feat(pps): add adaptive disciplined timing loop

soc/software/pps_python/pps_model.py

@@ -23,9 +23,9 @@ import numpy as np
 
 
 C = 299_792_458.0
-RF_HZ = 16_368_000.0
+RF_HZ = 16_367_981.0
 TRACKING_HZ = 125_000_000.0
-SAMPLES_PER_CODE = 16_368.0  # samples per millisecond in the C code
+SAMPLES_PER_CODE = 16_367.981  # physical RF samples/ms used by the C code
 CODE_FREQ_BASIS = 1.023e6
 START_OFFSET_MS = 68.802
 START_OFFSET_S = START_OFFSET_MS / 1000.0
@@ -139,6 +139,7 @@ class EpochResult:
     transmit_true_s: float
     reference_arrival_true_s: float
     snapshot_ready_true_s: float
+    reference_tracking_tick_raw: int
     reference_tracking_tick: float
     reference_abs_sample: float
     reference_svid: int
@@ -642,10 +643,12 @@ class ReceiverEpochSimulator:
         tracking_tick_continuous = float(self.tracking_clock.ticks_at(raw_event_true_s))
         tracking_tick_raw = int(np.floor(tracking_tick_continuous))
         # The software correction refers to the code boundary before the raw
-        # RF edge. Apply the same time displacement to the tracking timestamp.
-        tracking_tick_corrected = tracking_tick_raw - (
-            rem / CODE_FREQ_BASIS
-        ) * (TRACKING_HZ / RF_HZ)
+        # RF edge. The mailbox accepts an integer 125 MHz epoch counter, so
+        # mirror the C implementation's nearest-tick rounding.
+        capture_correction_ticks = round(
+            (rem / CODE_FREQ_BASIS) * (TRACKING_HZ / RF_HZ)
+        )
+        tracking_tick_corrected = tracking_tick_raw - capture_correction_ticks
         return ChannelMeasurement(
             satellite=satellite,
             satellite_position_m=satellite.ecef_m.copy(),
@@ -725,6 +728,7 @@ class ReceiverEpochSimulator:
             transmit_true_s=transmit_true_s,
             reference_arrival_true_s=reference.arrival_true_s,
             snapshot_ready_true_s=snapshot_ready,
+            reference_tracking_tick_raw=reference.tracking_tick_raw,
             reference_tracking_tick=reference.tracking_tick_corrected,
             reference_abs_sample=reference.corrected_abs_unwrapped,
             reference_svid=reference.satellite.svid,