PARTICLE-BASED BAYESIAN STATE–SPACE PROCESSORS
In this chapter we develop particle-based processors using the state–space representation of signals and show how they evolve from the Bayesian perspective using their inherent Markovian structure along with importance sampling techniques as our basic construct. Particle filters offer an alternative to the Kalman model-based processors discussed in the previous chapters possessing the capability not just to characterize unimodal distributions but also to characterize multimodal distributions. We first introduce the generic state–space particle filter (SSPF) and investigate some of its inherent distributions and implementation requirements. We develop a generic sampling-importance-resampling (SIR) processor and then perhaps its most popular form—the “bootstrap” particle filter. Next we investigate the resampling problem and some of the more popular resampling techniques also incorporated into the bootstrap filter from necessity. The bootstrap and its variants are compared to the classical and modern processors of the previous chapters. Finally, we apply these processors to a variety of problems and evaluate their performance using statistical testing as part of the design methodology.
7.2 BAYESIAN STATE–SPACE PARTICLE FILTERS
Particle filtering (PF) is a sequential Monte Carlo method employing the sequential estimation of relevant probability distributions using the “importance sampling” techniques developed in Chapter ...