On Duality of Exponential and Linear Forgetting

Regularized (stabilized) versions of exponential and linear forgetting in parameter tracking are shown to be dual to each other. Both are derived by solving essentially the same Bayesian decision-making problem where Kullback-Leibler divergence is used to measure (quasi)distance between posterior probability distributions of estimated parameters. The type of forgetting depends solely on the order of arguments in Kullback-Leibler divergence. This general view indicates under which conditions one technique is superior to the other. Applied to the case of ARX models, the approach results in a class of regularized (stabilized) forgetting strategies that are naturally robust with respect to poor system excitation.