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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?

Thanks

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The question lacks context. You may or may not have to generate all possible states depending on the context. You added the Monte Carlo tag; a Monte Carlo simulation typically doesn't generate all possible states. If your question is just whether the number of different possible values for $(x,y,z)$ is $MNL$ when there are $M$ different possible values for $x$, $N$ possible values for $y$ and $L$ different possible values for $z$, the answer is yes. – joriki Jul 7 '11 at 8:14
Thank Joriki. I can not tag "particle filter" or "condensation" so I had to tag "monte carlo" instead. If we dont generate all possible states, we may miss some important states, dont we? – user10128 Jul 7 '11 at 14:24
As I said, there's not enough context to say anything about that. – joriki Jul 7 '11 at 14:33

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