Bayesian Estimation and Tracking: A Practical Guide

15.3 Summary

In this chapter we have presented two main concepts, methods for the representation of a density function based on a set of samples drawn from that density, and the general concept of Monte Carlo importance sampling in the numerical integration of functions weighted by an arbitrary pdf. At present, a practical method for estimation and tracking cannot be presented based solely on these results and additional modifications must be made to develop practical methods.

Tracking filters based on a sequential generation of the recursive sets of Monte Carlo points and weights {}have come to be called Sequential Monte Carlo (SMC) methods. They offer a number of significant advantages over many of the other techniques currently available as a result of the generality of the SMC approach. They allow for an inference of the full posterior distribution in terms of general state space models including both nonlinear and non-Gaussian. SMC methods therefore allow for computation of all kinds of moments, quantiles, and maximum posterior density regions, whereas the Gaussian Kalman filter variants allow only approximations of the first-and second-order moments. In addition, by appropriately specifying the state space model, the SMC methods can incorporate constraints on the state space such as limits on the range of the state space, representing such physical limitations such as speed ...