What does a too-clean odometry twin do to a SLAM loop-closure gate?

What it found

A back end accepts a loop closure when its squared residual is below a gate; true closures are N(0, s²I), aliased ones are wider, and the cost is a weighted sum of two chi-square probabilities with a closed-form optimal gate in 2-D. A twin whose odometry noise is half the real value picks a gate that claims a cost of 0.094 and 2.1% of true closures rejected; in reality it rejects 38.2% (checked against simulation), costs 4.4× the claim and has 62% regret; a conventional α = 1% gate rejects α^1/ρ2 = 32%. A too-pessimistic twin (ρ = 0.5) is not safe either (145% regret), regret depends strongly on how costly a false closure is, a fixed inflation factor is a bet on the true noise, and re-fitting the variance from about 59 ground-truthed closures brings regret under 1% of the twin’s. Stylised: isotropic Gaussian 2-D residuals, hard gate, known costs, no real odometry data.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
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More in Digital twins & sim-to-real

• What does an odometry twin that is too clean do to a loop-closure gate?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.
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• What does a simulator tuned on one-step odometry noise get wrong about drift, relocalisation and loop closure?A twin tuned on one-step odometry noise cannot see drift: variance ratio exactly 1+(T−1)ρ, relocalisation interval 3.4× too long (real miss 51.6% vs 5%), twin-tuned loop-closure gate recall 0.64 at T=200, closed-loop runaway, aliasing limits calibrated gates.
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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.