Bayesian Estimation and Tracking: A Practical Guide

7.1 One-Dimensional Consideration

First, for the one-dimensional case, the state prediction equations (5.51) and (5.52) become

(7.1)

(7.2)

with

(7.3)

From (5.55) to (5.57), for the one-dimensional case, the observation prediction equations become

(7.4)

(7.5)

(7.6)

with

(7.7)

7.1.1 One-Dimensional State Prediction

A general one-dimensional M th-order Taylor polynomial was presented in equation (2.38). For a third-order one-dimensional Taylor polynomial for expanded about the zero-mean value of (2.38) becomes

(7.8)

Inserting this into (7.1) yields

(7.9)

Evaluating the integrals using the ...