
+
+    return np.sqrt(
+        ura * ura
+        + elevation * elevation
+        + code * code * code_variance_factor
+    )
+
+
+def ecef_to_lla(ecef_m: np.ndarray) -> tuple[float, float, float]:
+    x, y, z = np.asarray(ecef_m, dtype=float)
+    a = 6_378_137.0
+    inverse_flattening = 298.257223563
+    flattening = 1.0 / inverse_flattening
+    eccentricity_squared = flattening * (2.0 - flattening)
+    longitude = np.arctan2(y, x)
+    horizontal = np.hypot(x, y)
+    latitude = np.arctan2(
+        z,
+        horizontal * (1.0 - eccentricity_squared),
+    )
+    height = 0.0
+    for _ in range(12):
+        sine = np.sin(latitude)
+        prime_vertical = a / np.sqrt(1.0 - eccentricity_squared * sine * sine)
+        height = horizontal / max(np.cos(latitude), 1.0e-15) - prime_vertical
+        next_latitude = np.arctan2(
+            z,
+            horizontal
+            * (
+                1.0
+                - eccentricity_squared
+                * prime_vertical
+                / max(prime_vertical + height, 1.0)
+            ),
+        )
+        if abs(next_latitude - latitude) < 1.0e-14:
+            latitude = next_latitude
+            break
+        latitude = next_latitude
+    return (
+        float(np.rad2deg(latitude)),
+        float(np.rad2deg(longitude)),
+        float(height),
+    )
+
+
+def lla_to_ecef(latitude_deg: float, longitude_deg: float, height_m: float) -> np.ndarray:
+    a = 6_378_137.0
+    inverse_flattening = 298.257223563
+    flattening = 1.0 / inverse_flattening
+    eccentricity_squared = flattening * (2.0 - flattening)
+    latitude = np.deg2rad(latitude_deg)
+    longitude = np.deg2rad(longitude_deg)
+    sine = np.sin(latitude)
+    cosine = np.cos(latitude)
+    prime_vertical = a / np.sqrt(1.0 - eccentricity_squared * sine * sine)
+    return np.asarray(
+        [
+            (prime_vertical + height_m) * cosine * np.cos(longitude),
+            (prime_vertical + height_m) * cosine * np.sin(longitude),
+            (
+                prime_vertical * (1.0 - eccentricity_squared)
+                + height_m
+            )
+            * sine,
+        ],
+        dtype=float,
+    )
+
+
+def enu_axes(receiver_ecef_m: np.ndarray) -> np.ndarray:
+    latitude_deg, longitude_deg, _ = ecef_to_lla(receiver_ecef_m)
+    latitude = np.deg2rad(latitude_deg)
+    longitude = np.deg2rad(longitude_deg)
+    east = np.asarray([-np.sin(longitude), np.cos(longitude), 0.0])
+    north = np.asarray(
+        [
+            -np.sin(latitude) * np.cos(longitude),
+            -np.sin(latitude) * np.sin(longitude),
+            np.cos(latitude),
+        ]
+    )
+    up = np.asarray(
+        [
+            np.cos(latitude) * np.cos(longitude),
+            np.cos(latitude) * np.sin(longitude),
+            np.sin(latitude),
+        ]
+    )
+    return np.vstack([east, north, up])
+
+
+def satellites_from_azel(
+    receiver_ecef_m: np.ndarray,
+    azimuth_deg: np.ndarray,
+    elevation_deg: np.ndarray,
+    range_m: float = 21_000_000.0,
+) -> np.ndarray:
+    axes = enu_axes(receiver_ecef_m)
+    satellites: list[np.ndarray] = []
+    for azimuth, elevation in zip(azimuth_deg, elevation_deg):
+        azimuth_rad = np.deg2rad(azimuth)
+        elevation_rad = np.deg2rad(elevation)
+        los_enu = np.asarray(
+            [
+                np.cos(elevation_rad) * np.sin(azimuth_rad),
+                np.cos(elevation_rad) * np.cos(azimuth_rad),
+                np.sin(elevation_rad),
+            ]
+        )
+        los_ecef = axes.T @ los_enu
+        satellites.append(receiver_ecef_m + range_m * los_ecef)
+    return np.asarray(satellites)
+
+
+def position_error_enu_m(
+    estimated_ecef_m: np.ndarray,
+    true_ecef_m: np.ndarray,
+) -> np.ndarray:
+    return enu_axes(true_ecef_m) @ (estimated_ecef_m - true_ecef_m)
+
+
+def _candidate(
+    satellite_positions_m: np.ndarray,
+    observations_m: np.ndarray,
+    sigma_m: np.ndarray,
+    initial_state: np.ndarray,
+    used_indices: np.ndarray,
+) -> WlsSolution:
+    state = np.asarray(initial_state, dtype=float).copy()
+    weights = 1.0 / np.square(sigma_m)
+    design = np.empty((len(observations_m), 4), dtype=float)
+
+    for _ in range(10):
+        difference = satellite_positions_m - state[:3]
+        geometric_range = np.linalg.norm(difference, axis=1)
+        design[:, :3] = -difference / geometric_range[:, None]
+        design[:, 3] = 1.0
+        residual = observations_m - geometric_range - state[3]
+        normal = design.T @ (weights[:, None] * design)
+        rhs = design.T @ (weights * residual)
+        update = np.linalg.solve(normal, rhs)
+        state += update
+        if np.linalg.norm(update) < 1.0e-4:
+            break
+
+    difference = satellite_positions_m - state[:3]
+    geometric_range = np.linalg.norm(difference, axis=1)
+    design[:, :3] = -difference / geometric_range[:, None]
+    design[:, 3] = 1.0
+    residual = observations_m - geometric_range - state[3]
+    normal = design.T @ (weights[:, None] * design)
+    covariance = np.linalg.inv(normal)
+    chi_square = float(np.sum(weights * np.square(residual)))
+    degrees_of_freedom = len(observations_m) - 4
+    threshold = (
+        float(CHI_SQUARE_99[degrees_of_freedom])
+        if 0 < degrees_of_freedom < len(CHI_SQUARE_99)
+        else 0.0
+    )
+    chi_square_pass = degrees_of_freedom > 0 and chi_square <= threshold
+    valid = (
+        (len(observations_m) == 4 and degrees_of_freedom == 0)
+        or chi_square_pass
+    )
+    ratio = chi_square / threshold if threshold > 0.0 else float("inf")
+    return WlsSolution(
+        position_ecef_m=state[:3].copy(),
+        clock_bias_m=float(state[3]),
+        residual_m=residual.copy(),
+        sigma_m=sigma_m.copy(),
+        covariance=covariance,
+        chi_square=chi_square,
+        chi_square_ratio=ratio,
+        chi_square_pass=chi_square_pass,
+        valid=valid,
+        used_indices=used_indices.copy(),
+        excluded_index=None,
+    )
+
+
+def firmware_wls(
+    satellite_positions_m: np.ndarray,
+    observations_m: np.ndarray,
+    sigma_m: np.ndarray,
+    initial_state: np.ndarray,
+    *,
+    enable_fde: bool = True,
+) -> WlsSolution:
+    count = len(observations_m)
+    if count < 4:
+        raise ValueError("position WLS needs at least four satellites")
+    full_indices = np.arange(count, dtype=int)
+    full = _candidate(
+        satellite_positions_m,
+        observations_m,
+        sigma_m,
+        initial_state,
+        full_indices,
+    )
+    if full.chi_square_pass or not enable_fde or count < 7:
+        return full
+
+    selected = full
+    passing_found = False
+    full_state = np.concatenate([full.position_ecef_m, [full.clock_bias_m]])
+    for excluded in range(count):
+        used = full_indices[full_indices != excluded]
+        candidate = _candidate(
+            satellite_positions_m[used],
+            observations_m[used],
+            sigma_m[used],
+            full_state,
+            used,
+        )
+        candidate = WlsSolution(
+            **{
+                **candidate.__dict__,
+                "excluded_index": excluded,
+            }
+        )
+        if candidate.chi_square_pass:
+            if not passing_found or candidate.chi_square_ratio < selected.chi_square_ratio:
+                selected = candidate
+            passing_found = True
+        elif not passing_found and candidate.chi_square_ratio < selected.chi_square_ratio:
+            selected = candidate
+    return selected
diff --git a/soc/software/gps_measurement_python/measurement_scenarios.py b/soc/software/gps_measurement_python/measurement_scenarios.py
new file mode 100644
index 0000000..706740f
--- /dev/null
+++ b/soc/software/gps_measurement_python/measurement_scenarios.py
@@ -0,0 +1,368 @@
+"""Synthetic code-tracking scenarios shared by the analysis and tests."""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Callable
+
+import numpy as np
+
+from .firmware_wls_model import (
+    SigmaInputs,
+    SigmaMethod,
+    URA_SIGMA_M,
+    cn0_code_sigma_m,
+    elevation_sigma_m,
+    enu_axes,
+    firmware_sigma_m,
+    firmware_wls,
+    lla_to_ecef,
+    position_error_enu_m,
+    satellites_from_azel,
+)
+from .rtl_dll_model import expected_discriminator_std, synthesize_dll_window
+
+
+TRACKING_PERIOD_S = 0.020
+WLS_PERIOD_S = 0.200
+TRACKING_UPDATES_PER_WLS = int(round(WLS_PERIOD_S / TRACKING_PERIOD_S))
+FIRMWARE_CN0_ALPHA = 0.20
+DLL_RATIO_ALPHA = 0.10
+DLL_MEAN_ALPHA = 0.20
+
+GOOD_AZIMUTH_DEG = np.asarray([8.0, 55.0, 104.0, 151.0, 205.0, 253.0, 301.0, 342.0])
+GOOD_ELEVATION_DEG = np.asarray([73.0, 48.0, 31.0, 18.0, 64.0, 39.0, 24.0, 14.0])
+POOR_AZIMUTH_DEG = np.asarray([25.0, 46.0, 68.0, 89.0, 112.0, 136.0, 159.0, 182.0])
+POOR_ELEVATION_DEG = np.asarray([18.0, 22.0, 25.0, 29.0, 32.0, 27.0, 21.0, 16.0])
+
+
+Profile = Callable[[float, int, float], float]
+
+
+def _identity(_time_s: float, _satellite: int, baseline: float) -> float:
+    return baseline
+
+
+def _one(_time_s: float, _satellite: int, _baseline: float) -> float:
+    return 1.0
+
+
+def _zero(_time_s: float, _satellite: int, _baseline: float) -> float:
+    return 0.0
+
+
+@dataclass(frozen=True)
+class Scenario:
+    name: str
+    description: str
+    duration_s: float = 80.0
+    poor_geometry: bool = False
+    cn0_profile: Profile = _identity
+    jitter_profile: Profile = _one
+    discriminator_bias_profile: Profile = _zero
+    pseudorange_bias_profile: Profile = _zero
+
+
+@dataclass
+class ChannelQuality:
+    cn0_dbhz: float | None = None
+    dll_ratio: float = 1.0
+    dll_mean_z: float = 0.0
+
+    def update(
+        self,
+        raw_cn0_dbhz: float,
+        dll_samples: np.ndarray,
+    ) -> None:
+        if self.cn0_dbhz is None:
+            self.cn0_dbhz = raw_cn0_dbhz
+        else:
+            self.cn0_dbhz = (
+                FIRMWARE_CN0_ALPHA * raw_cn0_dbhz
+                + (1.0 - FIRMWARE_CN0_ALPHA) * self.cn0_dbhz
+            )
+
+        measured_variance = float(np.var(dll_samples, ddof=1))
+        expected_std = expected_discriminator_std(self.cn0_dbhz)
+        raw_ratio = measured_variance / max(expected_std * expected_std, 1.0e-15)
+        raw_ratio = float(np.clip(raw_ratio, 0.05, 25.0))
+        self.dll_ratio = (
+            DLL_RATIO_ALPHA * raw_ratio
+            + (1.0 - DLL_RATIO_ALPHA) * self.dll_ratio
+        )
+
+        standard_error = np.sqrt(
+            max(measured_variance, expected_std * expected_std)
+            / len(dll_samples)
+        )
+        raw_mean_z = abs(float(np.mean(dll_samples))) / max(standard_error, 1.0e-12)
+        raw_mean_z = float(np.clip(raw_mean_z, 0.0, 12.0))
+        self.dll_mean_z = (
+            DLL_MEAN_ALPHA * raw_mean_z
+            + (1.0 - DLL_MEAN_ALPHA) * self.dll_mean_z
+        )
+
+
+@dataclass(frozen=True)
+class EpochSample:
+    method: SigmaMethod
+    time_s: float
+    enu_error_m: np.ndarray
+    horizontal_error_m: float
+    position_error_3d_m: float
+    horizontal_sigma_m: float
+    valid: bool
+    chi_square_ratio: float
+    fde_applied: bool
+    mean_measurement_sigma_m: float
+    maximum_dll_ratio: float
+
+
+def scenario_matrix() -> tuple[Scenario, ...]:
+    return (
+        Scenario(
+            "clean_open_sky",
+            "C/N0 model and actual DLL jitter agree.",
+        ),
+        Scenario(
+            "weak_signal",
+            "All channels lose 11 dB; current C/N0 weighting already sees it.",
+            cn0_profile=lambda _t, _s, baseline: baseline - 11.0,
+        ),
+        Scenario(
+            "one_channel_hidden_jitter",
+            "One high-C/N0 channel has 4x DLL jitter not visible in C/N0.",
+            jitter_profile=lambda _t, satellite, _b: 4.0 if satellite == 1 else 1.0,
+        ),
+        Scenario(
+            "common_hidden_jitter",
+            "All channels have the same unmodelled 3x DLL jitter.",
+            jitter_profile=lambda _t, _satellite, _b: 3.0,
+        ),
+        Scenario(
+            "noise_burst_recovery",
+            "Two channels have 5x jitter from 22 s to 45 s, then recover.",
+            jitter_profile=lambda time_s, satellite, _b: (
+                5.0
+                if 22.0 <= time_s < 45.0 and satellite in (1, 5)
+                else 1.0
+            ),
+        ),
+        Scenario(
+            "dll_transient_stress",
+            "A channel has discriminator mean without excess variance during transient stress.",
+            discriminator_bias_profile=lambda time_s, satellite, _b: (
+                0.055
+                if 25.0 <= time_s < 34.0 and satellite == 3
+                else 0.0
+            ),
+            pseudorange_bias_profile=lambda time_s, satellite, _b: (
+                9.0
+                if 25.0 <= time_s < 34.0 and satellite == 3
+                else 0.0
+            ),
+        ),
+        Scenario(
+            "stable_multipath_bias",
+            "Low-jitter, high-C/N0 channel has a stable 14 m code bias.",
+            pseudorange_bias_profile=lambda _t, satellite, _b: (
+                14.0 if satellite == 6 else 0.0
+            ),
+        ),
+        Scenario(
+            "mixed_multipath",
+            "One channel has both a 10 m bias and 3x excess jitter.",
+            jitter_profile=lambda _t, satellite, _b: 3.0 if satellite == 2 else 1.0,
+            pseudorange_bias_profile=lambda _t, satellite, _b: (
+                10.0 if satellite == 2 else 0.0
+            ),
+        ),
+        Scenario(
+            "poor_geometry_hidden_jitter",
+            "Clustered geometry plus one channel with unmodelled 4x jitter.",
+            poor_geometry=True,
+            jitter_profile=lambda _t, satellite, _b: 4.0 if satellite == 4 else 1.0,
+        ),
+        Scenario(
+            "cn0_step_recovery",
+            "C/N0 is initially weak and improves; no hidden DLL noise exists.",
+            cn0_profile=lambda time_s, _satellite, baseline: (
+                baseline - 12.0 if time_s < 30.0 else baseline
+            ),
+        ),
+    )
+
+
+def _geometry(scenario: Scenario) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+    receiver = lla_to_ecef(39.9208, 32.8541, 930.0)
+    if scenario.poor_geometry:
+        azimuth = POOR_AZIMUTH_DEG
+        elevation = POOR_ELEVATION_DEG
+    else:
+        azimuth = GOOD_AZIMUTH_DEG
+        elevation = GOOD_ELEVATION_DEG
+    satellites = satellites_from_azel(receiver, azimuth, elevation)
+    return receiver, satellites, elevation.copy()
+
+
+def run_scenario(
+    scenario: Scenario,
+    seed: int,
+    methods: tuple[SigmaMethod, ...] = tuple(SigmaMethod),
+) -> list[EpochSample]:
+    rng = np.random.default_rng(seed)
+    receiver, satellites, elevations = _geometry(scenario)
+    satellite_count = len(satellites)
+    geometric_ranges = np.linalg.norm(satellites - receiver, axis=1)
+    baseline_cn0 = np.clip(34.0 + 0.16 * elevations, 30.0, 48.0)
+    ura_indices = np.zeros(satellite_count, dtype=np.uint8)
+    quality = [ChannelQuality() for _ in range(satellite_count)]
+
+    # These are deliberately slower/non-DLL terms.  They prevent a synthetic
+    # white-noise-only experiment from overstating what DLL weighting can fix.
+    ura_error = rng.normal(0.0, 0.45 * URA_SIGMA_M[0], satellite_count)
+    atmospheric_state = rng.normal(
+        0.0,
+        0.35 * elevation_sigma_m(elevations),
+        satellite_count,
+    )
+    code_noise_state = np.zeros(satellite_count)
+    initial_state = np.concatenate(
+        [
+            receiver + np.asarray([450.0, -300.0, 220.0]),
+            [0.0],
+        ]
+    )
+    method_state = {method: initial_state.copy() for method in methods}
+    samples: list[EpochSample] = []
+    clock_bias_m = 82.0
+    receiver_enu_axes = enu_axes(receiver)
+
+    tracking_steps = int(round(scenario.duration_s / TRACKING_PERIOD_S))
+    latest_actual_jitter = np.ones(satellite_count)
+    for tracking_step in range(tracking_steps):
+        time_s = tracking_step * TRACKING_PERIOD_S
+        for satellite in range(satellite_count):
+            true_cn0 = scenario.cn0_profile(
+                time_s,
+                satellite,
+                float(baseline_cn0[satellite]),
+            )
+            actual_jitter = scenario.jitter_profile(
+                time_s,
+                satellite,
+                1.0,
+            )
+            discriminator_bias = scenario.discriminator_bias_profile(
+                time_s,
+                satellite,
+                0.0,
+            )
+            latest_actual_jitter[satellite] = actual_jitter
+            dll_window = synthesize_dll_window(
+                rng,
+                cn0_dbhz=true_cn0,
+                jitter_multiplier=actual_jitter,
+                discriminator_bias=discriminator_bias,
+            )
+            # The hardware NWPR C/N0 estimate is noisy; firmware applies alpha=0.2.
+            raw_cn0 = float(np.clip(true_cn0 + rng.normal(0.0, 1.3), 10.0, 60.0))
+            quality[satellite].update(raw_cn0, dll_window.samples)
+
+        if (tracking_step + 1) % TRACKING_UPDATES_PER_WLS != 0:
+            continue
+
+        true_cn0 = np.asarray(
+            [
+                scenario.cn0_profile(
+                    time_s,
+                    satellite,
+                    float(baseline_cn0[satellite]),
+                )
+                for satellite in range(satellite_count)
+            ]
+        )
+        actual_code_sigma = cn0_code_sigma_m(true_cn0) * latest_actual_jitter
+        innovation = rng.normal(0.0, actual_code_sigma)
+        code_noise_state = (
+            0.25 * code_noise_state
+            + np.sqrt(1.0 - 0.25**2) * innovation
+        )
+        atmospheric_innovation = rng.normal(
+            0.0,
+            0.35 * elevation_sigma_m(elevations),
+        )
+        atmospheric_state = (
+            0.97 * atmospheric_state
+            + np.sqrt(1.0 - 0.97**2) * atmospheric_innovation
+        )
+        pseudorange_bias = np.asarray(
+            [
+                scenario.pseudorange_bias_profile(
+                    time_s,
+                    satellite,
+                    0.0,
+                )
+                for satellite in range(satellite_count)
