need helps about Kalman filter

Hello everyone. I used measurement position to estimate velocity by Kalman filter. But in simulation, Kalman gain change quickly and then remain constant when position and velocity continue to change (for example, position and velocity change in 0->0.5(s) and 3->4(s). But Kalman gain only change only 0->0.1(s)and then remain constant). My question is why Kalman gain is still constant when postion and velocity change? Sorry for my bad English.

[Jan]

I've deleted the duplicate thread with the identical question. I assume, this has been created by accident.

Perhaps there is a bug in your code. Could you provide a minimal example accompanied by your code, such that we can reproduce the problem? Otherwise too much guessing is required.

[Khoa]

I only used Simulink to estimate velocity.

"Predict"

x[k-] = Ax[k-1]

P[k-] = AP[k-1]A' + Q

"Correct"

K[k] = P[k-]H'/(HP[k-]H' + R)

x[k] = x[k-] + K[k] (z[k] - Hx[k-])

P[k] = (I-K[k]H) P[k-] With

A=[1 T; 0 1] (T is sampling time)

Q,R mean process noise and measurement noise. I set constant for them.

H=[1 0] (use only measurement position z[k] as input)

It seems be likely steady state Kalman filter I think (because Q,R are constant). Maybe I'm wrong when set matrix A because velocity is not same value when time = 0->0.5(s) and 3->4(s). And the result that Kalman gain is not change at that time. Can someone give me some helps?

Answer 1

[John Petersen]

The Kalman gain is not a function of the states. It is only a function of the covariances and the model of the system and measurements. If the system model is unchanging and the covariances converge, then the gains may also converge.