7.2 Multidimensional Consideration

For multidimensional functions with multidimensional arguments, the state prediction integrals for img img are given by (5.51)(5.57). In both the linear Kalman filter and the one-dimensional EKF it is obvious from (6.3) and (7.23) that the deterministic control function un is additive for the state prediction and does not appear in any of the remaining filter equations. So, for what follows, we will ignore un and add it back in if it is needed for the case studies.

The general multidimensional Taylor polynomial was presented in (2.63). For a second-order Taylor polynomial for imgimg expanded about the zero-mean value of c, using (2.69) in (2.63) results in

(7.30) equation

It follows immediately that (7.30) can be rewritten as

(7.31) equation

7.2.1 The State Prediction Equation

From (5.51), using the Taylor polynomial (7.31), we can express the predictive first moment as


Using ...

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