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Phase 7: realistic bearing error — the frozen fused tracker still beats the frozen IMM, but T2 alone is more robust

· 3 min read

So far every tracker in this project has seen only white bearing noise. Real bearings also carry correlated error and a slowly drifting bias. Phase 7 asks one question: does the fused tracker's G5 advantage over the reference IMM survive that error, with nothing re-trained or re-tuned?

The setup​

The owner chose three things:

  • frozen trackers;
  • an error model made of a correlated term (sd 1.0°, 30 s) and a drifting bias (sd 0.5°, 20 min). This setting is double the one first proposed. At σ = 1° the total bearing error goes from 1.0° to 1.5°;
  • G5's rules, unchanged.

The generator adds the error from its own random stream, so each scenario can be regenerated without it. The two versions have identical geometry and identical white noise, which makes a paired clean comparison possible.

Result: G5 passes (seed 218, 40,000 scenarios)​

Fused / IMMRatio (97.5% CI)Limit
Overall range0.766 [0.755, 0.778]< 1
Overall course0.907 [0.897, 0.918]< 1
Settled range0.774< 1.1
Settled course0.875< 1.1
Settled speed0.907< 1.1

Validation on seed 217 had already shown much the same: 0.777 for range and 0.922 for course. Five independent reviewers agreed the verdict is right, and one reproduced it byte for byte.

What the pass does not show​

The absolute errors are large: the fused tracker's 90th-percentile course error is 106°. The panel narrowed the claim.

Median error, all G5 rowsRangeCourseSpeed
Fused tracker13.2%27°2.6 kt
IMM (reference)17.3%30°2.9 kt
T2 alone12.1%26°2.9 kt
EKF16.8%31°2.4 kt
Batch least squares17.6%47°2.4 kt
Naive40%90°3.9 kt
  • T2 alone beats the fused tracker on range, by 1.10 × [1.08, 1.11] overall. Its error grows least under realistic error (1.47 × its clean value, against the IMM's 1.82 ×). The IMM's range ends up biased about 7% short under the drifting bias, while T2 stays nearly unbiased. The fusion setting, frozen from clean data, plausibly gives T2 too little weight; k was not re-swept. Fusing keeps one coherent track state, but under this error it is not the best range estimator.
  • On straight legs, classical methods still win. On settled rows the EKF beats the fused tracker on course (10.6° against 13.5°) and on speed, and batch least squares does too (8.1°, 1.8 kt). Before any manoeuvre, batch least squares is best of all: 7.3% range and 2.2° course.
  • The reference was frozen, not adapted. Neither filter models correlated or bias error. An IMM with an inflated measurement noise or a bias state might close the gap; this phase does not test that.
  • Every tracker is much worse. Median range error rises 1.5–1.8 × overall and about 2 × on settled rows.
  • Not measured. Filter consistency (NIS, NEES) and covariance health (non-PD steps) under correlated error.
  • Scope. The result covers one error model at one severity, σ = 1° rows and simulated data.

The one-line version​

Under one setting of realistic bearing error, the frozen fused tracker keeps its G5 advantage over the frozen IMM, which was not adapted to this error. The learned range (T2) is likely what makes it robust (a hypothesis), and on its own T2 is more robust still. The classical filters remain better on straight legs.

Record: experiments/20261108-p7-g5/ (verdict, baselines, clean comparison, panel review); validation experiments/20261108-p7-val/; decision experiments/20261108-p7-decision/; G0 experiments/20261108-g0-p7-r1/; spec 019.