I get Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN. What does this mean? and how can I fix it?

I don't understand what is going wrong with my code!! I would copy the code but it is very long! However, I get this error in the fourth line of the code below.

   % Extended Kalman Filter
  % EKF Cycle
  Pstar=A*P*A'+F*Q*F';
  % Estimate the state
  [~,xest]=ode45('PlantModel',[t(k),t(k+1)],x(k,:)); % Estimation of states
  x(k+1,:)=xest(end,:);                              % Assign a variable to the estimated states
  % Correction
 L=inv((C*Pstar*C'+R))*C*Pstar;                     % Update the value of the observer
     P=(eye(3)-L'*C)*Pstar;                             % Update the Estimation Error
     x(k+1,:)=(eye(3)-L'*C)*x(k+1,:)'+L'*y(k+1,:)';     % Update the States

[Suhan]

I understand that you would like to know the reasoning behind the warning message you are receiving.

The warning message itself is self explanatory. That is, you are tryning to take the inverse of a singular matrix. In this case, in the line 4, the matrix (C*Pstar*C'+ R) is 'nearly' singular and you are trying to take the inverse of this matrix using inv() function. The inverse function inv() requires the input matrix to be a well conditioned matrix. Since, in your case, (C*Pstar*C'+R) is probably ill-conditioned, MATLAB will throw a warning message.

How close a matrix is to be singular ( I mean, 'well' or 'ill' conditioned ) is determined by the condition number of the matrix. A large condition number implies the matrix is closer to the singularity (i,e Condition number is inversely proportional to the 'closeness' to singularity).

To fix this warning, you need to make sure you are giving a well-conditoned matrix to inv(). That is, check why (C*Pstar*C'+R) is singular. You need to fix this first.

I hope you will find this post useful.

[Walter Roberson]

I would extend this and say that you are probably trying to take the inverse of an all-zero matrix or perhaps an empty matrix

[Jan]

[MOVED from flags] rui gao wrote:

Useful

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