FGO NHC/ZUPT FIX-rate audit

Objective

Determine whether vehicle-motion constraints improve the float state presented to ambiguity resolution without relaxing LAMBDA, adding a TDCP promotion rule, or increasing wrong FIX. NHC and ZUPT remain default-off until every staged gate passes.

Tokyo run1 is the only development run. Run2 stays sealed until a full-run1 activation passes, and run3 stays sealed until the unchanged run2 activation passes.

Research and code audit

• Kilic et al. add zero-velocity information to a GNSS/INS factor graph for wheeled robots: https://arxiv.org/abs/2112.07176.
• Liu et al. formulate NHC as a factor in ground-vehicle FGO and emphasize the no-side-slip/no-vertical-motion assumption: https://doi.org/10.3390/mi13091400.
• The local tightly-coupled-gnss-imu-fgo reference applies body-frame lateral/vertical velocity constraints and gates ZUPT with causal IMU-window statistics plus an optional previous-velocity check.

The current C++ NHC residual and GTSAM Jacobians use the correct body-to-ENU rotation convention. The ZUPT statistics do not exactly match their stated reference, however: the reference computes the RMS vector deviation from the window mean, while C++ computes the standard deviation of per-sample vector norms. The latter can hide directional vibration at nearly constant norm. This discrepancy must be corrected and covered by a deterministic test before any activation result is accepted.

The other central risk is observability. Quiet constant-speed travel can look stationary to accelerometer/gyro dispersion, while a true stop whose velocity estimate already drifted above the 0.5 m/s gate cannot receive ZUPT. Therefore removing the velocity gate or tuning only IMU thresholds is out of scope.

Frozen development protocol

Gate 0: correctness and non-interference

• correct the IMU-window statistic to the documented vector-deviation RMS;
• unit-test directional vibration, true stationary data, ZUPT speed rejection, NHC speed/turn rejection, and NHC residual/Jacobians;
• with both switches off, the shipping solution remains unchanged.

Gate 1: fixed 500-epoch development slice

Use a 500-epoch Tokyo run1 replay beginning at source epoch 5000. It was selected before any NHC/ZUPT replay because the corresponding preserved full-run window contains 60 correct FLOAT opportunities and zero wrong FIX epochs, unlike the nearly saturated opening 500 epochs. --start-epoch starts a fresh solve at epoch 5000 rather than retaining the full run's solver history, so its baseline is frozen independently before any active constraint replay: 333 FIX, 167 FLOAT, zero NONE/non-finite, and 0.024057 m fixed horizontal RMS (21.1719 s solver wall time).

Compare exactly four configurations using the shipping preset:

1. baseline;
2. NHC only;
3. ZUPT only; and
4. NHC + ZUPT.

A configuration advances only with:

• zero additional wrong FIX epochs;
• zero lost correct FIX epochs;
• at least three additional correct FIX epochs;
• no additional NONE/non-finite epoch;
• fixed horizontal RMS and P95 regression no greater than 5%; and
• solver wall-time overhead no greater than 10%.

No sigma or detector threshold is tuned after this four-way replay. If none passes, stop activation and retain only corrected tests/telemetry.

Gate 2: full run1

Run only Gate-1 survivors over all 11,905 epochs. Require zero increase in wrong-FIX distance, no decrease in correct-FIX distance, no solver/matched- distance regression, at least +0.2 percentage points correct-FIX distance, and no more than 5% fixed RMS/P95 regression.

Gate 3: sealed holdouts

Freeze the configuration after run1. Run2 and then run3 once each. Each must independently have zero wrong-FIX-distance increase, no correct-FIX-distance decrease, no solver/matched-distance regression, and at most 5% fixed RMS/P95 regression. Any failure ends activation without tuning against that run.

Result

Gate 0 passed. The focused deterministic tests cover directional vibration, ZUPT application, NHC application, and turn rejection. A 500-epoch monitor-off/monitor-on replay had zero differences in every pre-existing CSV field; only the ten new motion-diagnostic fields changed.

The frozen Gate-1 replay produced:

configuration	correct FIX	wrong FIX	added correct	added wrong	fixed horizontal RMS	P95	wall time	result
baseline	333	0	--	--	0.024085 m	0.0340 m	21.1719 s	reference
NHC	333	0	0	0	0.023850 m	0.0334 m	18.4081 s	fail: no FIX gain
ZUPT	333	0	0	0	0.023802 m	0.0330 m	20.8266 s	fail: no FIX gain
NHC + ZUPT	333	2	0	2	0.961176 m	0.0330 m	24.6932 s	fail: wrong FIX, RMS, runtime, and no correct-FIX gain

The combined configuration changed two baseline FLOAT epochs into wrong FIX at TOW 188564.0 and 188564.2; their 3-D errors were 22.399 m and 22.361 m. The shadow observed 87 ZUPT and 316 NHC candidates in the baseline. NHC-only applied 316 factors; ZUPT-only applied 108 as its velocity feedback changed later candidate decisions. Neither changed the FIX classification.

No configuration passes Gate 1, so the audit stops without a full run1 or any inspection of sealed run2/run3. NHC and ZUPT remain default-off. The accepted deliverable is limited to the corrected vector-deviation statistic, authority-neutral telemetry, deterministic tests, and the reproducible offline A/B scorer. The machine-readable result is generated with:

python scripts/analysis/analyze_fgo_motion_constraint_ab.py `
  --baseline build-ffrt-msvc/validation/tokyo1_motion_e5000_n500_baseline.csv `
  --baseline-runtime-s 21.1719 `
  --variant nhc=build-ffrt-msvc/validation/tokyo1_motion_e5000_n500_nhc.csv `
  --runtime-s nhc=18.4081 `
  --variant zupt=build-ffrt-msvc/validation/tokyo1_motion_e5000_n500_zupt.csv `
  --runtime-s zupt=20.8266 `
  --variant both=build-ffrt-msvc/validation/tokyo1_motion_e5000_n500_both.csv `
  --runtime-s both=24.6932 `
  --json build-ffrt-msvc/validation/tokyo1_motion_e5000_n500_ab.json