As I understand the basic idea of particle filter is to predict the state of the particle by generating $N$ different possible states. 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 $M\cdot N \cdot L$?
Thanks