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Particle filtering is a general Monte Carlo (sampling) method for performing inference in state-space models where the state of a system evolves in time and information about the state is obtained via noisy measurements made at each time step

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The third line comes from what it is called Markov Assumption and it is Stochastic Processes stuff. Basically, it says that a distribution is not altered by the insertion and/or remotion of variables …
answered Mar 7 '19 by Akindart