As I understand the basic idea of particle filter is to predict the state of the particle by generating N different possible state. After that, each possible state is evaluated by a predict model (give the weight to each particle).
So...let say, if my particle is (x, y, z). Then, because there are M different possible values for x, N possible values for y and L different possible values for z. The number of particles that I need to generate is M*N*L?