Design of variable exponential forgetting for estimation of the statistics of the Normal-Wishart distribution

This paper addresses the adaptive estimation problem of time-varying systems in the Bayesian framework. The version of exponential forgetting with the variable factor is derived by solving the decision problem where the Kullback-Leibler divergence is used. This divergence is applied to evaluate the distance of two antagonistic model hypotheses from the model of parameter variations. The first hypothesis assumes no parameter changes, while the second one admits that the parameters may arbitrarily evolve throughout the parameter space. In this respect, the forgetting factor is interpreted as the probability that the first hypothesis meets the reality. This concept brings another technique into the class of self-tuned forgetting strategies for the discarding of obsolete information. The developed concept of forgetting is designed to complement the data learning process propagating the statistics of the Normal-Wishart distribution.