+            ]
+        )
+        observations = (
+            geometric_ranges
+            + clock_bias_m
+            + ura_error
+            + atmospheric_state
+            + code_noise_state
+            + pseudorange_bias
+        )
+        sigma_inputs = SigmaInputs(
+            ura_index=ura_indices,
+            elevation_deg=elevations,
+            cn0_dbhz=np.asarray([item.cn0_dbhz for item in quality], dtype=float),
+            dll_variance_ratio=np.asarray([item.dll_ratio for item in quality]),
+            dll_mean_z=np.asarray([item.dll_mean_z for item in quality]),
+            actual_jitter_multiplier=latest_actual_jitter.copy(),
+        )
+
+        for method in methods:
+            sigma = firmware_sigma_m(sigma_inputs, method)
+            solution = firmware_wls(
+                satellites,
+                observations,
+                sigma,
+                method_state[method],
+            )
+            # NavEquations.c updates its persistent WLS seed only after an
+            # integrity-valid solution.
+            if solution.valid:
+                method_state[method] = np.concatenate(
+                    [solution.position_ecef_m, [solution.clock_bias_m]]
+                )
+            enu_error = position_error_enu_m(solution.position_ecef_m, receiver)
+            enu_covariance = (
+                # The top-left block is ECEF position covariance.
+                # R * Q * R' maps it to ENU.
+                receiver_enu_axes
+                @ solution.covariance[:3, :3]
+                @ receiver_enu_axes.T
+            )
+            horizontal_sigma = float(
+                np.sqrt(max(0.0, enu_covariance[0, 0] + enu_covariance[1, 1]))
+            )
+            samples.append(
+                EpochSample(
+                    method=method,
+                    time_s=time_s,
+                    enu_error_m=enu_error,
+                    horizontal_error_m=float(np.linalg.norm(enu_error[:2])),
+                    position_error_3d_m=float(np.linalg.norm(enu_error)),
+                    horizontal_sigma_m=horizontal_sigma,
+                    valid=solution.valid,
+                    chi_square_ratio=solution.chi_square_ratio,
+                    fde_applied=solution.excluded_index is not None,
+                    mean_measurement_sigma_m=float(np.mean(sigma)),
+                    maximum_dll_ratio=float(
+                        max(item.dll_ratio for item in quality)
+                    ),
+                )
+            )
+    return samples
diff --git a/soc/software/gps_measurement_python/output/01_position_3d_rms.png b/soc/software/gps_measurement_python/output/01_position_3d_rms.png
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diff --git a/soc/software/gps_measurement_python/output/ANALYSIS.md b/soc/software/gps_measurement_python/output/ANALYSIS.md
new file mode 100644
index 0000000..57ff813
--- /dev/null
+++ b/soc/software/gps_measurement_python/output/ANALYSIS.md
@@ -0,0 +1,94 @@
+# GPS code measurement model sonuçları
+
+Monte Carlo seed sayısı: `12`. İlk 5 saniye metriklere alınmadı.
+
+## Yöntem karşılaştırması
+
+| Senaryo | Yöntem | 3D RMS (m) | Mevcuda göre | P95 (m) | Valid (%) | >25 m false-valid (%) |
+|---|---|---:|---:|---:|---:|---:|
+| clean_open_sky | Mevcut C/N0 | 10.05 | +0.0% | 17.35 | 100.0 | 0.31 |
+| clean_open_sky | Naif DLL ekle | 10.02 | +0.3% | 17.25 | 100.0 | 0.31 |
+| clean_open_sky | DLL excess | 10.05 | +0.0% | 17.32 | 100.0 | 0.33 |
+| clean_open_sky | DLL excess+mean | 10.05 | +0.0% | 17.32 | 100.0 | 0.33 |
+| clean_open_sky | Oracle variance | 10.05 | +0.0% | 17.35 | 100.0 | 0.31 |
+| weak_signal | Mevcut C/N0 | 32.73 | +0.0% | 56.44 | 100.0 | 56.31 |
+| weak_signal | Naif DLL ekle | 32.31 | +1.3% | 55.46 | 100.0 | 56.18 |
+| weak_signal | DLL excess | 32.65 | +0.3% | 56.12 | 100.0 | 56.22 |
+| weak_signal | DLL excess+mean | 32.65 | +0.3% | 56.12 | 100.0 | 56.22 |
+| weak_signal | Oracle variance | 32.73 | +0.0% | 56.44 | 100.0 | 56.31 |
+| one_channel_hidden_jitter | Mevcut C/N0 | 12.27 | +0.0% | 19.94 | 100.0 | 1.07 |
+| one_channel_hidden_jitter | Naif DLL ekle | 10.49 | +14.5% | 17.75 | 100.0 | 0.33 |
+| one_channel_hidden_jitter | DLL excess | 10.47 | +14.7% | 17.68 | 100.0 | 0.33 |
+| one_channel_hidden_jitter | DLL excess+mean | 10.47 | +14.7% | 17.68 | 100.0 | 0.33 |
+| one_channel_hidden_jitter | Oracle variance | 10.46 | +14.7% | 17.74 | 100.0 | 0.33 |
+| common_hidden_jitter | Mevcut C/N0 | 33.79 | +0.0% | 59.76 | 94.8 | 52.40 |
+| common_hidden_jitter | Naif DLL ekle | 27.61 | +18.3% | 47.56 | 100.0 | 43.93 |
+| common_hidden_jitter | DLL excess | 27.69 | +18.1% | 47.83 | 100.0 | 43.89 |
+| common_hidden_jitter | DLL excess+mean | 27.69 | +18.1% | 47.83 | 100.0 | 43.89 |
+| common_hidden_jitter | Oracle variance | 27.74 | +17.9% | 47.83 | 100.0 | 43.87 |
+| noise_burst_recovery | Mevcut C/N0 | 12.96 | +0.0% | 22.13 | 98.9 | 2.58 |
+| noise_burst_recovery | Naif DLL ekle | 10.52 | +18.8% | 18.03 | 100.0 | 0.53 |
+| noise_burst_recovery | DLL excess | 10.49 | +19.0% | 18.00 | 100.0 | 0.49 |
+| noise_burst_recovery | DLL excess+mean | 10.49 | +19.0% | 18.00 | 100.0 | 0.49 |
+| noise_burst_recovery | Oracle variance | 10.47 | +19.2% | 17.90 | 100.0 | 0.49 |
+| dll_transient_stress | Mevcut C/N0 | 10.15 | +0.0% | 17.43 | 100.0 | 0.36 |
+| dll_transient_stress | Naif DLL ekle | 10.12 | +0.3% | 17.33 | 100.0 | 0.38 |
+| dll_transient_stress | DLL excess | 10.14 | +0.0% | 17.38 | 100.0 | 0.38 |
+| dll_transient_stress | DLL excess+mean | 10.12 | +0.2% | 17.37 | 100.0 | 0.33 |
+| dll_transient_stress | Oracle variance | 10.15 | +0.0% | 17.43 | 100.0 | 0.36 |
+| stable_multipath_bias | Mevcut C/N0 | 12.55 | +0.0% | 21.00 | 100.0 | 1.67 |
+| stable_multipath_bias | Naif DLL ekle | 12.39 | +1.3% | 20.87 | 100.0 | 1.47 |
+| stable_multipath_bias | DLL excess | 12.54 | +0.1% | 21.02 | 100.0 | 1.64 |
+| stable_multipath_bias | DLL excess+mean | 12.54 | +0.1% | 21.02 | 100.0 | 1.64 |
+| stable_multipath_bias | Oracle variance | 12.55 | +0.0% | 21.00 | 100.0 | 1.67 |
+| mixed_multipath | Mevcut C/N0 | 14.43 | +0.0% | 25.38 | 100.0 | 5.64 |
+| mixed_multipath | Naif DLL ekle | 11.26 | +22.0% | 19.60 | 100.0 | 0.73 |
+| mixed_multipath | DLL excess | 11.07 | +23.3% | 19.23 | 100.0 | 0.73 |
+| mixed_multipath | DLL excess+mean | 11.07 | +23.3% | 19.23 | 100.0 | 0.73 |
+| mixed_multipath | Oracle variance | 11.06 | +23.4% | 19.20 | 100.0 | 0.73 |
+| poor_geometry_hidden_jitter | Mevcut C/N0 | 293.82 | +0.0% | 574.96 | 100.0 | 94.31 |
+| poor_geometry_hidden_jitter | Naif DLL ekle | 206.13 | +29.8% | 405.15 | 100.0 | 92.42 |
+| poor_geometry_hidden_jitter | DLL excess | 196.87 | +33.0% | 390.64 | 100.0 | 91.40 |
+| poor_geometry_hidden_jitter | DLL excess+mean | 196.87 | +33.0% | 390.64 | 100.0 | 91.40 |
+| poor_geometry_hidden_jitter | Oracle variance | 196.20 | +33.2% | 386.58 | 100.0 | 91.27 |
+| cn0_step_recovery | Mevcut C/N0 | 22.59 | +0.0% | 47.95 | 100.0 | 21.62 |
+| cn0_step_recovery | Naif DLL ekle | 22.27 | +1.4% | 47.59 | 100.0 | 21.42 |
+| cn0_step_recovery | DLL excess | 22.59 | -0.0% | 47.91 | 100.0 | 21.49 |
+| cn0_step_recovery | DLL excess+mean | 22.59 | -0.0% | 47.91 | 100.0 | 21.49 |
+| cn0_step_recovery | Oracle variance | 22.59 | +0.0% | 47.95 | 100.0 | 21.62 |
+
+## Modelden çıkan karar özeti
+
+- C/N0 ile uyumlu nominal DLL jitter'da `dll_excess`, mevcut çözümü değiştirmemelidir.
+- Bütün measurement sigmaları aynı sabitle çarpılırsa WLS konum noktası değişmez; yalnız covariance/integrity değişir. Fakat ortak DLL jitter çarpanı, C/N0/elevation bileşimi kanaldan kanala farklı olduğu için toplam sigmaları eşit oranda büyütmez.
+- Kanal-bağımlı ve C/N0'da görünmeyen excess jitter varsa dinamik sigma o kanalı down-weight ederek konumu iyileştirebilir.
+- Stable multipath bias düşük DLL variance bırakabildiği için variance-only yöntem çözüm değildir.
+- 50 Hz'de DLL ratio alpha=0.10 yaklaşık 0.19 s zaman sabiti ve 0.57 s yüzde-95 geçiş verir.
+- Aşağıdaki yüzdeler seçilen sentetik hata büyüklüklerine koşulludur; kart için kazanç tahmini değildir.
+
+## Bozulma penceresi odaklı 3D RMS
+
+| Senaryo/pencere | Mevcut (m) | DLL excess (m) | DLL excess+mean (m) | Oracle variance (m) |
+|---|---:|---:|---:|---:|
+| noise_burst_recovery [22,45) s | 17.83 | 11.36 | 11.36 | 11.30 |
+| dll_transient_stress [25,34) s | 10.83 | 10.82 | 10.65 | 10.83 |
+| cn0_step_recovery [5,30) s | 36.48 | 36.48 | 36.48 | 36.48 |
+
+## Code smoothing ve carrier CFO
+
+| Carrier-rate koşulu | Ham RMSE (m) | Kör IIR RMSE (m) | Raw Doppler RMSE (m) | FW-IIR Doppler RMSE (m) | Kör IIR peak (m) | Raw Doppler peak (m) | FW-IIR Doppler peak (m) |
+|---|---:|---:|---:|---:|---:|---:|---:|
+| cfo_compensated | 3.99 | 248.61 | 0.94 | 16.42 | 414.08 | 2.05 | 84.13 |
+| cfo_residual_0p5_mps | 3.99 | 248.61 | 1.30 | 16.41 | 414.08 | 2.57 | 83.23 |
+| cfo_residual_3_mps | 3.99 | 248.61 | 5.48 | 17.06 | 414.08 | 7.07 | 78.73 |
+
+## Yorum sınırları
+
+- `current_cn0`, firmware'deki URA/elevation/C/N0 sigma modelidir.
+- `naive_add_dll`, aynı thermal jitter'ı iki kere saymanın negatif kontrolüdür.
+- `dll_excess`, yalnız ölçülen DLL variance'ın C/N0 beklentisini aşan kısmını code variance'a ekler.
+- `dll_excess_guard`, variance'a ek olarak sürekli discriminator mean stress'ini kullanır.
+- `oracle_variance`, sentetik gerçek jitter çarpanını bilir; yalnız variance kaynakları için erişilebilir üst sınırdır, bias'ı bilmez.
+- Stable multipath DLL'nin yeni denge noktasında düşük residual variance bırakabilir. Bu nedenle variance-only yönteminin onu çözmesi beklenmez.
+- Discriminator gürültü ölçeği kart correlator kayıtları gelene kadar kalibrasyon varsayımıdır; oran tabanlı yöntem mutlak ölçeğe göre daha az hassastır.
+- Sonuçlar bitstream veya firmware değişikliği değildir; karar öncesi executable tasarım keşfidir.
diff --git a/soc/software/gps_measurement_python/output/DOPPLER_ESKF_ANALYSIS.md b/soc/software/gps_measurement_python/output/DOPPLER_ESKF_ANALYSIS.md
new file mode 100644
index 0000000..55df3c4
--- /dev/null
+++ b/soc/software/gps_measurement_python/output/DOPPLER_ESKF_ANALYSIS.md
@@ -0,0 +1,65 @@
+# Doppler WLS -> ESKF model sonuçları
+
+Monte Carlo seed sayısı: `20`; ilk 5 saniye RMS metriklerinden çıkarıldı.
+50 Hz tracking, önceki `alpha=0.05` Doppler IIR, 5 Hz dört-state velocity WLS, fusion adapter'ın `2/2/3 m/s` ENU sigma tabanları, TDK profiliyle 100 Hz IMU propagation ve 3-DOF `%99.9` NIS kapısı modellenmiştir.
+
+## Sonuç tablosu
+
+| Senaryo | Yol | ESKF RMS (m/s) | Dynamic RMS | WLS RMS | Accept (%) | 95% cov. (%) | Exclude (%) |
+|---|---|---:|---:|---:|---:|---:|---:|
+| steady_cruise | Önceki sabit IIR | 0.182 | - | 0.068 | 100.0 | 100.0 | 0.0 |
+| steady_cruise | Ham Doppler + ESKF | 0.190 | - | 0.416 | 100.0 | 100.0 | 0.0 |
+| steady_cruise | Adaptif IIR + ESKF | 0.182 | - | 0.068 | 100.0 | 100.0 | 0.0 |
+| steady_cruise | Ham + robust WLS + ESKF | 0.190 | - | 0.416 | 100.0 | 100.0 | 0.0 |
+| airliner_maneuver | Önceki sabit IIR | 0.416 | 0.438 | 0.440 | 100.0 | 99.7 | 0.0 |
+| airliner_maneuver | Ham Doppler + ESKF | 0.190 | 0.179 | 0.416 | 100.0 | 100.0 | 0.0 |
+| airliner_maneuver | Adaptif IIR + ESKF | 0.194 | 0.189 | 0.135 | 100.0 | 100.0 | 0.0 |
+| airliner_maneuver | Ham + robust WLS + ESKF | 0.190 | 0.179 | 0.416 | 100.0 | 100.0 | 0.0 |
+| aggressive_maneuver | Önceki sabit IIR | 0.942 | 0.919 | 1.178 | 100.0 | 55.9 | 0.0 |
+| aggressive_maneuver | Ham Doppler + ESKF | 0.190 | 0.186 | 0.416 | 100.0 | 100.0 | 0.0 |
+| aggressive_maneuver | Adaptif IIR + ESKF | 0.200 | 0.197 | 0.171 | 100.0 | 100.0 | 0.0 |
+| aggressive_maneuver | Ham + robust WLS + ESKF | 0.190 | 0.186 | 0.416 | 100.0 | 100.0 | 0.0 |
+| low_cn0_airliner | Önceki sabit IIR | 0.419 | 0.443 | 0.485 | 100.0 | 99.7 | 0.0 |
+| low_cn0_airliner | Ham Doppler + ESKF | 0.251 | 0.242 | 1.317 | 100.0 | 100.0 | 0.0 |
+| low_cn0_airliner | Adaptif IIR + ESKF | 0.206 | 0.203 | 0.338 | 100.0 | 100.0 | 0.0 |
+| low_cn0_airliner | Ham + robust WLS + ESKF | 0.251 | 0.242 | 1.317 | 100.0 | 100.0 | 0.0 |
+| single_satellite_outliers | Önceki sabit IIR | 0.495 | 0.478 | 1.146 | 100.0 | 97.7 | 0.0 |
+| single_satellite_outliers | Ham Doppler + ESKF | 0.257 | 0.229 | 1.451 | 100.0 | 100.0 | 0.0 |
+| single_satellite_outliers | Adaptif IIR + ESKF | 0.356 | 0.312 | 1.154 | 100.0 | 100.0 | 0.0 |
+| single_satellite_outliers | Ham + robust WLS + ESKF | 0.191 | 0.179 | 0.418 | 100.0 | 100.0 | 2.9 |
+| clock_drift_steps | Önceki sabit IIR | 0.416 | 0.438 | 0.440 | 100.0 | 99.7 | 0.0 |
+| clock_drift_steps | Ham Doppler + ESKF | 0.190 | 0.179 | 0.416 | 100.0 | 100.0 | 0.0 |
+| clock_drift_steps | Adaptif IIR + ESKF | 0.194 | 0.189 | 0.135 | 100.0 | 100.0 | 0.0 |
+| clock_drift_steps | Ham + robust WLS + ESKF | 0.190 | 0.179 | 0.416 | 100.0 | 100.0 | 0.0 |
+| gps_gap_recovery | Önceki sabit IIR | 0.397 | 0.413 | 0.431 | 100.0 | 99.9 | 0.0 |
+| gps_gap_recovery | Ham Doppler + ESKF | 0.208 | 0.192 | 0.417 | 100.0 | 100.0 | 0.0 |
+| gps_gap_recovery | Adaptif IIR + ESKF | 0.208 | 0.197 | 0.129 | 100.0 | 100.0 | 0.0 |
+| gps_gap_recovery | Ham + robust WLS + ESKF | 0.208 | 0.192 | 0.417 | 100.0 | 100.0 | 0.0 |
+| mixed_flight_faults | Önceki sabit IIR | 0.940 | 0.913 | 1.515 | 100.0 | 60.4 | 0.0 |
+| mixed_flight_faults | Ham Doppler + ESKF | 0.224 | 0.209 | 1.498 | 100.0 | 100.0 | 0.0 |
+| mixed_flight_faults | Adaptif IIR + ESKF | 0.295 | 0.275 | 0.838 | 100.0 | 99.9 | 0.0 |
+| mixed_flight_faults | Ham + robust WLS + ESKF | 0.221 | 0.206 | 1.013 | 100.0 | 100.0 | 1.9 |
+
+## Bulgular
+
+- Sabit hızda pre-IIR ESKF RMS'i `0.182` m/s, ham yol `0.190` m/s. Yani pre-IIR sakin durumda daha düzgün çıktı veriyor; ESKF ham gürültüyü zaten `0.416` m/s WLS RMS'ten bu seviyeye indiriyor.
+- Airliner manevrasında sabit IIR `0.416` m/s ve `%0.0` NIS ret oranı verirken ham yol `0.190` m/s ve `%0.0` ret verdi. Konservatif adapter tabanları rejection'ı sınırlasa bile covariance'ın temsil etmediği IIR gecikmesi fused velocity'de dinamik hata bırakır.
+- Düşük C/N0 manevrasında sabit/ham/adaptif RMS sırasıyla `0.419`, `0.251`, `0.206` m/s oldu. Adaptif yol bu sentetik koşulda gürültü/gecikme uzlaşmasını sağladı; gerçek eşikler kart verisi ister.
+- Tek uydu burst'ünde raw WLS RMS `1.451` m/s, robust leave-one-out ile `0.418` m/s. ESKF son RMS farkı daha küçük; çünkü mevcut residual covariance inflation aggregate hatayı zaten zayıflatıyor. Robust kapı yine de hatalı kanalı bütün epoch'u reddetmeden ayırır.
+- Common clock-drift step raw velocity RMS'ini bozmadı; clock-drift state RMS'i `0.269` m/s. Dördüncü WLS bilinmeyeni ortak frekans hatasını üç hız bileşeninden ayırıyor.
+
+## Mimari kararı
+
+- ESKF açıkken uygulanan ana yol: 20 ms ham Doppler snapshot -> kanal validity/outlier kontrolü -> 5 Hz robust velocity WLS + gerçek covariance -> adapter tabanları -> ESKF. Sabit `alpha=0.05` temporal IIR yalnız PPS drift-predictor yolunda kalır.
+- ESKF yalnız 3D aggregate velocity gördüğü için tek uydu hatasını sonradan teşhis edemez. Per-satellite robust gate/FDE WLS öncesinde kalmalıdır.
+- Standalone GPS speed, PPS aiding veya ESKF kapalı build için ayrı, yavaş filtrelenmiş Doppler çıktısı tutulabilir. Aynı filtered değeri hem code aiding hem ESKF velocity için kullanmak uygun değildir.
+- Adaptif IIR mümkündür; modelde C/N0 sakin-state alpha'sını, düşük geçiren IMU navigation acceleration ise dynamic alpha'yı seçer. Ancak ESKF'li ana yol için ham ölçüm daha sade ve gecikmesizdir.
+
+## Model sınırları
+
+- Sonuçlar sentetik hata büyüklüklerine koşulludur; kartta yüzde kazanç iddiası değildir.
+- Uydu geometrisi sabit sekiz-kanal local LOS modelidir. Satellite velocity/clock düzeltmelerinin doğru yapıldığı varsayılmıştır.
+- ESKF, bu soruya etki eden `[velocity, accel-bias]` alt sistemine indirgenmiştir; attitude, lever-arm ve tam position cross-covariance modellenmemiştir.
+- Tam firmware'deki position update'in velocity/accel-bias cross-covariance üzerinden sağlayabileceği kısmi recovery bu azaltılmış modelde yoktur. Bu nedenle uzun NIS-ret zincirinin mutlak büyüklüğü değil, pre-IIR'in gecikme ve ret mekanizması karar girdisidir.
+- Carrier loop gürültüsü C/N0 sigma yasasıyla üretilmiştir. Gerçek correlation, oscillator phase noise ve cycle slip dağılımları kart loguyla kalibre edilmelidir.
+- Robust WLS'nin `3.5 sigma`, en az altı uydu ve bütün tek-kanal leave-one-out seçimi C implementasyonuyla aynıdır. RTL değişmez; raw/filtered ayrımı firmware'dedir.
diff --git a/soc/software/gps_measurement_python/output/doppler_eskf_summary.csv b/soc/software/gps_measurement_python/output/doppler_eskf_summary.csv
new file mode 100644
index 0000000..a9025cd
--- /dev/null
+++ b/soc/software/gps_measurement_python/output/doppler_eskf_summary.csv
@@ -0,0 +1,33 @@
+scenario,path,seeds,fused_rms_mps,fused_rms_seed_std_mps,fused_p95_mps,quiet_rms_mps,dynamic_rms_mps,wls_rms_mps,wls_p95_mps,clock_drift_rms_mps,velocity_accept_percent,nis_reject_percent,fused_95_coverage_percent,excluded_epoch_percent,mean_covariance_scale,mean_alpha
+steady_cruise,fixed_iir_wls_eskf,20,0.1821998934975134,0.040897665127266884,0.27466022199861373,0.1821998934975134,nan,0.0681533332956358,0.11645920599554568,0.04445747832784426,100.0,0.0,100.0,0.0,1.0000030764799477,0.05000000000000001
+steady_cruise,raw_wls_eskf,20,0.19046432375253602,0.040009781644375395,0.28906917942032884,0.19046432375253602,nan,0.4164164729808367,0.720889200812689,0.268944777665747,100.0,0.0,100.0,0.0,1.2633800541343088,1.0
+steady_cruise,adaptive_iir_wls_eskf,20,0.1821998934975134,0.040897665127266884,0.27466022199861373,0.1821998934975134,nan,0.0681533332956358,0.11645920599554568,0.04445747832784426,100.0,0.0,100.0,0.0,1.0000030764799477,0.05000000000000001
+steady_cruise,raw_robust_wls_eskf,20,0.19046432375253602,0.040009781644375395,0.28906917942032884,0.19046432375253602,nan,0.4164164729808367,0.720889200812689,0.268944777665747,100.0,0.0,100.0,0.0,1.2633800541343088,1.0
+airliner_maneuver,fixed_iir_wls_eskf,20,0.41605194656716626,0.04357555329949249,0.7083141902703941,0.4019739347287984,0.4380205569605863,0.440222331186762,0.9391237648850084,0.04445747832784397,100.0,0.0,99.71411764705883,0.0,1.0000030764799477,0.05000000000000001
