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

A recursive algorithm for estimating the statistics of the Normal distribution is designed, making it adaptive in the sense that the forgetting factor is driven by data. A mechanism to suppress obsolete information is proposed, following the principles of Bayesian decision-making. Specifically, the best combination of two time-evolution model hypotheses in terms of the geometric mean is performed. The first hypothesis assumes no change in the parameter evolution, while the second one assumes that all parameter changes are equally admitted. In order to provide data-driven forgetting, complementary probabilities assigned to each hypothesis are determined as the maximizers of the decision problem. Simulations, including a performance comparison with a recently proposed self-tuning estimator, are presented.