What does a Kalman filter tuned in an ideal-sensor twin cost on a quantizing real sensor?

research/quantization-twin

A Kalman filter tuned in an ideal-sensor twin, run on a quantizing sensor: twin gain costs +11% (R=1, D=4) to +64% (R=0.01), Sheppard R+D²/12 retune is within 1% of best, but its MSE claim under-predicts by up to 43% once the step exceeds the state's scale.

6 tests

What it found

A twin whose sensor is ideal (y=x+v) tunes the gain for variance R, but the real sensor rounds to a step D. In simulation (a=0.9, Q=1) the twin’s gain costs +11% at D=4 for R=1, and up to +64% when R=0.01. Retuning on R+D²/12 (Sheppard) lands within 1% of the best gain in all 12 configurations, but its closed-form MSE claim under-predicts the real error by 28–43% once D exceeds the state’s scale (1.61 vs 2.82 at D=8, R=0.01). Stylised: scalar linear-Gaussian plant, fixed gain, one seed per cell.

A figure from its own output

Figure produced by research/quantization-twin: regret — quantization-twin/experiments/regret.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.