+airliner_maneuver,raw_wls_eskf,20,0.19046432375253933,0.04000978164437598,0.28906917942032373,0.196483054968526,0.1789145728432288,0.4164164729808368,0.720889200812707,0.2689447776657465,100.0,0.0,100.0,0.0,1.2633800541343085,1.0
+airliner_maneuver,adaptive_iir_wls_eskf,20,0.19421091770965,0.04161706926344872,0.2913238026993562,0.19649429208827177,0.18911500227901482,0.1349904626304289,0.2634780317604405,0.06996150326971154,100.0,0.0,100.0,0.0,1.0000030764799477,0.11647550111358576
+airliner_maneuver,raw_robust_wls_eskf,20,0.19046432375253933,0.04000978164437598,0.28906917942032373,0.196483054968526,0.1789145728432288,0.4164164729808368,0.720889200812707,0.2689447776657465,100.0,0.0,100.0,0.0,1.2633800541343085,1.0
+aggressive_maneuver,fixed_iir_wls_eskf,20,0.9420862291590975,0.03697606175587584,1.7661046896298587,0.9551353937753919,0.918769792345089,1.1782538620062029,2.634559496211176,0.04445747832784312,100.0,0.0,55.891176470588235,0.0,1.0000030764799477,0.05000000000000001
+aggressive_maneuver,raw_wls_eskf,20,0.19046432375254996,0.04000978164436178,0.2890691794203225,0.1928303776618579,0.18561935253806933,0.41641647298083734,0.7208892008127159,0.2689447776657467,100.0,0.0,100.0,0.0,1.2633800541343083,1.0
+aggressive_maneuver,adaptive_iir_wls_eskf,20,0.20034438129208682,0.04215736847319882,0.3027038479248761,0.2017392380134829,0.19713256311771804,0.17059135831478262,0.3555978539018994,0.08938088837068828,100.0,0.0,100.0,0.0,1.0001185178364316,0.17603563474387524
+aggressive_maneuver,raw_robust_wls_eskf,20,0.19046432375254996,0.04000978164436178,0.2890691794203225,0.1928303776618579,0.18561935253806933,0.41641647298083734,0.7208892008127159,0.2689447776657467,100.0,0.0,100.0,0.0,1.2633800541343083,1.0
+low_cn0_airliner,fixed_iir_wls_eskf,20,0.4194988293998554,0.04110688289349549,0.7094271250760412,0.4045729059455276,0.4427791039662977,0.4845544319763686,0.9431345662991619,0.14058689054355467,100.0,0.0,99.74176470588235,0.0,1.0000281042403611,0.05000000000000001
+low_cn0_airliner,raw_wls_eskf,20,0.25103588282812916,0.04464089418791806,0.4041748199164089,0.2555504221567221,0.2416319579439005,1.3168245098334108,2.2796518151866563,0.8504780622313423,100.0,0.0,100.0,0.0,1.26385941740462,1.0
+low_cn0_airliner,adaptive_iir_wls_eskf,20,0.20588009483954214,0.040099541607423995,0.3090368268997948,0.2069944088941925,0.20293127741446826,0.337603473203961,0.684354700050294,0.21325106769335284,100.0,0.0,100.0,0.0,1.0000902389090656,0.1040055679287305
+low_cn0_airliner,raw_robust_wls_eskf,20,0.25103588282812916,0.04464089418791806,0.4041748199164089,0.2555504221567221,0.2416319579439005,1.3168245098334108,2.2796518151866563,0.8504780622313423,100.0,0.0,100.0,0.0,1.26385941740462,1.0
+single_satellite_outliers,fixed_iir_wls_eskf,20,0.49511238386612133,0.053875439119808514,0.8173709856169348,0.5050054814659805,0.4779542859711989,1.1463378050509494,0.9892652696081077,0.8027251360930692,100.0,0.0,97.6964705882353,0.0,6.927634385063575,0.05000000000000001
+single_satellite_outliers,raw_wls_eskf,20,0.2570227443883875,0.05273042903908908,0.39439133440568985,0.27216019157834215,0.22927677845507954,1.4512624341492657,0.8297158565959334,1.0630956381619745,100.0,0.0,100.0,0.0,11.13597527632786,1.0
+single_satellite_outliers,adaptive_iir_wls_eskf,20,0.3556263234893831,0.05851649747663683,0.595609347562141,0.3792437361871613,0.31186327209433895,1.1538474734782178,0.5683617007748845,0.8527337411854743,100.0,0.0,100.0,0.0,7.7254775572955,0.11647550111358576
+single_satellite_outliers,raw_robust_wls_eskf,20,0.19054941715698687,0.03971061631217381,0.2889429468862187,0.19658211712738688,0.1789788721793858,0.4181969381744313,0.7254268588122093,0.27034697594947305,100.0,0.0,100.0,2.8953229398663693,1.2641999517115465,1.0
+clock_drift_steps,fixed_iir_wls_eskf,20,0.4160519465671664,0.04357555329949111,0.7083141902703948,0.4019739347287993,0.4380205569605854,0.44022233118676146,0.9391237648850096,1.8177258394243663,100.0,0.0,99.71411764705883,0.0,1.0000030764799477,0.05000000000000001
+clock_drift_steps,raw_wls_eskf,20,0.19046432375253802,0.04000978164437644,0.28906917942032334,0.19648305496852497,0.17891457284322693,0.41641647298083695,0.7208892008126868,0.268944777665747,100.0,0.0,100.0,0.0,1.2633800541343085,1.0
+clock_drift_steps,adaptive_iir_wls_eskf,20,0.19421091770965143,0.0416170692634497,0.29132380269935765,0.19649429208827301,0.18911500227901648,0.1349904626304289,0.26347803176043993,1.818528619384018,100.0,0.0,100.0,0.0,1.0000030764799477,0.11647550111358576
+clock_drift_steps,raw_robust_wls_eskf,20,0.19046432375253802,0.04000978164437644,0.28906917942032334,0.19648305496852497,0.17891457284322693,0.41641647298083695,0.7208892008126868,0.268944777665747,100.0,0.0,100.0,0.0,1.2633800541343085,1.0
+gps_gap_recovery,fixed_iir_wls_eskf,20,0.3971781427894736,0.044796626065109466,0.7104470646835127,0.3873196668983798,0.41253405912166263,0.43094056066637465,0.9463346669492851,0.04458606585950929,100.0,0.0,99.90529411764706,0.0,1.0000036934211136,0.05
+gps_gap_recovery,raw_wls_eskf,20,0.2082177514862905,0.03682283889189333,0.32879462613500177,0.21668463381045563,0.1921901394048915,0.41707211010710354,0.7203717161799947,0.26913433965877315,100.0,0.0,100.0,0.0,1.2631217416869522,1.0
+gps_gap_recovery,adaptive_iir_wls_eskf,20,0.20776527476484566,0.044556420313135676,0.3257106582800945,0.21357805324970008,0.19661285828638408,0.12935782738837362,0.2613749696102362,0.06764578524374312,100.0,0.0,100.0,0.0,1.0000036934211136,0.10814839572192514
+gps_gap_recovery,raw_robust_wls_eskf,20,0.2082177514862905,0.03682283889189333,0.32879462613500177,0.21668463381045563,0.1921901394048915,0.41707211010710354,0.7203717161799947,0.26913433965877315,100.0,0.0,100.0,0.0,1.2631217416869522,1.0
+mixed_flight_faults,fixed_iir_wls_eskf,20,0.9404176641021843,0.04319034103529422,1.7661662430364344,0.9555417869207146,0.9132850762857121,1.5154618461064036,2.663221132275041,0.7591896512045151,100.0,0.0,60.37294117647059,0.0,1.3397749809447188,0.05000000000000001
+mixed_flight_faults,raw_wls_eskf,20,0.22399771088975795,0.05069473595820174,0.3492819306443341,0.23151007332767243,0.2092729705094658,1.498455933396739,2.36689254151483,0.7603191788358898,100.0,0.0,100.0,0.0,2.1864248911994575,1.0
+mixed_flight_faults,adaptive_iir_wls_eskf,20,0.2952659489493427,0.07200078881833771,0.4874378367724045,0.30541797568187434,0.2754557634719251,0.838415542523151,0.9361678311586857,0.47500979673114047,100.0,0.0,99.92470588235294,0.0,1.250042525522558,0.178938679245283
+mixed_flight_faults,raw_robust_wls_eskf,20,0.2208132635451996,0.04372541489397352,0.3416439647301807,0.22864253849532457,0.20560052604298312,1.0129266912203836,2.2537697549366906,0.673490930924677,100.0,0.0,100.0,1.9103773584905661,1.5692458289027678,1.0
diff --git a/soc/software/gps_measurement_python/output/scenario_summary.csv b/soc/software/gps_measurement_python/output/scenario_summary.csv
new file mode 100644
index 0000000..5c1ed52
--- /dev/null
+++ b/soc/software/gps_measurement_python/output/scenario_summary.csv
@@ -0,0 +1,51 @@
+scenario,method,epochs,horizontal_rms_m,position_3d_rms_m,position_3d_p95_m,valid_percent,valid_3d_rms_m,horizontal_2sigma_coverage_percent,false_valid_over_25m_percent,fde_percent,mean_measurement_sigma_m
+clean_open_sky,current_cn0,4500,5.778805688412197,10.054230284262685,17.35250490247279,100.0,10.054230284262685,99.97777777777777,0.3111111111111111,0.0,8.840973580918838
+clean_open_sky,naive_add_dll,4500,5.768593681325036,10.022431815549082,17.253420427433362,100.0,10.022431815549082,100.0,0.3111111111111111,0.0,10.452052333958017
+clean_open_sky,dll_excess,4500,5.7784464702133524,10.05299246387535,17.320782018324902,100.0,10.05299246387535,99.97777777777777,0.33333333333333337,0.0,8.908174172560404
+clean_open_sky,dll_excess_guard,4500,5.7784464702133524,10.05299246387535,17.320782018324902,100.0,10.05299246387535,99.97777777777777,0.33333333333333337,0.0,8.908174172560404
+clean_open_sky,oracle_variance,4500,5.778805688412197,10.054230284262685,17.35250490247279,100.0,10.054230284262685,99.97777777777777,0.3111111111111111,0.0,8.840973580918838
+weak_signal,current_cn0,4500,19.020289863331797,32.73415409569256,56.44388754013162,100.0,32.73415409569256,98.8,56.31111111111111,0.6222222222222222,20.84621216112656
+weak_signal,naive_add_dll,4500,18.802930957724488,32.313115706990146,55.45511304556428,100.0,32.313115706990146,100.0,56.177777777777784,0.0,28.674069502747358
+weak_signal,dll_excess,4500,18.986226727568837,32.6486650471064,56.115244341908046,100.0,32.6486650471064,98.91111111111111,56.222222222222214,0.5111111111111112,21.20058629982459
+weak_signal,dll_excess_guard,4500,18.986226727568837,32.6486650471064,56.115244341908046,100.0,32.6486650471064,98.91111111111111,56.222222222222214,0.5111111111111112,21.20058629982459
+weak_signal,oracle_variance,4500,19.020289863331797,32.73415409569256,56.44388754013162,100.0,32.73415409569256,98.8,56.31111111111111,0.6222222222222222,20.84621216112656
+one_channel_hidden_jitter,current_cn0,4500,8.804153682379612,12.268224803643907,19.936371518380813,100.0,12.268224803643907,96.46666666666667,1.0666666666666667,9.666666666666666,8.840973580918838
+one_channel_hidden_jitter,naive_add_dll,4500,6.529225405554112,10.487953223937716,17.74604536639535,100.0,10.487953223937716,99.97777777777777,0.33333333333333337,0.0,11.805515833602682
+one_channel_hidden_jitter,dll_excess,4500,6.455903980559815,10.46584556632944,17.675128387138177,100.0,10.46584556632944,99.97777777777777,0.33333333333333337,0.044444444444444446,10.358668146326426
+one_channel_hidden_jitter,dll_excess_guard,4500,6.455903980559815,10.46584556632944,17.675128387138177,100.0,10.46584556632944,99.97777777777777,0.33333333333333337,0.044444444444444446,10.358668146326426
+one_channel_hidden_jitter,oracle_variance,4500,6.4491935598492525,10.463101509886709,17.736218582311878,100.0,10.463101509886709,99.97777777777777,0.33333333333333337,0.06666666666666667,10.315229331071063
+common_hidden_jitter,current_cn0,4500,19.733300930595462,33.79270185129192,59.76307034516212,94.75555555555556,33.15386252421736,56.39999999999999,52.400000000000006,46.577777777777776,8.840973580918838
+common_hidden_jitter,naive_add_dll,4500,16.033969673897577,27.61407554068951,47.55915451805768,100.0,27.61407554068951,99.46666666666667,43.93333333333334,0.26666666666666666,18.882004393424943
+common_hidden_jitter,dll_excess,4500,16.085615037536463,27.688964211504615,47.828684727805175,100.0,27.688964211504615,98.97777777777777,43.888888888888886,0.4444444444444444,18.04555007574287
+common_hidden_jitter,dll_excess_guard,4500,16.085615037536463,27.688964211504615,47.828684727805175,100.0,27.688964211504615,98.97777777777777,43.888888888888886,0.4444444444444444,18.04555007574287
+common_hidden_jitter,oracle_variance,4500,16.106964558267112,27.740128015702773,47.83188793884836,100.0,27.740128015702773,98.88888888888889,43.86666666666667,0.4888888888888889,18.035214487051437
+noise_burst_recovery,current_cn0,4500,9.325915933961204,12.96069950118485,22.132869786417263,98.93333333333332,12.552632065384056,94.71111111111111,2.577777777777778,12.11111111111111,8.840973580918838
+noise_burst_recovery,naive_add_dll,4500,6.470839383968352,10.523606281690133,18.031622500344657,100.0,10.523606281690133,100.0,0.5333333333333333,0.06666666666666667,11.60221083527078
+noise_burst_recovery,dll_excess,4500,6.397124977878571,10.493909835494788,17.99630946143617,100.0,10.493909835494788,99.97777777777777,0.4888888888888889,0.13333333333333333,10.131003114059961
+noise_burst_recovery,dll_excess_guard,4500,6.397124977878571,10.493909835494788,17.99630946143617,100.0,10.493909835494788,99.97777777777777,0.4888888888888889,0.13333333333333333,10.131003114059961
+noise_burst_recovery,oracle_variance,4500,6.367173301653832,10.473649717876942,17.90212603773505,100.0,10.473649717876942,99.97777777777777,0.4888888888888889,0.044444444444444446,10.187907003764948
+dll_transient_stress,current_cn0,4500,5.803776392869777,10.145785618162538,17.425227799952054,100.0,10.145785618162538,99.97777777777777,0.35555555555555557,0.0,8.840973580918838
+dll_transient_stress,naive_add_dll,4500,5.793995520088368,10.118871049708806,17.333372587049784,100.0,10.118871049708806,100.0,0.37777777777777777,0.0,10.45205253980181
+dll_transient_stress,dll_excess,4500,5.8034283726190745,10.144627133073621,17.380953993070463,100.0,10.144627133073621,99.97777777777777,0.37777777777777777,0.0,8.908174353046816
+dll_transient_stress,dll_excess_guard,4500,5.79072382051268,10.123295335548953,17.368844982312577,100.0,10.123295335548953,99.97777777777777,0.33333333333333337,0.0,8.947656011912292
+dll_transient_stress,oracle_variance,4500,5.803776392869777,10.145785618162538,17.425227799952054,100.0,10.145785618162538,99.97777777777777,0.35555555555555557,0.0,8.840973580918838
+stable_multipath_bias,current_cn0,4500,7.12694286036133,12.545413964352555,20.99675149186582,100.0,12.545413964352555,99.8888888888889,1.6666666666666667,0.022222222222222223,8.840973580918838
+stable_multipath_bias,naive_add_dll,4500,7.072680893174009,12.386663925234807,20.866871605887997,100.0,12.386663925234807,99.97777777777777,1.4666666666666666,0.0,10.452052333958017
+stable_multipath_bias,dll_excess,4500,7.125500558670432,12.536689588412326,21.02122766562977,100.0,12.536689588412326,99.91111111111111,1.6444444444444446,0.022222222222222223,8.908174172560404
+stable_multipath_bias,dll_excess_guard,4500,7.125500558670432,12.536689588412326,21.02122766562977,100.0,12.536689588412326,99.91111111111111,1.6444444444444446,0.022222222222222223,8.908174172560404
+stable_multipath_bias,oracle_variance,4500,7.12694286036133,12.545413964352555,20.99675149186582,100.0,12.545413964352555,99.8888888888889,1.6666666666666667,0.022222222222222223,8.840973580918838
+mixed_multipath,current_cn0,4500,8.529840854093363,14.426936007413373,25.381172069686816,100.0,14.426936007413373,97.11111111111111,5.644444444444444,5.0,8.840973580918838
+mixed_multipath,naive_add_dll,4500,6.586489015624914,11.258484405711224,19.599950438767102,100.0,11.258484405711224,100.0,0.7333333333333333,0.044444444444444446,11.636563744509052
+mixed_multipath,dll_excess,4500,6.45479117311332,11.067801578489938,19.233225446062768,100.0,11.067801578489938,100.0,0.7333333333333333,0.08888888888888889,10.202310406784667
+mixed_multipath,dll_excess_guard,4500,6.45479117311332,11.067801578489938,19.233225446062768,100.0,11.067801578489938,100.0,0.7333333333333333,0.08888888888888889,10.202310406784667
+mixed_multipath,oracle_variance,4500,6.448333589783235,11.058021985103961,19.19754215965981,100.0,11.058021985103961,99.95555555555555,0.7333333333333333,0.08888888888888889,10.144307488606447
+poor_geometry_hidden_jitter,current_cn0,4500,79.38795978543642,293.8222926191477,574.9617330272,100.0,293.8222926191477,79.0,94.31111111111112,1.1555555555555554,10.734703317378012
+poor_geometry_hidden_jitter,naive_add_dll,4500,57.59864532145799,206.13456070122297,405.1527013193,100.0,206.13456070122297,99.66666666666667,92.42222222222222,0.022222222222222223,14.604104871190987
+poor_geometry_hidden_jitter,dll_excess,4500,55.3927819274298,196.86935630824075,390.63687676393124,100.0,196.86935630824075,99.24444444444444,91.4,0.022222222222222223,12.779670971493758
+poor_geometry_hidden_jitter,dll_excess_guard,4500,55.3927819274298,196.86935630824075,390.63687676393124,100.0,196.86935630824075,99.24444444444444,91.4,0.022222222222222223,12.779670971493758
+poor_geometry_hidden_jitter,oracle_variance,4500,55.24662489772763,196.2046647890204,386.5771391089706,100.0,196.2046647890204,99.28888888888889,91.26666666666667,0.022222222222222223,12.721163297137666
+cn0_step_recovery,current_cn0,4500,12.974359636882712,22.585010269106,47.95054105970103,100.0,22.585010269106,99.42222222222222,21.622222222222224,0.2222222222222222,13.475047639913695
+cn0_step_recovery,naive_add_dll,4500,12.797089787478507,22.265941453345402,47.59129168788298,100.0,22.265941453345402,100.0,21.422222222222224,0.0,17.44366868773946
+cn0_step_recovery,dll_excess,4500,12.96657717120691,22.586113735655264,47.91159461508304,100.0,22.586113735655264,99.46666666666667,21.488888888888887,0.2,13.653801199442478
+cn0_step_recovery,dll_excess_guard,4500,12.96657717120691,22.586113735655264,47.91159461508304,100.0,22.586113735655264,99.46666666666667,21.488888888888887,0.2,13.653801199442478
+cn0_step_recovery,oracle_variance,4500,12.974359636882712,22.585010269106,47.95054105970103,100.0,22.585010269106,99.42222222222222,21.622222222222224,0.2222222222222222,13.475047639913695
diff --git a/soc/software/gps_measurement_python/requirements.txt b/soc/software/gps_measurement_python/requirements.txt
new file mode 100644
index 0000000..e7ea6c1
--- /dev/null
+++ b/soc/software/gps_measurement_python/requirements.txt
@@ -0,0 +1,2 @@
+numpy>=1.24
+matplotlib>=3.7
diff --git a/soc/software/gps_measurement_python/rtl_dll_model.py b/soc/software/gps_measurement_python/rtl_dll_model.py
new file mode 100644
index 0000000..7298e9f
--- /dev/null
+++ b/soc/software/gps_measurement_python/rtl_dll_model.py
@@ -0,0 +1,200 @@
+"""Small executable model of the RTL code-tracking observables.
+
+This is deliberately scoped to the parts that matter to the navigation
+measurement study:
+
+* the normalized early-minus-late magnitude discriminator;
+* its signed Q2.13 output;
+* the fixed C1/C2 code-loop filter and Q20 NCO command;
+* the 20 one-millisecond discriminator samples available per NAV bit.
+
+It is not an RF waveform simulator.  The C/N0-to-discriminator-noise mapping
+is an explicit calibration assumption until real correlator/DLL telemetry is
+recorded from the board.
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+
+import numpy as np
+
+
+DLL_OUTPUT_FRACTION_BITS = 13
+DLL_OUTPUT_WORD_BITS = 15
+DLL_SPACING_CHIPS = 0.5
+CODE_LOOP_C1 = 21.25
+CODE_LOOP_C2 = 0.05712890625
+CODE_LOOP_OUTPUT_FRACTION_BITS = 20
+CODE_LOOP_OUTPUT_WORD_BITS = 28
+DLL_SAMPLES_PER_NAV_BIT = 20
+CODE_FREQUENCY_BASIS_HZ = 1.023e6
+ABS_SAMPLE_COUNTER_MODULUS = 1 << 32
+
+# Synthetic calibration point.  It only fixes the scale of the Monte Carlo
+# discriminator telemetry.  Dynamic weighting uses a measured/expected ratio,
+# so the absolute choice cancels in the correctly modelled case.
+DLL_STD_AT_45_DBHZ = 0.020
+
+
+def _signed_saturate(value: int, word_bits: int) -> int:
+    minimum = -(1 << (word_bits - 1))
