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Kalman filter tuning

Process noise Q: 0.40 Measurement noise R (sensor σ): 6.0 km/h Sensor update interval: 1.0 s

Traffic scenario

Live Kalman state

True speed—

Last measurement—

Estimate (speed)—

Estimate std (±1σ)—

Estimated trend—

Variance P₀₀—

Kalman gain K (speed)—

Time since measurement—

Accuracy so far

RMSE — Kalman estimate—

RMSE — raw sensor—

Estimate improvement—

State x = [speed, trend]. Every tick runs the real predict step x⁻=Fx, P⁻=FPFᵀ+Q. Each sensor reading runs the real update step: K=P⁻Hᵀ(HP⁻Hᵀ+R)⁻¹, x=x⁻+K(z−Hx⁻), P=(I−KH)P⁻(I−KH)ᵀ+KRKᵀ (Joseph form). Watch P₀₀ shrink on every update and grow during the predict-only gaps, especially during a sensor dropout.