Bayesian Estimation and Tracking: A Practical Guide

3.5 Discussion of General Estimation Methods

In this chapter, two main results have been developed for Bayesian estimation that have almost no restrictions on either the form of the probability densities or on the linearity of the dynamic or observation equations. The first, through the use of (3.23) and (3.24), is a method for a recursive link between the previous posterior and the current posterior that requires specification of the predictive density given by and the likelihood function .

In many problems of interest, recursive Monte Carlo evaluation of these densities provide visual insight into the probable location and spread of the state vector, conditioned on all observations. Part III of this book will expand on these Monte Carlo estimation methods applicable to nonlinear systems and non-Gaussian densities (linear and Gaussian cases are included as a subset). In addition, Monte Carlo methods will be presented that allow evaluation of the density-weighted integrals, where Monte Carlo samples of x_n are used to create discrete density functions that reduce the integrals to weighted ...