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 and
it follows that
(5.32)
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)
Now, from Bayes' law, the prior density can be obtained from
(5.34)
making Gaussian, since the product of two Gaussian densities is also Gaussian. Assuming that all density functions are Gaussian, we can identify
Assuming that vn and wn are zero-mean Gaussian processes, and substituting (5.36) into (5.3) and ...
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