+    maximum = (1 << (word_bits - 1)) - 1
+    return min(maximum, max(minimum, value))
+
+
+def quantize_signed(value: float, word_bits: int, fraction_bits: int) -> int:
+    scaled = int(np.rint(value * (1 << fraction_bits)))
+    return _signed_saturate(scaled, word_bits)
+
+
+def dequantize_signed(value: int, fraction_bits: int) -> float:
+    return float(value) / float(1 << fraction_bits)
+
+
+def triangular_correlation(code_offset_chips: float) -> float:
+    """Ideal one-chip triangular GPS C/A autocorrelation main lobe."""
+
+    return max(0.0, 1.0 - abs(code_offset_chips))
+
+
+def ideal_early_late_magnitudes(
+    code_error_chips: float,
+    spacing_chips: float = DLL_SPACING_CHIPS,
+) -> tuple[float, float]:
+    half_spacing = 0.5 * spacing_chips
+    early = triangular_correlation(code_error_chips + half_spacing)
+    late = triangular_correlation(code_error_chips - half_spacing)
+    return early, late
+
+
+def normalized_early_minus_late(early_magnitude: float, late_magnitude: float) -> float:
+    denominator = early_magnitude + late_magnitude
+    if denominator <= 0.0:
+        return 0.0
+    return (early_magnitude - late_magnitude) / denominator
+
+
+def rtl_discriminator(code_error_chips: float) -> tuple[int, float]:
+    """Return the RTL-like Q2.13 discriminator code and dequantized value."""
+
+    early, late = ideal_early_late_magnitudes(code_error_chips)
+    value = normalized_early_minus_late(early, late)
+    code = quantize_signed(
+        value,
+        DLL_OUTPUT_WORD_BITS,
+        DLL_OUTPUT_FRACTION_BITS,
+    )
+    return code, dequantize_signed(code, DLL_OUTPUT_FRACTION_BITS)
+
+
+def expected_discriminator_std(cn0_dbhz: float) -> float:
+    """Expected normalized DLL jitter used by the synthetic calibration.
+
+    The 20 dB amplitude-domain law mirrors the firmware's code-sigma model.
+    The result is bounded because the normalized discriminator is finite.
+    """
+
+    value = DLL_STD_AT_45_DBHZ * 10.0 ** ((45.0 - cn0_dbhz) / 20.0)
+    return float(np.clip(value, 0.002, 0.35))
+
+
+def quantized_code_epoch_measurement(
+    true_abs_sample: float,
+) -> tuple[int, int, float]:
+    """Model ABS_SAMPLE + REM_CODE_PHASE and firmware reconstruction.
+
+    ``true_abs_sample`` is the ideal code boundary in RF-sample units.  The
+    hardware captures the following integer sample and reports the overshoot
+    with the remainder scale used by the C correction formula.
+    """
+
+    raw_unwrapped = int(np.ceil(true_abs_sample))
+    overshoot_samples = raw_unwrapped - true_abs_sample
+    remainder = int(np.rint(overshoot_samples * CODE_FREQUENCY_BASIS_HZ))
+    raw_register = raw_unwrapped % ABS_SAMPLE_COUNTER_MODULUS
+    corrected = raw_unwrapped - remainder / CODE_FREQUENCY_BASIS_HZ
+    return raw_register, remainder, corrected
+
+
+@dataclass(frozen=True)
+class DllWindow:
+    samples: np.ndarray
+    mean: float
+    variance: float
+    expected_variance: float
+    variance_ratio: float
+    mean_z_score: float
+
+
+def synthesize_dll_window(
+    rng: np.random.Generator,
+    *,
+    cn0_dbhz: float,
+    jitter_multiplier: float = 1.0,
+    discriminator_bias: float = 0.0,
+    sample_count: int = DLL_SAMPLES_PER_NAV_BIT,
+) -> DllWindow:
+    """Generate and Q2.13-quantize one NAV-bit DLL telemetry window."""
+
+    if sample_count < 2:
+        raise ValueError("DLL variance needs at least two samples")
+    expected_std = expected_discriminator_std(cn0_dbhz)
+    actual_std = expected_std * max(0.0, jitter_multiplier)
+    raw = discriminator_bias + rng.normal(0.0, actual_std, sample_count)
+    minimum = -(1 << (DLL_OUTPUT_WORD_BITS - 1))
+    maximum = (1 << (DLL_OUTPUT_WORD_BITS - 1)) - 1
+    quantized_codes = np.clip(
+        np.rint(raw * (1 << DLL_OUTPUT_FRACTION_BITS)),
+        minimum,
+        maximum,
+    ).astype(np.int32)
+    samples = quantized_codes.astype(float) / float(1 << DLL_OUTPUT_FRACTION_BITS)
+    mean = float(np.mean(samples))
+    variance = float(np.var(samples, ddof=1))
+    expected_variance = expected_std * expected_std
+    ratio = variance / max(expected_variance, 1.0e-15)
+    standard_error = np.sqrt(max(variance, expected_variance) / sample_count)
+    mean_z = abs(mean) / max(float(standard_error), 1.0e-12)
+    return DllWindow(
+        samples=samples,
+        mean=mean,
+        variance=variance,
+        expected_variance=expected_variance,
+        variance_ratio=float(ratio),
+        mean_z_score=float(mean_z),
+    )
+
+
+@dataclass
+class CodeLoopFilterRtl:
+    """Update-rate model of LF_code.sv, including coefficient quantization."""
+
+    integrator_q20: int = 0
+
+    c1_integer: int = int(CODE_LOOP_C1 * (1 << 2))
+    c2_integer: int = int(CODE_LOOP_C2 * (1 << 11))
+
+    def update_code(self, discriminator_q13: int) -> int:
+        # C1 product has Q15 and is zero-padded to Q20 in LF_code.sv.
+        proportional_q20 = (self.c1_integer * discriminator_q13) << 5
+
+        # C2 product has Q24 and LF_code.sv slices it back to Q20.
+        integral_increment_q20 = (self.c2_integer * discriminator_q13) >> 4
+        self.integrator_q20 = _signed_saturate(
+            self.integrator_q20 + integral_increment_q20,
+            CODE_LOOP_OUTPUT_WORD_BITS,
+        )
+        return _signed_saturate(
+            self.integrator_q20 + proportional_q20,
+            CODE_LOOP_OUTPUT_WORD_BITS,
+        )
+
+    def update(self, discriminator: float) -> float:
+        discriminator_q13 = quantize_signed(
+            discriminator,
+            DLL_OUTPUT_WORD_BITS,
+            DLL_OUTPUT_FRACTION_BITS,
+        )
+        command_q20 = self.update_code(discriminator_q13)
+        return dequantize_signed(command_q20, CODE_LOOP_OUTPUT_FRACTION_BITS)
diff --git a/soc/software/gps_measurement_python/test_doppler_eskf_model.py b/soc/software/gps_measurement_python/test_doppler_eskf_model.py
new file mode 100644
index 0000000..bf678ee
--- /dev/null
+++ b/soc/software/gps_measurement_python/test_doppler_eskf_model.py
@@ -0,0 +1,148 @@
+"""Regression tests for the project-specific Doppler/WLS/ESKF model."""
+
+from __future__ import annotations
+
+import unittest
+
+import numpy as np
+
+from .doppler_eskf_model import (
+    AdaptiveAlpha,
+    DopplerPath,
+    FIXED_DOPPLER_ALPHA,
+    flight_scenarios,
+    local_los_matrix,
+    run_doppler_eskf_scenario,
+    velocity_wls,
+)
+
+
+def _scenario(name: str):
+    return next(item for item in flight_scenarios() if item.name == name)
+
+
+def _fused_rms(trace) -> float:
+    selected = trace.time_s >= 5.0
+    error = trace.fused_velocity_mps[selected] - trace.truth_velocity_mps[selected]
+    return float(np.sqrt(np.mean(np.sum(np.square(error), axis=1))))
+
+
+def _wls_rms(trace) -> float:
+    truth = np.column_stack(
+        [
+            np.interp(
+                trace.wls_time_s,
+                trace.time_s,
+                trace.truth_velocity_mps[:, axis],
+            )
+            for axis in range(3)
+        ]
+    )
+    error = trace.wls_velocity_mps - truth
+    return float(np.sqrt(np.mean(np.sum(np.square(error), axis=1))))
+
+
+class DopplerWlsTest(unittest.TestCase):
+    def test_four_state_wls_separates_velocity_and_clock_drift(self) -> None:
+        velocity = np.asarray([145.0, -32.0, 7.5])
+        clock_drift = 18.0
+        observation = -local_los_matrix() @ velocity + clock_drift
+        result = velocity_wls(observation, np.full(8, 45.0))
+
+        np.testing.assert_allclose(result.velocity_mps, velocity, atol=1.0e-10)
+        self.assertAlmostEqual(result.clock_drift_mps, clock_drift, places=10)
+        self.assertAlmostEqual(result.covariance_scale, 1.0)
+
+    def test_robust_wls_excludes_a_single_bad_channel(self) -> None:
+        velocity = np.asarray([120.0, 20.0, -2.0])
+        observation = -local_los_matrix() @ velocity + 4.0
+        observation[2] += 12.0
+
+        plain = velocity_wls(observation, np.full(8, 43.0))
+        robust = velocity_wls(observation, np.full(8, 43.0), robust=True)
+
+        self.assertEqual(robust.excluded_satellite, 2)
+        self.assertGreater(np.linalg.norm(plain.velocity_mps - velocity), 1.0)
+        np.testing.assert_allclose(robust.velocity_mps, velocity, atol=1.0e-9)
+
+
+class AdaptiveAlphaTest(unittest.TestCase):
+    def test_motion_switches_alpha_and_quiet_state_recovers(self) -> None:
+        selector = AdaptiveAlpha()
+        for _ in range(80):
+            quiet = selector.update(np.zeros(3), 35.0)
+        self.assertAlmostEqual(quiet, 0.03)
+
+        dynamic_values = [
+            selector.update(np.asarray([4.0, 0.0, 0.0]), 35.0)
+            for _ in range(30)
+        ]
+        self.assertGreaterEqual(max(dynamic_values), 0.40)
+
+        for _ in range(120):
+            recovered = selector.update(np.zeros(3), 40.0)
+        self.assertAlmostEqual(recovered, FIXED_DOPPLER_ALPHA)
+
+
+class DopplerEskfIntegrationTest(unittest.TestCase):
+    def test_eskf_filters_raw_doppler_without_pre_iir(self) -> None:
+        traces = run_doppler_eskf_scenario(
+            _scenario("steady_cruise"),
+            seed=7,
+            paths=(DopplerPath.RAW,),
+        )
+        raw = traces[DopplerPath.RAW]
+        self.assertLess(_fused_rms(raw), 0.45 * _wls_rms(raw))
+        self.assertGreater(float(np.mean(raw.wls_accepted)), 0.99)
+
+    def test_raw_path_avoids_fixed_iir_manoeuvre_lag(self) -> None:
+        traces = run_doppler_eskf_scenario(
+            _scenario("airliner_maneuver"),
+            seed=3,
+            paths=(DopplerPath.FIXED_IIR, DopplerPath.RAW),
+        )
+        fixed = traces[DopplerPath.FIXED_IIR]
+        raw = traces[DopplerPath.RAW]
+        self.assertLess(_fused_rms(raw), 0.35 * _fused_rms(fixed))
+        # The production 2/2/3 m/s adapter floors keep both paths inside the
+        # NIS gate; the fixed-IIR penalty now appears as lag error, not reject.
+        self.assertGreater(float(np.mean(raw.wls_accepted)), 0.99)
+        self.assertGreater(float(np.mean(fixed.wls_accepted)), 0.99)
+
+    def test_common_clock_step_does_not_leak_into_raw_velocity(self) -> None:
+        airliner = run_doppler_eskf_scenario(
+            _scenario("airliner_maneuver"),
+            seed=11,
+            paths=(DopplerPath.RAW,),
+        )[DopplerPath.RAW]
+        clock_step = run_doppler_eskf_scenario(
+            _scenario("clock_drift_steps"),
+            seed=11,
+            paths=(DopplerPath.RAW,),
+        )[DopplerPath.RAW]
+
+        np.testing.assert_allclose(
+            airliner.wls_velocity_mps,
+            clock_step.wls_velocity_mps,
+            atol=1.0e-10,
+        )
+        np.testing.assert_allclose(
+            airliner.fused_velocity_mps,
+            clock_step.fused_velocity_mps,
+            atol=1.0e-10,
+        )
+
+    def test_robust_wls_contains_channel_bursts_before_eskf(self) -> None:
+        traces = run_doppler_eskf_scenario(
+            _scenario("single_satellite_outliers"),
+            seed=5,
+            paths=(DopplerPath.RAW, DopplerPath.RAW_ROBUST),
+        )
+        raw = traces[DopplerPath.RAW]
+        robust = traces[DopplerPath.RAW_ROBUST]
+        self.assertLess(_wls_rms(robust), 0.65 * _wls_rms(raw))
+        self.assertGreater(float(np.mean(robust.excluded_satellites >= 0)), 0.02)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/soc/software/gps_measurement_python/test_measurement_model.py b/soc/software/gps_measurement_python/test_measurement_model.py
new file mode 100644
index 0000000..bd0fc7d
--- /dev/null
+++ b/soc/software/gps_measurement_python/test_measurement_model.py
@@ -0,0 +1,182 @@
+from __future__ import annotations
+
+import unittest
+
+import numpy as np
+
+from gps_measurement_python.code_smoothing_model import run_smoothing_trial
+from gps_measurement_python.firmware_wls_model import (
+    SigmaInputs,
+    SigmaMethod,
+    firmware_sigma_m,
+)
+from gps_measurement_python.measurement_scenarios import (
+    run_scenario,
+    scenario_matrix,
+)
+from gps_measurement_python.rtl_dll_model import (
+    CodeLoopFilterRtl,
+    quantized_code_epoch_measurement,
+    rtl_discriminator,
+    synthesize_dll_window,
+)
+
+
+class RtlDllModelTests(unittest.TestCase):
+    def test_discriminator_zero_and_q13_symmetry(self):
+        self.assertEqual(rtl_discriminator(0.0)[0], 0)
+        positive = rtl_discriminator(0.05)[1]
+        negative = rtl_discriminator(-0.05)[1]
+        self.assertAlmostEqual(positive, -negative, places=6)
+        self.assertLess(positive, 0.0)
+
+    def test_code_loop_integrator_accumulates_constant_error(self):
+        loop = CodeLoopFilterRtl()
+        first = loop.update(0.01)
+        twentieth = first
+        for _ in range(19):
+            twentieth = loop.update(0.01)
+        self.assertGreater(first, 0.0)
+        self.assertGreater(twentieth, first)
+
+    def test_dll_window_detects_excess_variance(self):
+        rng = np.random.default_rng(42)
+        nominal = synthesize_dll_window(
+            rng,
+            cn0_dbhz=45.0,
+            jitter_multiplier=1.0,
+            sample_count=4000,
+        )
+        noisy = synthesize_dll_window(
+            rng,
+            cn0_dbhz=45.0,
+            jitter_multiplier=3.0,
+            sample_count=4000,
+        )
+        self.assertAlmostEqual(nominal.variance_ratio, 1.0, delta=0.10)
+        self.assertAlmostEqual(noisy.variance_ratio, 9.0, delta=0.70)
+
+    def test_abs_sample_remainder_reconstructs_subsample_epoch(self):
+        for true_sample in (
+            12_345_678.314159,
+            12_345_678.0000001,
+            12_345_678.9999999,
+            12_345_678.0,
+        ):
+            raw, remainder, corrected = quantized_code_epoch_measurement(true_sample)
+            self.assertEqual(raw, int(np.ceil(true_sample)))
+            self.assertLessEqual(
+                abs(corrected - true_sample),
+                0.5 / 1.023e6 + 1.0e-12,
+            )
+            self.assertGreaterEqual(remainder, 0)
+
+
+class FirmwareSigmaTests(unittest.TestCase):
+    @staticmethod
+    def inputs(ratio: float = 1.0, mean_z: float = 0.0) -> SigmaInputs:
+        return SigmaInputs(
+            ura_index=np.asarray([0]),
+            elevation_deg=np.asarray([90.0]),
+            cn0_dbhz=np.asarray([45.0]),
+            dll_variance_ratio=np.asarray([ratio]),
+            dll_mean_z=np.asarray([mean_z]),
+            actual_jitter_multiplier=np.asarray([np.sqrt(ratio)]),
+        )
+
+    def test_current_matches_c_formula(self):
+        sigma = firmware_sigma_m(self.inputs(), SigmaMethod.CURRENT)[0]
+        expected = np.sqrt(2.4**2 + 3.0**2 + 3.0**2)
+        self.assertAlmostEqual(sigma, expected, places=12)
+
+    def test_excess_method_does_not_double_count_nominal_dll_noise(self):
+        current = firmware_sigma_m(self.inputs(), SigmaMethod.CURRENT)[0]
+        excess = firmware_sigma_m(self.inputs(), SigmaMethod.DLL_EXCESS)[0]
+        naive = firmware_sigma_m(self.inputs(), SigmaMethod.NAIVE_ADD_DLL)[0]
+        self.assertAlmostEqual(excess, current, places=12)
+        self.assertGreater(naive, current)
+
+    def test_excess_method_inflates_hidden_jitter(self):
+        current = firmware_sigma_m(self.inputs(9.0), SigmaMethod.CURRENT)[0]
+        excess = firmware_sigma_m(self.inputs(9.0), SigmaMethod.DLL_EXCESS)[0]
+        self.assertGreater(excess, 1.8 * current)
+
+
+class ScenarioTests(unittest.TestCase):
+    def test_hidden_jitter_dynamic_sigma_improves_seeded_case(self):
+        scenario = next(
+            item
+            for item in scenario_matrix()
+            if item.name == "one_channel_hidden_jitter"
+        )
+        samples = run_scenario(
+            scenario,
+            17,
+            (SigmaMethod.CURRENT, SigmaMethod.DLL_EXCESS),
+        )
+        current = np.asarray(
+            [
+                item.position_error_3d_m
+                for item in samples
+                if item.method == SigmaMethod.CURRENT and item.time_s >= 5.0
+            ]
+        )
+        dynamic = np.asarray(
+            [
+                item.position_error_3d_m
+                for item in samples
+                if item.method == SigmaMethod.DLL_EXCESS and item.time_s >= 5.0
+            ]
+        )
+        self.assertLess(
+            np.sqrt(np.mean(dynamic * dynamic)),
+            0.90 * np.sqrt(np.mean(current * current)),
+        )
+
+    def test_stable_multipath_is_not_solved_by_variance_only(self):
+        scenario = next(
+            item
+            for item in scenario_matrix()
+            if item.name == "stable_multipath_bias"
+        )
+        samples = run_scenario(
+            scenario,
+            23,
+            (SigmaMethod.CURRENT, SigmaMethod.DLL_EXCESS),
+        )
+        current = np.asarray(
+            [
+                item.position_error_3d_m
+                for item in samples
+                if item.method == SigmaMethod.CURRENT and item.time_s >= 5.0
+            ]
+        )
+        dynamic = np.asarray(
+            [
+                item.position_error_3d_m
+                for item in samples
+                if item.method == SigmaMethod.DLL_EXCESS and item.time_s >= 5.0
+            ]
+        )
+        relative_difference = abs(
+            np.sqrt(np.mean(dynamic * dynamic))
+            / np.sqrt(np.mean(current * current))
+            - 1.0
+        )
+        self.assertLess(relative_difference, 0.08)
+
+    def test_doppler_prediction_avoids_blind_iir_dynamic_lag(self):
+        result = run_smoothing_trial(31, doppler_cfo_mps=0.0)
+        self.assertLess(result.doppler_smoothed_rmse_m, result.raw_rmse_m)
+        self.assertLess(
+            result.doppler_peak_dynamic_error_m,
+            0.10 * result.scalar_iir_peak_dynamic_error_m,
+        )
+        self.assertGreater(
+            result.firmware_iir_doppler_peak_dynamic_error_m,
+            result.doppler_peak_dynamic_error_m,
+        )
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/soc/software/gps_system/README.md b/soc/software/gps_system/README.md
index 5175f69..3cb7614 100644
--- a/soc/software/gps_system/README.md
+++ b/soc/software/gps_system/README.md
@@ -811,23 +811,23 @@ range_rate_mps = -doppler_hz * c / 1575420000
 
