Transfer Function of an Observer designed by Kalman filter

Hi to all,

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