System identification using Extended Kalman Filter

Dear friends,

I am trying to solve a system identification problem using EKF. The state which I need to estimate include displacement (d), velocity (v) and system stiffness (k), i.e. X=[d v k]'.

Because only d & v change with time, time derivative of state vector X will produce zero value for the third term (since k=const), i.e. dX/dt=[v a 0]' (in which a is acceleration).

Time update equation using EKF:

X(k+1)=X(k)+dX/dt*T

where T is time step.

Following this equation, my stiffness component k of the state vector X can not be updated meaning that the initial guess value of k is kept unchanged through time update process.

In the observation equation update

X(k+1)=X(k+1)+K*(z(k+1)-h(X))

My observation is displacement d, the Kalman gain K has the size of 3x1 with the last component having zero value at every time instant. My stiffness component of the state vector is thus can not be updated either.

Hence, following EKF procedure, my last component of state vector k can not be updated meanwhile d & v is updated correctly.

Could you please kindly advise my?

Thank you very much for your time and attention.

Best regards,

tvauce