Discrete Filtering Using Branching and Interacting Particle Systems

The stochastic ltering problem deals with the estimation of the current state of a signal process given the information supplied by an associate process, usually called the observation process. We describe a particle algorithm designed for solving numerically discrete ltering problems. The algorithm involves the use of a system of n particles which evolve (mutate) in correlation with each other (interact) according to law of the signal process and, at xed times, give birth to a number of oosprings depending on the observation process. We present several possible branching mechanisms and prove, in a general context the convergence of the particle systems (as n tends to 1) to the conditional distribution of the signal given the observation. We then apply the result to the discrete ltering and give several example when the results can be applied.

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