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# System identification using Extended Kalman Filter

12/27/2007 2:19 AM EST

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.

Thank you very much for your time and attention.
Best regards,
tvauce

tvauce

12/27/2007 12:35 AM EST

All of my variable have the relationship through a second order differential equation:
m*a+0*v+k*d=u
in which m is known constant, u is observed time history input and
dd/dt=v; dv/dt=a (time derivative of d and v, respectively)

Leroy.Smith

8/8/2011 1:14 PM EDT

Your state is [d,v,a]', the stiffness k is one of your coefficients. It will appear in the A matrix.

Ceto150