3.1. Adaptive filter (AF)

The idea underlying the AF is to construct a filter which uses feedback in the form of the PE signal (innovation) to adjust the free parameters in the gain to optimize the filter performance. If in the KF, the optimality is defined as a minimum mean squared error (MMS), in the AF, optimality is understood in the sense of MMS for the prediction output error (innovation). This definition allows to define the optimality of the filter in the realization space, but not in the probability space as done in the KF.

The optimal gain thus can be determined from solving the optimization problem by adjusting all elements of the filter gain. There are two major difficulties:

