◆ LIT — verified / checkable
The Kalman filter fuses a motion prediction with each noisy measurement, weighting them by their uncertainties: the gain K = P/(P+R) blends prediction variance P against measurement variance R, and the fused estimate's variance is smaller than either input's. The instrument runs a true moving target, scatters measurements around it with the chosen noise, and tracks with the predict-then-update loop — the filtered error settles well below the raw measurement error (reported live), and the uncertainty ellipse shrinks then holds. Optimal linear estimation, the real thing that flew Apollo and smooths every GPS.
▲ AMBER — the figure
A constant-velocity 1-D-per-axis toy with fixed process noise, not the full matrix Kalman filter; a real one models correlated states, manoeuvres and a proper covariance. The core — gain from variances, fused error below the measurement — is exact.
a point is fixed from THREE — and the point they fix is Top, at the centre.