Bayesian Estimation and Tracking: A Practical Guide

5.1 Summary of Important Results From Chapter 3

The important results of Chapter 3 are summarized. Consider a dynamic process of the form

(5.1)

with observations generated from the observation process

(5.2)

A point prediction estimate of the state vector at time t_n, based on all observations up to and including time t_n−1, is given by the density weighted integral

(5.3)

Similarly, a point prediction estimate of the state covariance at time t_n, based on all observations up to and including time t_n−1, is given by the density weighted integral

(5.4)

In addition, point prediction estimates of the observation vector z_n, the covariance of z_n, and its cross-covariance with x_n are given by

(5.5)

(5.6)

(5.7)

where Q and R are defined by

(5.8)

and

(5.9)