Hello everyone,
I have experience in UKF but seem that when involve to EKF, things start to out of the track!
I followed the instruction on Wiki of EKF about Discrete-Time predict & update equations but have a struggling with Sk.
https://en.wikipedia.org/wiki/Extended_Kalman_filter
Based on my application of Parameter & State estimation of Mechanical System , my State Equation (4 disp, 4 velo, 4 stiffness, 4 damper) is 16x1 so the Initial Covariance Matrix is 16x16.
However, the Measurement Equation (4 disp, 4 velo, 4 accel) is only 12x1 so the Transition Measurement Matrix is only 12x12
So it is IMPOSSIBLE when I try to use: Sk = Hk * Pk * Hk^T + R -> I can't calculate Sk because (12x12) * (16x16) * (12x12)^T is non-sense!
Can you please point out the reason for this issue?
I would be appreciated if you can help me find a more possible way to do this!
Thank you & wish those who care have a nice day!
#EKF
If the number of measurements are 12 then the "H" matrix must be 12x16 since it relates the state vector with the measurement vector. This is valid for also the nonlinear case with the jacobian of h(.) with respect to x.
After taking the the jacobian of h(.) if there is no damper related term, cascading a 4x4 zero matrix to H (to obtain a new 12x16 H) may work.
I have found out the answer thanks to the suggestion of Mr. Ipek so my mistake is try to derive Measurement Transition Matrix by the Measurement Variable (12x1) when I should derive it by State Variable (16x1)
Eventually, my Measurement Transition Matrix Hk will have the dimension of (12x16)!
Thank you again, Mr. Ipek!
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