Improved Particle Filters and Smoothing

Exact recursive Bayesian inference is essentially impossible except in very special scenarios, such as the linear-Gaussian dynamic systems that are amenable 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 in this chapter), but nowadays it is more common to carry forward, as an estimate of the current distribution of the items of interest, what is claimed to be a simulated sample from that distribution, in other words, a particle filter.