 Ham 20 ms carrier snapshot'inda kartta gorulen birkac hertz jitter, L1'de
 metre/saniye seviyesinde range-rate gurultusune ve zayif geometride daha buyuk
-receiver velocity hatasina donusur. Bu nedenle Doppler ayni PRN icin software
-ISR state'inde:
+receiver velocity hatasina donusur. Software ISR her PRN icin ham degeri
+degistirmeden korur ve yalniz PPS predictor yolu icin ayri bir state'te:
 
 ```text
 doppler_filtered = 0.05 * doppler_raw + 0.95 * doppler_previous
 ```
 
-ile filtrelenir ve range-rate filtrelenmis Doppler'dan tekrar hesaplanir.
-50 Hz measurement cadence'inde bu yaklasik `0.39 s` zaman sabitidir.
-Reacquisition/PRN degisiminde eski kanal state'i kullanilmaz.
+hesaplar. Ham ve filtreli range-rate ayri alanlarda tutulur. 50 Hz measurement
+cadence'inde bu yaklasik `0.39 s` zaman sabitidir. Reacquisition/PRN
+degisiminde eski kanal state'i kullanilmaz.
 
 IIR donanimda da uygulanabilirdi; bunun icin kanal basina state,
 coefficient-multiply, rounding/saturation ve reacquisition reset kurali
 gerekir. Mevcut sistemde gerekli degildir: RTL'nin gorevi ham, atomik ve
-20 ms sabit olcumu sunmaktir; C/N0/WLS zaten software'dedir, katsayi hareket
-profiline gore bitstream almadan degistirilebilir ve ham Doppler debug icin
-korunur. Board testinde CPU/interrupt yolu measurement kaybetmedigi icin
+20 ms sabit olcumu sunmaktir; C/N0/WLS zaten software'dedir, ham ve filtreli
+yollar bitstream almadan ayrilabilir. Board testinde CPU/interrupt yolu
+measurement kaybetmedigi icin
 RTL filtresinin karsilayacagi bir bant genisligi veya latency problemi de
 gorulmemistir. Ileride tamamen RTL icinde bir tuketici eklenirse ham register
 yaninda ayri bir filtered register mantikli olabilir.
@@ -844,20 +844,71 @@ sigma_rate = clamp(30 * 10^(-C/N0_dbhz / 20), 0.05, 5.0)
 weight = 1 / sigma_rate^2
 ```
 
+Her 200 ms navigation epoch'unda iki velocity tuketicisi vardir:
+
+```text
+raw range-rate      -> robust velocity WLS -> fusion adapter -> ESKF
+filtered range-rate -> robust velocity WLS -> PPS bias-drift predictor
+```
+
+Ham ESKF yolu temporal filtreleme isini ESKF'ye birakir ve `alpha=0.05`
+IIR'in yaklasik 390 ms dinamik gecikmesini velocity measurement'a eklemez.
+PPS'in ana olcumu position WLS `clock_bias_m` sonucudur. Filtreli velocity
+yalniz bu referans-datum bias'inin 200 ms epoch'lar arasindaki turevini
+ongormek ve PPS kalite profilini siniflandirmak icin kullanilir. Doppler
+WLS'nin dorduncu `receiver_clock_drift_mps` state'i PPS'e dogrudan verilmez.
+
+Position WLS ile Doppler WLS iki ayri fiziksel observation kullanir:
+code-phase pseudorange konum/ofseti, carrier Doppler ise hiz/frekans hatasini
+olcer. Klasik mutlak-pseudorange modelinde ayni receiver zaman hatasi
+`delta_t_r(t)` icin:
+
+```text
+code WLS:     [x, y, z, b_r],       b_r    = c * delta_t_r       [m]
+Doppler WLS:  [vx, vy, vz, bdot_r], bdot_r = c * d(delta_t_r)/dt [m/s]
+```
+
+Doppler WLS'nin dorduncu bilinmeyeni receiver clock/frequency drift'idir.
+Receiver oscillator `0.1 ppm` hizliysa `bdot_r` yaklasik `29.98 m/s` olur.
+Bu etki butun uydu Doppler'larina ortak girer; cozulmezse bir kismi
+`vx/vy/vz` receiver hareketi sanilir.
+
+Bu projedeki position WLS'e verilen capture zamanlarindan ortak receiver
+zamani cikarilir ve `STARTOFFSET` eklenir. Dolayisiyla
+`solution.clock_bias_m`, saf `c*delta_t_r` yerine yaklasik
+`c*STARTOFFSET - reference_range` olan referans-uyduya bagli goreli bir
+datumdur. Doppler `solution.clock_drift_mps` ile bunun arasinda turev kisiti
+kurulmaz.
+
+Fit'ler matematiksel olarak ayridir ve `solution_valid`/`velocity_valid`
+bagimsizdir. Bununla birlikte velocity WLS LOS birim vektorlerini hesaplamak
+icin position WLS'nin guncel receiver ECEF konumunu kullanir; uydu ECEF
+konumlari, hizlari ve satellite clock drift'leri broadcast ephemeristen gelir.
+Position kabul edilip velocity reddedilebilir; velocity NIS reject ayni
+epoch'taki position update'ini geri almaz.
+
 En az dort uydu gerekir. Dort uyduda velocity residual serbestlik derecesi
 yoktur; bes uydu ve dusuk PDOP'ta bile zayif geometri velocity gurultusunu
-buyutebilir. WLS, `inverse(H'WH)` matrisinden ECEF velocity covariance uretir.
-`N>4` ise weighted post-fit reduced chi-square yalniz covariance'i buyutebilir;
-tek bir sessiz epoch formal belirsizligi kucultemez. Sonuc `velocity_valid`,
-ECEF velocity/covariance, `speed_mps` ve `velocity_residual_rms_mps`
-alanlarinda yayinlanir.
+buyutebilir. Alti veya daha fazla kullanilabilir uyduda full-fit maksimum
+normalized residual `3.5 sigma`'yi asarsa butun tek-kanal leave-one-out
+adaylari cozulur; en dusuk weighted post-fit residual enerjili aday secilir.
+Boylece ESKF'nin aggregate 3D velocity NIS kapisina gelmeden once bozuk kanal
+ayrilabilir. Dort/bes uyduda redundancy yetersiz oldugu icin velocity FDE
+uygulanmaz.
+
+WLS, `inverse(H'WH)` matrisinden ECEF velocity covariance uretir. `N>4` ise
+weighted post-fit reduced chi-square yalniz covariance'i buyutebilir; tek bir
+sessiz epoch formal belirsizligi kucultemez. Sonuc `velocity_valid`, ECEF
+velocity/covariance, `speed_mps`, `velocity_residual_rms_mps`,
+`velocity_fde_applied` ve `velocity_excluded_row_mask` alanlarinda yayinlanir.
 
 Fusion adapter covariance'i `R_ecef_to_enu * P * R^T` ile ENU'ya dondurur.
 2026-07-25 sabit kart verisinde zayif geometriyle gorulen
 `p95=6.020 m/s` speed hatasi nedeniyle default alt sinirlar yatay eksenlerde
-`2.0 m/s`, dikey eksende `3.0 m/s`'dir. Bunlar IIR ile korelasyonlu ard arda
-epoch'larin ESKF'yi asiri guvenle cekmesini onler; formal covariance daha
-buyukse aynen korunur. Velocity innovation 3-DOF `%99.9`
+`2.0 m/s`, dikey eksende `3.0 m/s`'dir. ESKF artik ham Doppler WLS aldigi icin
+bu konservatif tabanlar temporal korelasyondan cok zayif geometri ve kartta
+henuz yeniden kalibre edilmemis raw-Doppler hata kuyruklarini sinirlar; formal
+covariance daha buyukse aynen korunur. Velocity innovation 3-DOF `%99.9`
 `NIS=16.266` kapisindan gecer. Kabul/red sayilari ve son velocity NIS'i
 `[FUSION]` UART status satirinda `velocity=accepted/rejected` ve `vel_nis`
 olarak yayinlanir.
@@ -1137,9 +1188,10 @@ make -C soc/software/gps_system/tests sanitize
 make -C hardware/external/gps/rtl/trck_src/tb test
 ```
 
