Titlebook: Sequential Monte Carlo Methods in Practice; Arnaud Doucet,Nando Freitas,Neil Gordon Book 2001 Springer Science+Business Media New York 200

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Improvement Strategies for Monte Carlo Particle Filtersques have been suggested in the literature. In this paper we collect a group of these developments that seem to be particularly important for time series applications and give a broad discussion of the methods, showing the relationships between them. We firstly present a general importance sampling

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Combined Parameter and State Estimation in Simulation-Based Filteringhods of filtering for time-varying state vectors. We now have quite effective algorithms for time-varying states, as represented throughout this volume. Variants of the auxiliary particle filtering algorithm (Pitt and Shephard 1999b), in particular, are of proven applied efficacy in quite elaborate

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Auxiliary Variable Based Particle Filtersovian. The task will be to use simulation to estimate .(..|..), . = 1, ..., ., where .. is contemporaneously available information. We assume a known measurement density .(..|..) and the ability to simulate from the transition density .(..|..). Sometimes we will also assume that we can evaluate .(..

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Improved Particle Filters and Smoothingenable to the Kalman filter and associated methods. Otherwise, some form of approximation is necessary. In some contexts, a parametric approximation might still be workable, as in (Titterington 1973)’s use of two-component Normal mixtures in a simple extremum-tracking problem (which we revisit later

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Approximating and Maximising the Likelihood for a General State-Space Modelfly, but concentrate mainly on the frequentist approach where one has to compute and maximise the likelihood. Exact methods are usually not feasible, but the Monte Carlo methods allow us to approximate the likelihood function.