5.3 The General Bayesian Point Prediction Integrals for Gaussian Densities

Remembering the dynamic equation (5.1), and assuming that vn is a zero-mean Gaussian random variable independent of both img and img it follows that

(5.32) equation

Similarly, in the observation equation (5.2), assume that wn is a zero-mean Gaussian random variables independent of both xn and zn, that is

(5.33) equation

Now, from Bayes' law, the prior density can be obtained from


making img Gaussian, since the product of two Gaussian densities is also Gaussian. Assuming that all density functions are Gaussian, we can identify

(5.35) equation

(5.36) equation

Assuming that vn and wn are zero-mean Gaussian processes, and substituting (5.36) into (5.3) and ...

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