What does an odometry twin that is too clean do to a loop-closure gate?

research/loop-closure-twin

A chi-square loop-closure gate tuned in a too-clean odometry twin: exact real error 2.1× the claim at drift-sd ratio 2, rejected genuine closures compound into lock-out (9–16× the ungated error, growing with horizon), the gate halves aliasing error when the twin is right but is 8× worse than no gate when it is not, and ~30 measured drifts make the repair safe.

8 tests

What it found

A scalar position filter is tuned in a twin with drift variance T and gates loop closures by a chi-square test on its own covariance. With every closure accepted the real posterior variance is exact (1.47×, 2.14×, 4.03× the twin’s claim for real/twin drift-sd ratios 1.5, 2, 3; simulation within 1%), and genuine closures fail the 99% design gate 5% of the time at ratio 2. With the gate on, rejection compounds into lock-out: real error is 9–16× the ungated value at ratio 2 and 56–182× at ratio 3, growing with horizon. The gate halves error against aliased closures when the twin is right (0.52 vs 1.27) but is 8× worse than no gate at ratio 2 (13.9 vs 1.72), and a gate retuned with the real drift beats no gate only up to ratio 2. Fitting drift from measured ground truth fixes the median by 10 cycles but the lock-out tail needs about 30 (28% of trials lock out at 3). Stylised: scalar error, Gaussian drift, simulated not measured.

A figure from its own output

Figure produced by research/loop-closure-twin: variance_vs_rho — loop-closure-twin/experiments/variance_vs_rho.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.