Data-Driven Stabilized Forgetting Design Using the Geometric Mean of Normal Probability Densities

This paper contributes to the solution of adaptive tracking issues adopting Bayesian principles. The incomplete model of parameter variations is substituted by relaying on the use of data-suppressing procedure with two goals pursued: to provide automatic memory scheduling through the data-driven forgetting factor, and to compensate for the potential loss of persistency. The solution we propose is the geometric mean of the posterior probability density function (pdf) and its proper alternative, which, for the normal distribution, can be reduced to the convex combination of the information matrix and its regular counterpart. This coupling policy results from maximin decision-making, where the Kullback-Leibler divergence (KLD) occurs as a measure of discrepancy. In this context, the weight (probability) assigned to the information matrix is regarded as the forgetting factor and is controlled by a globally convergent Newton algorithm.