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) equation

with observations generated from the observation process

(5.2) equation

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

(5.3) equation

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

(5.4) equation

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

(5.5) equation

(5.6) equation

(5.7) equation

where Q and R are defined by

(5.8)

and

(5.9)

Get Bayesian Estimation and Tracking: A Practical Guide now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.