Discrete Stochastic Processes and Optimal Filtering

Appendix B

We are going to arrive at this result starting from the definition and by using the expression of the function K already obtained.

NOTE.– Different from the calculation developed in section 7.3.6 we will not show that obtained is minimal.

Another way of showing the following result:

Demonstration

Starting from the definition of the covariance matrix of the filtering error, i.e.:

It becomes with and

So

Let us now use these results to calculate

We observe that:

but I_j ⊥ I_K and ...