Particle Filters in Discrete Time
The purpose of this chapter is to present a rigorous mathematical treatment of the convergence of particle filters in the (simpler) framework where both the signal X and the observation Y are discrete time processes. This restriction means that this chapter does not use stochastic calculus. The chapter is organized as follows. In the following section we describe the discrete time framework. In Section 10.2 we deduce the recurrence formula for the conditional distribution of the signal in discrete time. In Section 10.3 we deduce necessary and sufficient conditions for sequences of (random) measures to converge to the conditional distribution of the signal. In Section 10.4 we describe a generic class of particle filters which are shown to converge in the following section.
KeywordsProbability Measure Discrete Time Particle Filter Weak Topology Multinomial Distribution
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