-`run` ve `sanitize`, C/N0 estimator'i, Q7 Doppler/range-rate donusumu,
-coherent mailbox read'i, weighted velocity WLS/covariance ve satellite
-velocity/clock drift hesaplarini kapsar. Fusion regression'i ayrica
+`run` ve `sanitize`, C/N0 estimator'i, Q7 ham/filtreli Doppler-range-rate
+donusumu, coherent mailbox read'i, weighted velocity WLS/covariance,
+tek-kanal robust FDE ve satellite velocity/clock drift hesaplarini kapsar.
+Fusion regression'i ayrica
 ECEF->ENU velocity/covariance rotasyonunu, velocity NIS kabul/redini ve ayni
 epoch position+velocity delayed replay esdegerligini kapsar. RTL
 Questa/vlog-vsim testi prompt akumulasyonu,
@@ -1260,8 +1312,10 @@ T_rx = TOW_ref + POSTPONE_TOW + STARTOFFSET/1000 - b/c
   diye `1.024 us` tutulur. Watchdog, quality holdover ve `20 ppm` slew clamp
   buyuk arizalari ayri olarak sinirlar.
 - Yazilim filtresi PI'nin yerine gecmez. Yalnizca 5 Hz WLS clock-bias
-  olcumunde Doppler clock-drift prediction, bounded innovation ve aykiri
-  olcum reddi yapar. Ilk yerlesmede commit'ler coarse ve PPS invalid tutulur.
+  olcumunde filtreli-Doppler velocity'den turetilen referans-datum drift
+  prediction, bounded innovation ve aykiri olcum reddi yapar. Position WLS
+  `clock_bias_m` ana PPS olcumu olarak kalir; Doppler yalnız prediction'dir.
+  Ilk yerlesmede commit'ler coarse ve PPS invalid tutulur.
   Periyodik background watchdog iki saniye yeni referans gelmezse cikis
   validligini holdover ile kapatir; fakat ayni referans geri gelirse Doppler
   prediction ve donanim PI state'i 30 saniyeye kadar korunur. Referans SVID
diff --git a/soc/software/gps_system/header/gps/NavEquations.h b/soc/software/gps_system/header/gps/NavEquations.h
index aec4b49..e979e35 100644
--- a/soc/software/gps_system/header/gps/NavEquations.h
+++ b/soc/software/gps_system/header/gps/NavEquations.h
@@ -32,8 +32,12 @@
 			double elevation_deg[GPS_TRCK_IP_COUNT];
 			double measurement_sigma_m[GPS_TRCK_IP_COUNT];
 			double cn0_dbhz[GPS_TRCK_IP_COUNT];
+			/* Raw Doppler is published with the ESKF velocity solution. */
 			double doppler_hz[GPS_TRCK_IP_COUNT];
 			double pseudorange_rate_mps[GPS_TRCK_IP_COUNT];
+			/* Separate slow path used only by the PPS bias-drift predictor. */
+			double filtered_doppler_hz[GPS_TRCK_IP_COUNT];
+			double filtered_pseudorange_rate_mps[GPS_TRCK_IP_COUNT];
 			double full_postfit_residual_m[GPS_TRCK_IP_COUNT];
 			double full_elevation_deg[GPS_TRCK_IP_COUNT];
 			double full_measurement_sigma_m[GPS_TRCK_IP_COUNT];
@@ -53,6 +57,7 @@
 			unsigned int degrees_of_freedom;
 			uint32_t used_row_mask;
 			uint32_t excluded_row_mask;
+			uint32_t velocity_excluded_row_mask;
 			uint64_t candidate_cycles;
 			uint64_t full_solution_cycles;
 			uint64_t fde_cycles;
@@ -65,6 +70,7 @@
 			bool fde_applied;
 			bool solution_valid;
 			bool velocity_valid;
+			bool velocity_fde_applied;
 		} gps_nav_solution_t;
 
