Subject: Questions Regarding State Covariance Calculation in Particle Filter Code

[zhangbb-john]

Dear Professor Manon Kok,

I am a student from Zhejiang University, and I have some questions regarding the following code in parcileFilter.m:

for i = 1:N_P
    P_mean = w(i) * ( P(:,:,i) + (xl_mean - xl(:,i)) * (xl_mean - xl(:,i))');
end

Here, P represents the state covariance of the 515 coefficients of the basis functions, which are regarded as linear states within the filter.

In typical particle filters, P_mean is usually calculated as follows:

    weighted_mean = sum(xn .* weights, 2);
    
    % Compute covariance of particles
    P_mean = zeros(size(xn, 1));
    for j = 1:N_P
        diff = xn(:,j) - weighted_mean;
        P_mean = P_mean + weights(j) * (diff * diff');
    end

I have a couple of concerns regarding your implementation:

• Variation with Particle Index: In your code, P_mean varies with the particle index i, which seems unusual. Could you clarify the reasoning behind this approach?

• Addition of P(:,:,i): Additionally, I am curious why (xl_mean - xl(:,i)) * (xl_mean - xl(:,i))' adds P(:,:,i). This appears to differ from the typical formulation used in particle filters.

Thank you for your time and assistance.

Best regards,
Bingbing
[email protected]