2D Kalman Filter — Position vs Time Companion

Kalman Filter (2D companion)

True-motion pattern Measurement noise R: 9.0 Process noise Q: 0.05

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Step k0

Uncertainty σ²—

Uncertainty σ—

Estimate error—

Measurement error—

Kalman gain K—

RMSE (filtered)—

RMSE (measured)—

Predict: x' = Fx, P' = FPFᵀ + Q. Update: K = P'Hᵀ(HP'Hᵀ + R)⁻¹, x = x' + K(z − Hx'), P = (I − KH)P'. The shaded band is ±2σ around the filtered estimate — watch it shrink as measurements arrive.

true measured filtered (Kalman) ±2σ band