 		    void satpos(gps_ephemeris_t* eph, double* pos, double* vel, double* clk, double* clockCorr);
diff --git a/soc/software/gps_system/header/gps/gps_tracking_measurement.h b/soc/software/gps_system/header/gps/gps_tracking_measurement.h
index 50143d3..2be86c8 100644
--- a/soc/software/gps_system/header/gps/gps_tracking_measurement.h
+++ b/soc/software/gps_system/header/gps/gps_tracking_measurement.h
@@ -17,8 +17,12 @@ typedef struct {
 	int32_t cn0_sum_q;
 	uint64_t cn0_wbp;
 	unsigned int cn0_sample_count;
+	/* Raw coherent 20 ms carrier snapshot used by velocity WLS/ESKF. */
 	double doppler_hz;
 	double pseudorange_rate_mps;
+	/* Slow software IIR path retained only for PPS bias-drift prediction. */
+	double filtered_doppler_hz;
+	double filtered_pseudorange_rate_mps;
 	double cn0_dbhz;
 	bool nav_bit;
 	bool locked;
@@ -59,4 +63,23 @@ bool gps_tracking_velocity_wls(
 	double* receiver_clock_drift_mps_out,
 	double* residual_rms_mps_out);
 
+/*
+ * Raw-Doppler velocity solution with a one-channel leave-one-out FDE trial.
+ * FDE runs only for six or more usable channels and only when the full-fit
+ * maximum normalized residual exceeds 3.5 sigma. The returned bit mask uses
+ * indices from the input measurement array, not compacted WLS row indices.
+ */
+bool gps_tracking_velocity_wls_robust(
+	const double receiver_ecef_m[3],
+	const double satellite_positions_m[][3],
+	const double satellite_velocities_mps[][3],
+	const double satellite_clock_drifts_sps[],
+	const gps_tracking_measurement_t measurements[],
+	unsigned int count,
+	double receiver_velocity_ecef_mps_out[3],
+	double receiver_velocity_covariance_ecef_mps2_out[3][3],
+	double* receiver_clock_drift_mps_out,
+	double* residual_rms_mps_out,
+	uint32_t* excluded_measurement_mask_out);
+
 #endif
diff --git a/soc/software/gps_system/src/adapters/gps_system_uart.c b/soc/software/gps_system/src/adapters/gps_system_uart.c
index 923d1b0..cc09bfb 100644
--- a/soc/software/gps_system/src/adapters/gps_system_uart.c
+++ b/soc/software/gps_system/src/adapters/gps_system_uart.c
@@ -27,12 +27,13 @@ void gps_system_uart_publish_location(
 	GPS_LOG(DEBUG_STATUS, GPS_LOG_CAT_LOCATION,
 	        "source=%s lat=%.20lf lon=%.20lf height=%.3lf "
 	        "gdop=%.10lf pdop=%.10lf hdop=%.10lf vdop=%.10lf tdop=%.10lf "
-	        "tracked=%u used=%u velocity_valid=%u speed=%.3lf "
+	        "tracked=%u used=%u velocity_valid=%u velocity_fde=%u speed=%.3lf "
 	        "velocity_rms=%.3lf\r\n",
 	        source, latitude_deg, longitude_deg, height_m,
 	        gps->gdop, gps->pdop, gps->hdop, gps->vdop, gps->tdop,
 	        gps->tracked_satellite_count, gps->used_satellite_count,
 	        gps->velocity_valid ? 1u : 0u,
+	        gps->velocity_fde_applied ? 1u : 0u,
 	        gps->speed_mps, gps->velocity_residual_rms_mps);
 }
 
diff --git a/soc/software/gps_system/src/gps/gps_interrupt_handlers.c b/soc/software/gps_system/src/gps/gps_interrupt_handlers.c
index bc0277c..660196c 100644
--- a/soc/software/gps_system/src/gps/gps_interrupt_handlers.c
+++ b/soc/software/gps_system/src/gps/gps_interrupt_handlers.c
@@ -156,13 +156,13 @@ static void gps_update_tracking_measurement_isr(
 		 * A 0.05 pole at the 50 Hz navigation-bit cadence has an approximately
 		 * 0.4 s time constant while retaining real receiver dynamics.
 		 */
-		measurement.doppler_hz =
+		measurement.filtered_doppler_hz =
 			GPS_TRACK_DOPPLER_SMOOTH_ALPHA * measurement.doppler_hz +
 			(1.0 - GPS_TRACK_DOPPLER_SMOOTH_ALPHA) *
-			previous->doppler_hz;
-		measurement.pseudorange_rate_mps =
+			previous->filtered_doppler_hz;
+		measurement.filtered_pseudorange_rate_mps =
 			gps_tracking_doppler_to_range_rate_mps(
-				measurement.doppler_hz);
+				measurement.filtered_doppler_hz);
 	}
 	measurement.local_timestamp_ticks = local_timestamp_ticks;
 	gps_latest_tracking_measurement[tracking_index] = measurement;
diff --git a/soc/software/gps_system/src/gps/gps_ip.c b/soc/software/gps_system/src/gps/gps_ip.c
index 72f0f64..8cd0285 100644
--- a/soc/software/gps_system/src/gps/gps_ip.c
+++ b/soc/software/gps_system/src/gps/gps_ip.c
@@ -853,6 +853,9 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 	bool ok = false;
 	bool pps_clock_bias_drift_valid = false;
 	double pps_clock_bias_drift_mps = 0.0;
+	bool pps_velocity_valid = false;
+	double pps_velocity_residual_rms_mps = 0.0;
+	uint32_t pps_velocity_excluded_row_mask = 0u;
 	gps_nav_solution_t solution;
 	memset(&solution, 0, sizeof(solution));
 	memset(solution_out, 0, sizeof(*solution_out));
@@ -954,6 +957,10 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 		solution.doppler_hz[row] = measurements[row].doppler_hz;
 		solution.pseudorange_rate_mps[row] =
 			measurements[row].pseudorange_rate_mps;
+		solution.filtered_doppler_hz[row] =
+			measurements[row].filtered_doppler_hz;
+		solution.filtered_pseudorange_rate_mps[row] =
+			measurements[row].filtered_pseudorange_rate_mps;
 	}
 	if(ok && solution.solution_valid)
 	{
@@ -976,7 +983,7 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 				velocity_measurements[row].valid = false;
 			}
 		}
-		solution.velocity_valid = gps_tracking_velocity_wls(
+		solution.velocity_valid = gps_tracking_velocity_wls_robust(
 			solution.ecef_m,
 			satellite_positions_array,
 			satellite_velocities_array,
@@ -986,7 +993,10 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 			solution.velocity_ecef_mps,
 			solution.velocity_covariance_ecef_mps2,
 			&solution.clock_drift_mps,
-			&solution.velocity_residual_rms_mps);
+			&solution.velocity_residual_rms_mps,
+			&solution.velocity_excluded_row_mask);
+		solution.velocity_fde_applied =
+			solution.velocity_excluded_row_mask != 0u;
 		if(solution.velocity_valid)
 		{
 			solution.speed_mps =
@@ -996,15 +1006,57 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 				     solution.velocity_ecef_mps[1] +
 				     solution.velocity_ecef_mps[2] *
 				     solution.velocity_ecef_mps[2]);
+		}
+
+		/*
+		 * PPS keeps the existing slow Doppler path as a low-noise derivative
+		 * predictor for the position-WLS reference datum.  This result is not
+		 * published to fusion; fusion receives the raw robust solution above.
+		 */
+		for(unsigned int row = 0u; row < satellite_count; row++)
+		{
+			velocity_measurements[row].doppler_hz =
+				measurements[row].filtered_doppler_hz;
+			velocity_measurements[row].pseudorange_rate_mps =
+				measurements[row].filtered_pseudorange_rate_mps;
+		}
+		double pps_velocity_ecef_mps[3];
+		double pps_velocity_covariance_ecef_mps2[3][3];
+		double pps_receiver_clock_drift_mps = 0.0;
+		pps_velocity_valid = gps_tracking_velocity_wls_robust(
+			solution.ecef_m,
+			satellite_positions_array,
+			satellite_velocities_array,
+			clockDrift,
+			velocity_measurements,
+			satellite_count,
+			pps_velocity_ecef_mps,
+			pps_velocity_covariance_ecef_mps2,
+			&pps_receiver_clock_drift_mps,
+			&pps_velocity_residual_rms_mps,
+			&pps_velocity_excluded_row_mask);
+		if(pps_velocity_valid)
+		{
 			pps_clock_bias_drift_valid =
 				gps_pps_reference_bias_drift(
 					solution.ecef_m,
-					solution.velocity_ecef_mps,
+					pps_velocity_ecef_mps,
 					satellite_positions_array[reference_index],
 					satellite_velocities_array[reference_index],
 					clockDrift[reference_index],
 					&pps_clock_bias_drift_mps);
 		}
+		if(solution.velocity_fde_applied ||
+		   (pps_velocity_excluded_row_mask != 0u))
+		{
+			GPS_LOG(DEBUG_EVENTS, GPS_LOG_CAT_NAV,
+			        "velocity FDE raw_mask=0x%02lx pps_mask=0x%02lx "
+			        "raw_rms=%.3lf pps_rms=%.3lf\r\n",
+			        (unsigned long)solution.velocity_excluded_row_mask,
+			        (unsigned long)pps_velocity_excluded_row_mask,
+			        solution.velocity_residual_rms_mps,
+			        pps_velocity_residual_rms_mps);
+		}
 	}
 	if(ok && solution.fde_applied)
 	{
@@ -1056,12 +1108,13 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 			(cn0_count != 0u) ? minimum_cn0 : NAN;
 		pps_quality.chi_square_ratio = solution.chi_square_ratio;
 		pps_quality.velocity_residual_rms_mps =
-			solution.velocity_valid ?
-				solution.velocity_residual_rms_mps : 0.0;
+			pps_velocity_valid ? pps_velocity_residual_rms_mps : 0.0;
 		pps_quality.used_satellites = solution.used_satellite_count;
 		pps_quality.residual_test_valid = solution.residual_test_valid;
-		pps_quality.velocity_valid = solution.velocity_valid;
-		pps_quality.fde_applied = solution.fde_applied;
+		pps_quality.velocity_valid = pps_velocity_valid;
+		pps_quality.fde_applied =
+			solution.fde_applied ||
+			(pps_velocity_excluded_row_mask != 0u);
 	}
 	bool pps_profile_changed = false;
 	/*
@@ -1141,7 +1194,8 @@ static bool nav_software_from_snapshot(const gps_ephemeris_t* ephemeris,
 			        "drift=%.3lf tdop=%.2lf\r\n",
 			        gps_pps_profile_name(pps_profile),
 			        solution.clock_bias_m,
-			        solution.clock_drift_mps,
+			        pps_clock_bias_drift_valid ?
+					pps_clock_bias_drift_mps : NAN,
 			        solution.tdop);
 			goto pps_anchor_done;
 		}
diff --git a/soc/software/gps_system/src/gps/gps_tracking_measurement.c b/soc/software/gps_system/src/gps/gps_tracking_measurement.c
index 16ed743..a997bb7 100644
--- a/soc/software/gps_system/src/gps/gps_tracking_measurement.c
+++ b/soc/software/gps_system/src/gps/gps_tracking_measurement.c
@@ -8,6 +8,8 @@
 #define GPS_TRACK_MEASUREMENT_MIN_SATELLITES 4u
 #define GPS_TRACK_MEASUREMENT_MAX_SATELLITES GPS_TRCK_IP_COUNT
 #define GPS_TRACK_MEASUREMENT_EPSILON 1.0e-12
+#define GPS_TRACK_VELOCITY_FDE_MIN_SATELLITES 6u
+#define GPS_TRACK_VELOCITY_FDE_SIGMA_GATE 3.5
 
 static double clamp_double(double value, double minimum, double maximum)
 {
@@ -135,6 +137,10 @@ bool gps_tracking_measurement_read(
 		measurement_out->pseudorange_rate_mps =
 			gps_tracking_doppler_to_range_rate_mps(
 				measurement_out->doppler_hz);
+		measurement_out->filtered_doppler_hz =
+			measurement_out->doppler_hz;
+		measurement_out->filtered_pseudorange_rate_mps =
+			measurement_out->pseudorange_rate_mps;
 
 		unsigned int version =
 			meta >> GPS_TRCK_MEAS_META_VERSION_SHIFT;
@@ -149,7 +155,9 @@ bool gps_tracking_measurement_read(
 			(measurement_out->cn0_sample_count == 20u) &&
 			cn0_valid &&
 			isfinite(measurement_out->doppler_hz) &&
-			isfinite(measurement_out->pseudorange_rate_mps);
+			isfinite(measurement_out->pseudorange_rate_mps) &&
+			isfinite(measurement_out->filtered_doppler_hz) &&
+			isfinite(measurement_out->filtered_pseudorange_rate_mps);
 		return measurement_out->valid;
 	}
 
