A twin whose sensor never produces outliers: does an innovation gate help or hurt the real estimator, and what does it do after a jump?

research/gate-twin

Gaussian-sensor twin vs a real sensor with outliers under an innovation gate: the twin says the gate costs 8.5% MSE, the real sensor gains 3.0× from it, the worst outlier scale for a gated filter is finite (κ≈4) while ungated error grows as κ², and a gate locks out recovery from a jump for ≈76·D² steps. Stylised.

14 tests

What it found

With a Gaussian-sensor twin an innovation gate (z = 2.58) costs 8.5% of the update MSE, since every gated measurement is good data; with 5% real outliers at 10× the noise scale the same gate cuts the MSE 1.74 → 0.58 (3.0×) while still passing 28% of the outliers. The ungated error grows like κ² in the outlier scale, the gated error is bounded and worst at a finite κ* ≈ 4, and a better-tuned gate width gains only 0–6%. After a jump D in a random-walk state the gate rejects the correct measurements and re-convergence takes ≈ 76D² steps (30,512 at D = 20) against 30 with no gate. Exact post-update MSE checked by quadrature and Monte Carlo. Stylised: scalar update, simulated outliers, simplified covariance rule in the jump experiment.

A figure from its own output

Figure produced by research/gate-twin: mse_vs_kappa — gate-twin/experiments/mse_vs_kappa.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.