I have a doubt with likelihood calculation in particle filtering.
In my understanding the particle filter consists of the following steps
Generate particles from initial point
Propagate through system model ($X_p(k) = A*X_f(k-1) + Q$) (I am generating Gaussian noise and adding to state equation based on $Q$ for each particle)
Weight update using likelihood calculation For likelihood calculation I need measurement from sensor (with Gaussian noise) and predicted measurement
For the predicted measurements, I have to use the measurement equation $$y = H*x + R$$ For each particle I have to calculate corresponding $y$ value.
Should I generate Gaussian noise based of R for every particle while calculating predicted measurement y?
In the Kalman filter we use $y = H*x$ ( since we are calculating mean), what should I do in particle filter...?