Norm of Covariance Matrix

Hi to all,

I have been also confused about the covariance matrix of the Kalman
filter. I have a Kalman filter which has 9 states and therefore 9 X 9
error covariance matrix which is updated at the every time step.

My question is;

How can i be sure that the Kalman filter works properly by using the
error covariance matrices. Should the norm of the error covariance
matrix converge to zero or any constant value?

The same problem is valid for the Kalman gains. Should the Kalman
gains converge to zero or to any constant value?

Are there any other metrics for evaluating the Kalman filter
performance?

Best regards from Germany

Volkan Ozturk

Robert Bosch GmbH

Stuttgart/Germany

On May 15, 2:08 am, WalkyTalky <ozturkvol...@gmail.com> wrote:
> Hi to all,
>
> I have been also confused about the covariance matrix of the Kalman
> filter. I have a Kalman filter which has 9 states and therefore 9 X 9
> error covariance matrix which is updated at the every time step.
>
> My question is;
>
> How can i be sure that the Kalman filter works properly by using the
> error covariance matrices. Should the norm of the error covariance
> matrix converge to zero or any constant value?
>
> The same problem is valid for the Kalman gains. Should the Kalman
> gains converge to zero or to any constant value?
>
> Are there any other metrics for evaluating the Kalman filter
> performance?
>
> Best regards from Germany
>
> Volkan Ozturk
>
> Robert Bosch GmbH
>
> Stuttgart/Germany

The Kalman gains and error covariance matrix converge in the
stationary case to the stationary Wiener filter.
The solution of the Ricatti equation is equivalant to a spectral
factorization and remooval of the {.}+ brackets in a Wiener filter.
You can possibly test your system on a simulated stationary noise case
to see if it converges.

Best to look at the mean-square error to see what happens to it -
reduces to a minimum.

The Kalman gain matrix will never converge to zero. Yes the norm of P
will reduce over time in the statioanry case. In the non-stationary
case you hold your breath and hope you have ag ood enough model that
it will track.

K.