Kalman Gain Interactive

Kalman gain intuition

Kalman example

P (prior variance): 2.00 R (meas noise): 4.00 x(−) (prior): 5.0 z (meas): 12.0

Gain K = P / (P + R) balances trust between prior (x(−), variance P) and measurement (z, noise R). Posterior: x(+) = x(−) + K (z − x(−)), P(+) = (1 − K) P.

Toy problem: find the hidden number (1D scalar Kalman update)

True value t: 10.0 Initial P0: 2.00 R (meas variance): 4.00 Initial x0: 5.0

Each click samples z = t + N(0, R). With current uncertainty P and measurement variance R, the scalar Kalman gain K = P/(P+R). Update: x ← x + K (z − x), P ← (1 − K) P. Watch the estimate converge and K shrink as P decreases.