FGO multi-band AR FIX-rate audit¶
Decision¶
Keep conditional multi-band ambiguity resolution shadow-only. The two-stage candidate generator is useful telemetry, but the available Tokyo run1 evidence does not support turning its candidates into FIX labels or graph priors.
This work intentionally does not make TDCP the main FIX mechanism. TDCP and Doppler remain complementary arc-integrity evidence; ambiguity acceptance is controlled by integer-estimation evidence and independent integrity checks.
Research basis¶
- Teunissen and Verhagen explain why ambiguity acceptance must control failure probability, and why a conventional ratio threshold is not by itself a guaranteed failure-rate test: https://doi.org/10.1007/978-3-540-74584-6_22.
- Odijk, Arora, and Teunissen describe partial ambiguity resolution by choosing a subset whose bootstrapped success-rate lower bound exceeds a required probability: https://doi.org/10.1017/S037346331400006X.
- Hou, Verhagen, and Wu evaluate a two-step success-rate criterion for PAR: https://doi.org/10.1016/j.asr.2016.07.029.
- RTKLIB supplies the operational comparison for multi-frequency arc handling, ambiguity validation, and consecutive-fix holding: https://github.com/tomojitakasu/RTKLIB/blob/master/src/rtkpos.c.
- GICI-LIB supplies the tightly-coupled comparison for ambiguity lifecycle and geometry-free cycle-slip handling: https://github.com/chichengcn/gici-open/blob/master/src/gnss/ambiguity_common.cpp.
- Suzuki's GNSS Odometry work shows the value of TDCP in a factor graph when cycle slips are explicitly detected and estimated, supporting its use as continuity evidence rather than an unconditional FIX authority: https://arxiv.org/abs/2312.02424.
The resulting design follows three constraints: select a primary subset, condition the remaining Gaussian ambiguity distribution correctly, and never activate a candidate until an offline truth audit demonstrates a low empirical failure rate under deployable gates.
Implementation¶
FGOConfig::monitor_conditional_multiband_ar is opt-in and independent of the
existing satellite-exclusion ratio-impact monitor. For every eligible epoch:
- choose one primary band per satellite using the established deterministic selector;
- run top-2 LAMBDA on the primary float vector and covariance;
- if its configured ratio gate passes, compute the secondary conditional mean and Schur-complement covariance given the primary integer candidate;
- run top-2 LAMBDA on the conditional secondary problem;
- reconstruct a complete counterfactual integer vector and position; and
- export dedicated ratios, bootstrapped success rates, counts, position, and float/IMU separation telemetry.
No estimator state, ambiguity generation, hold state, FIX/FLOAT status, or reported position reads the shadow result.
Reproducible 500-epoch A/B baseline¶
Dataset: PPC Tokyo run1. Both arms use the README fixed-lag-5 multi-frequency
preset including geometry-free slip reset. The shadow arm adds only
--conditional-mf-shadow; both use the same cached input problem.
| Metric | Baseline | Conditional shadow |
|---|---|---|
| Epochs | 500 | 500 |
| FIX epochs | 499 | 499 |
| Correct FIX, 3D error <= 0.5 m | 499 | 499 |
| Wrong FIX | 0 | 0 |
| Positioning epochs within 0.5 m | 500 | 500 |
| Conditional candidates | 0 | 197 |
| Changed status/position/ratio/AR-outcome rows | - | 0 |
Artifacts are
build-ffrt-msvc/validation/multiband_fixrate_baseline_e500.csv and
build-ffrt-msvc/validation/multiband_fixrate_shadow_e500.csv. Their SHA-256
digests are respectively
BE3AFB5280E00767AE23856BE5351FE2C568A5C0F35DD908E766E15A27B31E6E and
F4766B1BDC442FA3EAF276A954C4B1D36EC1A6711CC6DEF5F1AED9836CD646CE.
Promotion audit¶
A historical full-length Tokyo run1 shadow replay generated 1,376 complete two-stage candidates. Only 77 occurred on epochs not already labelled FIXED; 41 of those candidates were within 0.5 m and 36 were wrong. Tight IMU-position agreement did not isolate a safe region: at 0.05 m separation, 9 candidates were correct and 28 were wrong. These figures use reference truth only after the solver run and are therefore evaluation results, not runtime inputs.
Consequently, ratio passage, high bootstrapped success rate, and proximity to the IMU prediction are insufficient for activation on this data. Promoting the shadow now would raise raw FIX rate while materially worsening wrong FIX/FIX.
Next gate before activation¶
Activation requires a fresh full three-run Tokyo replay and a truth-free gate that adds genuinely independent evidence, such as surplus satellites excluded from the candidate construction or a clock-safe GF-triggered Doppler/TDCP arc check. It must improve correct-FIX distance without increasing wrong-FIX distance on any held-out run. Until that gate exists, the shipping preset is unchanged.