@@ -261,7 +269,94 @@ static bool invert_four_by_four(double input[4][4], double inverse[4][4])
 	return true;
 }
 
-bool gps_tracking_velocity_wls(
+typedef struct {
+	double solution[4];
+	double normal_inverse[4][4];
+	double residual_mps[GPS_TRACK_MEASUREMENT_MAX_SATELLITES];
+	double residual_square_sum;
+	double weighted_residual_square_sum;
+	unsigned int row_count;
+} gps_velocity_wls_candidate_t;
+
+static bool gps_velocity_solve_candidate(
+	const double design[][4],
+	const double observation[],
+	const double weights[],
+	unsigned int used,
+	unsigned int excluded_row,
+	gps_velocity_wls_candidate_t* candidate_out)
+{
+	if((design == NULL) || (observation == NULL) || (weights == NULL) ||
+	   (candidate_out == NULL) ||
+	   (used < GPS_TRACK_MEASUREMENT_MIN_SATELLITES) ||
+	   (used > GPS_TRACK_MEASUREMENT_MAX_SATELLITES))
+	{
+		return false;
+	}
+
+	double normal[4][4] = {{0.0}};
+	double rhs[4] = {0.0};
+	unsigned int selected = 0u;
+	for(unsigned int measurement_row = 0u;
+	    measurement_row < used;
+	    measurement_row++)
+	{
+		if(measurement_row == excluded_row)
+		{
+			continue;
+		}
+		double weight = weights[measurement_row];
+		for(unsigned int row = 0u; row < 4u; row++)
+		{
+			rhs[row] += weight * design[measurement_row][row] *
+			            observation[measurement_row];
+			for(unsigned int column = 0u; column < 4u; column++)
+			{
+				normal[row][column] +=
+					weight * design[measurement_row][row] *
+					design[measurement_row][column];
+			}
+		}
+		selected++;
+	}
+	if(selected < GPS_TRACK_MEASUREMENT_MIN_SATELLITES)
+	{
+		return false;
+	}
+
+	memset(candidate_out, 0, sizeof(*candidate_out));
+	if(!solve_four_by_four(normal, rhs, candidate_out->solution) ||
+	   !invert_four_by_four(normal, candidate_out->normal_inverse))
+	{
+		return false;
+	}
+	for(unsigned int measurement_row = 0u;
+	    measurement_row < used;
+	    measurement_row++)
+	{
+		candidate_out->residual_mps[measurement_row] = NAN;
+		if(measurement_row == excluded_row)
+		{
+			continue;
+		}
+		double predicted = 0.0;
+		for(unsigned int column = 0u; column < 4u; column++)
+		{
+			predicted += design[measurement_row][column] *
+			             candidate_out->solution[column];
+		}
+		double residual = observation[measurement_row] - predicted;
+		candidate_out->residual_mps[measurement_row] = residual;
+		candidate_out->residual_square_sum += residual * residual;
+		candidate_out->weighted_residual_square_sum +=
+			weights[measurement_row] * residual * residual;
+	}
+	candidate_out->row_count = selected;
+	return isfinite(candidate_out->residual_square_sum) &&
+	       isfinite(candidate_out->weighted_residual_square_sum);
+}
+
+static bool gps_tracking_velocity_wls_internal(
 	const double receiver_ecef_m[3],
 	const double satellite_positions_m[][3],
 	const double satellite_velocities_mps[][3],
@@ -271,8 +366,14 @@ bool gps_tracking_velocity_wls(
 	double receiver_velocity_ecef_mps_out[3],
 	double receiver_velocity_covariance_ecef_mps2_out[3][3],
 	double* receiver_clock_drift_mps_out,
-	double* residual_rms_mps_out)
+	double* residual_rms_mps_out,
+	bool robust,
+	uint32_t* excluded_measurement_mask_out)
 {
+	if(excluded_measurement_mask_out != NULL)
+	{
+		*excluded_measurement_mask_out = 0u;
+	}
 	if((receiver_ecef_m == NULL) || (satellite_positions_m == NULL) ||
 	   (satellite_velocities_mps == NULL) ||
 	   (satellite_clock_drifts_sps == NULL) ||
@@ -287,11 +388,10 @@ bool gps_tracking_velocity_wls(
 		return false;
 	}
 
-	double normal[4][4] = {{0.0}};
-	double rhs[4] = {0.0};
 	double design[GPS_TRACK_MEASUREMENT_MAX_SATELLITES][4];
 	double observation[GPS_TRACK_MEASUREMENT_MAX_SATELLITES];
 	double weights[GPS_TRACK_MEASUREMENT_MAX_SATELLITES];
+	unsigned int measurement_index[GPS_TRACK_MEASUREMENT_MAX_SATELLITES];
 	unsigned int used = 0u;
 
 	for(unsigned int satellite = 0u; satellite < count; satellite++)
@@ -342,17 +442,7 @@ bool gps_tracking_velocity_wls(
 		sigma_rate_mps = clamp_double(sigma_rate_mps, 0.05, 5.0);
 		double weight = 1.0 / (sigma_rate_mps * sigma_rate_mps);
 		weights[used] = weight;
-		for(unsigned int row = 0u; row < 4u; row++)
-		{
-			rhs[row] +=
-				weight * design[used][row] * observation[used];
-			for(unsigned int column = 0u; column < 4u; column++)
-			{
-				normal[row][column] +=
-					weight * design[used][row] *
-					design[used][column];
-			}
-		}
+		measurement_index[used] = satellite;
 		used++;
 	}
 
@@ -361,27 +451,47 @@ bool gps_tracking_velocity_wls(
 		return false;
 	}
 
-	double solution[4];
-	double normal_inverse[4][4];
-	if(!solve_four_by_four(normal, rhs, solution) ||
-	   !invert_four_by_four(normal, normal_inverse))
+	gps_velocity_wls_candidate_t full;
+	if(!gps_velocity_solve_candidate(
+		design, observation, weights, used,
+		GPS_TRACK_MEASUREMENT_MAX_SATELLITES, &full))
 	{
 		return false;
 	}
 
-	double residual_square_sum = 0.0;
-	double weighted_residual_square_sum = 0.0;
-	for(unsigned int row = 0u; row < used; row++)
+	gps_velocity_wls_candidate_t selected = full;
+	unsigned int excluded_row = GPS_TRACK_MEASUREMENT_MAX_SATELLITES;
+	if(robust && (used >= GPS_TRACK_VELOCITY_FDE_MIN_SATELLITES))
 	{
-		double predicted = 0.0;
-		for(unsigned int column = 0u; column < 4u; column++)
+		double maximum_normalized_residual = 0.0;
+		for(unsigned int row = 0u; row < used; row++)
 		{
-			predicted += design[row][column] * solution[column];
+			double normalized =
+				fabs(full.residual_mps[row]) * sqrt(weights[row]);
+			maximum_normalized_residual =
+				fmax(maximum_normalized_residual, normalized);
 		}
-		double residual = observation[row] - predicted;
-		residual_square_sum += residual * residual;
-		weighted_residual_square_sum +=
-			weights[row] * residual * residual;
+		if(maximum_normalized_residual > GPS_TRACK_VELOCITY_FDE_SIGMA_GATE)
+		{
+			double best_score = INFINITY;
+			for(unsigned int trial_row = 0u; trial_row < used; trial_row++)
+			{
+				gps_velocity_wls_candidate_t trial;
+				if(gps_velocity_solve_candidate(
+					design, observation, weights, used, trial_row, &trial) &&
+				   (trial.weighted_residual_square_sum < best_score))
+				{
+					best_score = trial.weighted_residual_square_sum;
+					selected = trial;
+					excluded_row = trial_row;
+				}
+			}
+		}
+	}
+	if((excluded_row < used) && (excluded_measurement_mask_out != NULL))
+	{
+		*excluded_measurement_mask_out =
+			1u << measurement_index[excluded_row];
 	}
 
 	/*
@@ -392,17 +502,19 @@ bool gps_tracking_velocity_wls(
 	 * the poor geometry appear directly in the inverse normal matrix.
 	 */
 	double covariance_scale = 1.0;
-	if(used > 4u)
+	if(selected.row_count > 4u)
 	{
 		covariance_scale = fmax(
-			1.0, weighted_residual_square_sum / (double)(used - 4u));
+			1.0,
+			selected.weighted_residual_square_sum /
+				(double)(selected.row_count - 4u));
 	}
 	for(unsigned int row = 0u; row < 3u; row++)
 	{
 		for(unsigned int column = 0u; column < 3u; column++)
 		{
 			receiver_velocity_covariance_ecef_mps2_out[row][column] =
-				covariance_scale * normal_inverse[row][column];
+				covariance_scale * selected.normal_inverse[row][column];
 			if(!isfinite(
 				receiver_velocity_covariance_ecef_mps2_out[row][column]))
 			{
@@ -410,10 +522,53 @@ bool gps_tracking_velocity_wls(
 			}
 		}
 	}
-	memcpy(receiver_velocity_ecef_mps_out, solution,
-	       3u * sizeof(solution[0]));
-	*receiver_clock_drift_mps_out = solution[3];
+	memcpy(receiver_velocity_ecef_mps_out, selected.solution,
+	       3u * sizeof(selected.solution[0]));
+	*receiver_clock_drift_mps_out = selected.solution[3];
 	*residual_rms_mps_out =
-		sqrt(residual_square_sum / (double)used);
+		sqrt(selected.residual_square_sum / (double)selected.row_count);
 	return isfinite(*residual_rms_mps_out);
 }
+
+bool gps_tracking_velocity_wls(
+	const double receiver_ecef_m[3],
+	const double satellite_positions_m[][3],
+	const double satellite_velocities_mps[][3],
+	const double satellite_clock_drifts_sps[],
+	const gps_tracking_measurement_t measurements[],
+	unsigned int count,
+	double receiver_velocity_ecef_mps_out[3],
+	double receiver_velocity_covariance_ecef_mps2_out[3][3],
+	double* receiver_clock_drift_mps_out,
+	double* residual_rms_mps_out)
+{
+	return gps_tracking_velocity_wls_internal(
+		receiver_ecef_m, satellite_positions_m,
+		satellite_velocities_mps, satellite_clock_drifts_sps,
+		measurements, count, receiver_velocity_ecef_mps_out,
+		receiver_velocity_covariance_ecef_mps2_out,
+		receiver_clock_drift_mps_out, residual_rms_mps_out,
+		false, NULL);
+}
+
+bool gps_tracking_velocity_wls_robust(
+	const double receiver_ecef_m[3],
+	const double satellite_positions_m[][3],
+	const double satellite_velocities_mps[][3],
+	const double satellite_clock_drifts_sps[],
+	const gps_tracking_measurement_t measurements[],
+	unsigned int count,
+	double receiver_velocity_ecef_mps_out[3],
+	double receiver_velocity_covariance_ecef_mps2_out[3][3],
+	double* receiver_clock_drift_mps_out,
+	double* residual_rms_mps_out,
+	uint32_t* excluded_measurement_mask_out)
+{
+	return gps_tracking_velocity_wls_internal(
+		receiver_ecef_m, satellite_positions_m,
+		satellite_velocities_mps, satellite_clock_drifts_sps,
+		measurements, count, receiver_velocity_ecef_mps_out,
+		receiver_velocity_covariance_ecef_mps2_out,
+		receiver_clock_drift_mps_out, residual_rms_mps_out,
+		true, excluded_measurement_mask_out);
+}
diff --git a/soc/software/gps_system/tests/test_gps_tracking_measurement.c b/soc/software/gps_system/tests/test_gps_tracking_measurement.c
index 9611f26..aa45c1a 100644
--- a/soc/software/gps_system/tests/test_gps_tracking_measurement.c
+++ b/soc/software/gps_system/tests/test_gps_tracking_measurement.c
@@ -78,6 +78,14 @@ static void test_cn0_and_mailbox_decode(void)
 		measurement.pseudorange_rate_mps,
 		expected_range_rate,
 		1.0e-9));
+	assert(close_to(
+		measurement.filtered_doppler_hz,
+		measurement.doppler_hz,
+		1.0e-12));
+	assert(close_to(
+		measurement.filtered_pseudorange_rate_mps,
+		measurement.pseudorange_rate_mps,
+		1.0e-12));
 
 	registers.MEASUREMENT_META &=
 		~(1u << GPS_TRCK_MEAS_META_LOCK_POS);
@@ -180,6 +188,86 @@ static void test_velocity_wls(void)
 		solved_velocity_covariance[0][1],
 		solved_velocity_covariance[1][0],
 		1.0e-12));
+	{
+		double clean_velocity[3];
+		double clean_covariance[3][3];
+		double clean_clock_drift;
+		double clean_residual_rms;
+		uint32_t clean_excluded_mask = UINT32_MAX;
+		assert(gps_tracking_velocity_wls_robust(
+			receiver_position,
+			satellite_positions,
+			satellite_velocities,
+			satellite_clock_drift,
+			measurements,
+			TEST_SATELLITES,
+			clean_velocity,
+			clean_covariance,
+			&clean_clock_drift,
+			&clean_residual_rms,
+			&clean_excluded_mask));
+		assert(clean_excluded_mask == 0u);
+		for(unsigned int component = 0u; component < 3u; component++)
+		{
+			assert(close_to(
+				clean_velocity[component],
+				solved_velocity[component],
+				1.0e-12));
+		}
+	}
+
+	/* One gross carrier burst must be isolated before aggregate ESKF fusion. */
+	measurements[2].pseudorange_rate_mps += 12.0;
+	double plain_velocity[3];
+	double plain_covariance[3][3];
+	double plain_clock_drift;
+	double plain_residual_rms;
+	assert(gps_tracking_velocity_wls(
+		receiver_position,
+		satellite_positions,
+		satellite_velocities,
+		satellite_clock_drift,
+		measurements,
+		TEST_SATELLITES,
+		plain_velocity,
+		plain_covariance,
+		&plain_clock_drift,
+		&plain_residual_rms));
+	double robust_velocity[3];
+	double robust_covariance[3][3];
+	double robust_clock_drift;
+	double robust_residual_rms;
+	uint32_t excluded_mask = 0u;
+	assert(gps_tracking_velocity_wls_robust(
+		receiver_position,
+		satellite_positions,
+		satellite_velocities,
+		satellite_clock_drift,
+		measurements,
+		TEST_SATELLITES,
+		robust_velocity,
+		robust_covariance,
+		&robust_clock_drift,
+		&robust_residual_rms,
+		&excluded_mask));
+	assert(excluded_mask == (1u << 2));
+	double plain_error_square = 0.0;
+	for(unsigned int component = 0u; component < 3u; component++)
+	{
+		double plain_error =
+			plain_velocity[component] - expected_velocity[component];
+		plain_error_square += plain_error * plain_error;
+		assert(close_to(
+			robust_velocity[component],
+			expected_velocity[component],
+			1.0e-8));
+	}
+	assert(sqrt(plain_error_square) > 1.0);
+	assert(close_to(
+		robust_clock_drift,
+		expected_clock_drift_mps,
+		1.0e-8));
+	assert(robust_residual_rms < 1.0e-8);
 }
 
 int main(void)