Numerical issues with UKF and SR-UKF

Error using cholupdate
Downdated matrix must be positive definite.

Error in Copy_2_of_UKF_Case1 (line 311)
S{k} = cholupdate((Sm{k}),U(:,i),'-');

Answer 1

[Vinay]

Hii Oussama ,

The “chol” function in the MATLAB does the Cholesky factorization of the matrix. The matrix must be symmetric positive definite for Cholesky factorization, but in the code the matrix “Rx” is not symmetric positive definite causing the error in factorization.

Sm{k} = cholupdate(Rx,Wc(1)*(xhi{k}(:,1)-xhm{k}),'-')';

The flag output of the “chol” function indicates the index of the pivot position where the factorization failed.

% flag to check the position where pivot failed 
[R,flag] = chol(Rx)

The following function check whether matrix is positive definite.

try chol(Rx)
    disp('Matrix is symmetric positive definite.')
catch ME
    disp('Matrix is not symmetric positive definite')
end

The error is due to the "Rx" matrix which is not symmetric positive definite causing error in the "Sm{K}" calculation

You can refer to the following documentations for “chol” and “cholupdate”:

• https://www.mathworks.com/help/matlab/ref/chol.html
• https://www.mathworks.com/help/matlab/ref/cholupdate.html?searchHighlight=cholupdate&s_tid=srchtitle_support_results_1_cholupdate

I hope this helps!