Norm of Covariance Matrix

The covariance array will converge to a constant value as long as the
process and measurement noise doesn't change.


The Kalman gains better not converge on zero because then there would
be no correction between the estimated and actual feedback.
The Kalman gains will converge on a non zero values.


I make simulations where I know what the process is doing because I
generate the transfer function.  I use the transfer function to
simulate the process but add process noise and measurement error to
generate feed back that resemble reality. I then use that data as the
input to the Kalman filter and compare the Kalman filter results with
the process without the noise. There isn't much  you can do to tweak
the output of the Kalman filter except to change the Q and R arrays
but if you do that you might as well use a steady state filterr and
just adjust the bandwidth to get the desired results.  Another thing
you should consider is calculating the Kalman gains ahead of time
( steady state ).   It will take a lot of processing time to calcalute
9 Kalman gains real time.

Peter Nachtwey

Hi Peter,

Another question of mine is about the transfer function of an observer
designed using a Kalman filter. How can we convert the observer
equation to a good form to analyze the frequency response of the
oberserver?

The observer equation is:

xdot=Ax+Bu+L(y-Cx);

where L is the Kalman gain, y is the measurement and the input u=0.

I want to get the transfer function between some states inside x and
y. I have acceleration estimates inside x, and y measurements are
speed measurements. If I take the input as y, and choose the
acceleration states from x, I am supposed to get a differentiator
characteristic.

I have 9 states which means my Kalman gain is a vector with 9
elements. My Kalman gain is updated in everytime step and converges to
constant values for all of the states.

Regards

Volkan