How much does a wrong process-noise guess cost a Kalman filter?

What it found

Exact steady-state MSE of a scalar Kalman filter run at the wrong process noise q_a = λq, matched to simulation within 1%. Underestimating costs far more than overestimating: at λ = 1/100 the excess is ×7.4 against ×1.6 at λ = 100; the over-estimate is bounded (MSE → r) and the under-estimate is not. The filter’s claimed variance is 5× too small at λ = 1/10. The gap closes at high signal-to-noise. Textbook-level and stylised: scalar, steady state, Gaussian.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

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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.