A data-driven forgetting factor for stabilized forgetting in approximate Bayesian filtering

The main focus of this paper is to extend Bayesian filtering to allow for time-variant parameters in the transition kernels. Since a finite-dimensional exact solution is not available, we adopt stabilized forgetting in order to restore a recursive signal processing algorithm in this case, involving the processing of fixed, finite-dimensional statistics. This approximate solution is amenable to online sequential estimation, and is derived for a rich class of observation models. The data-driven forgetting factor is optimized sequentially using an iterative variational Bayes approach. A number of Bayesian filtering problems involving parameter-variant Gaussian processes is addressed in this way. In simulations, we emphasize the performance enhancements achieved using the data-driven sequential assignment of the forgetting factor, when compared to the conventional approach, which adopts a fixed value.