7.1 One-Dimensional Consideration

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

(7.1) equation

(7.2) equation

with

(7.3) equation

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

(7.4) equation

(7.5) equation

(7.6) equation

with

(7.7) equation

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 img expanded about the zero-mean value of img (2.38) becomes

(7.8)

Inserting this into (7.1) yields

(7.9)

Evaluating the integrals using the ...

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