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Error using Kalman function - cannot compute stabilizing Riccati solution

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Please see below a snippet of my code:
sys=ss(A_ae_control,B_ae_control,C_ae_control,0);
Qn=0.0001;
Rn=0.01*eye(size(C_ae_control,1));
[kest,L,P]=kalman(sys,Qn,Rn);
I can't seem to figure out why this won't run. I keep getting the following error:
Cannot compute the stabilizing Riccati solution P for the Kalman filter.
This could be because:
* RN is singular,
* [QN NN;NN' RN] needs to be positive definite,
* The E matrix in the state equation is singular.
Any insight would be appreciated. I have attached my A, B and C matrices.
Also, is it possible to somehow create a Kalman estimator without any measurement noise (only a disturbance). I tried setting Rn to 0 but not sure why this does not work.
  4 Comments
Emir Acevedo
Emir Acevedo on 13 Sep 2022
I had designing a LQR controller and after an Kalman Filter. For mi satellite control, I used the same Q and R matrix in Ricatti to solve Kest. May that can fix your problem.
Regards.

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Answers (1)

Ivo Houtzager
Ivo Houtzager on 17 Apr 2023
Your state-space model is probably not a minimal realization, in other words not fully obervable or not fully controllable. Perform the function minreal to remove unobservable or uncontrollable states.
sys=ss(A_ae_control,B_ae_control,C_ae_control,0);
sys=minreal(sys);
Qn=0.0001;
Rn=0.01*eye(size(C_ae_control,1));
[kest,L,P]=kalman(sys,Qn,Rn);
  2 Comments
rajesh r
rajesh r on 17 Apr 2023
My model is:
A = [1 0.01; 0 1];
B = [0 ; 0];
C= [1 0];
D = 0;
after minreal,
the complete A matrix is zero
Ivo Houtzager
Ivo Houtzager on 17 Apr 2023
You have no inputs defined, because both B and D are zero. Thus your model is fully uncontrollable. So you have review your model inputs for correctness.

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