Please do the matlab problem Q36 only solution of Q30 Proble

Please do the matlab problem Q36 only

solution of Q30:

Problem:

30. Let X denote a random signal of known mean mx and known covariance matrix Cx Suppose that in order to estimate X, all we have available is the noisy measurement GX W. where G is a known gain matrix, and Wis a noise vector with zero mean and known covariance matrix Cw. Further assume that the covariance between the signal and noise, C is zero. Find the linear MMSE estimate of X based on Y assuming that CY is invertible. Remark. It is easy to see that Cy is invertible if Cw is positive definite or if GCxG is positive definite. If C is positive definite and if G is nonsingular, then GCKG is positive definite.

Solution

%Cx and Cw are identity matrices
Cx = [1 0 0 0;
    0 1 0 0;
    0 0 1 0;
    0 0 0 1];

Cw = [1 0 0 0;
    0 1 0 0;
    0 0 1 0;
    0 0 0 1];

%Defining G
G = [-2 1 -5 11;
    9 -4 -3 11;
    -10 -10 -25 -13;
    -3 -1 5 0];

Cxy = Cx*G\';
Cy = G*Cx*G\' + Cw;

%A = Cxy * inv(Cy)
A = Cy\\Cxy;

err = immse(Cxy, Cy);

%displaying values
disp(A);
disp([\'MSE = \', num2str(err)]);