trackingKF does not output Kalman Gain

Hello,

why does trackingKF do not output the Kalman Gain?

Also, I think that an option to specify 'time-varying' or 'time-invariant' KF would be useful.

Best Regards

Christian

Answer 1

[Prashant Arora]

Hi,

As of R2024a, trackingKF does not output Kalman gain. We will consider this enhancement in the future releases.

As a workaround, you can compute Kalman gain using the output of the residual method.

predict(kf);
[r, S] = residual(kf, z);
H = kf.MeasurementModel;
P = kf.StateCovariance;
kalmanGain = P*H'/S;

Hope this helps.

Prashant

[Christian Busse]

Hello, thanks for the response.

My workaround looks similar:

S = H*P*H' + R;

B = H*P';

K = (S \ B)';

Do you think both approaches are equal or maybe the other is numerically more robust/efficient in MATLAB?

[Prashant Arora]

Hi Christian,

Your approach looks equivalent to me.

You could consider modifying it a bit to reduce one transpose operation. However, I don't believe its going to have any noticeable impact on performance.

S = H*P*H' + R;
B = P*H';
K = B/S;

The only reason to use "residual" method would be to extend the same method to other Gaussian filters such as trackingEKF and trackingUKF. Internally, trackingEKF and trackingUKF also use numerically robust approach to compute the "S" (innovation covariance) using square root implementation. However, trackingKF is still plain vanilla (no square root) as of R2024a. So, your workaround looks equivalent trackingKF. We'll consider enhancing trackingKF in a future release to also use square-root implementation.

Hope this helps.