Approximate Bayesian filtering using stabilized forgetting

In this paper, we relax the modeling assumptions under which Bayesian filtering is tractable. In order to restore tractability, we adopt the stabilizing forgetting (SF) operator, which replaces the explicit time evolution model of Bayesian filtering. The principal contribution of the paper is to define a rich class of conditional observation models for which recursive, invariant, finite-dimensional statistics result from SF-based Bayesian filtering. We specialize the result to the mixture Kalman filter, verifying that the exact solution is available in this case. This allows us to consider the quality of the SF-based approximate solution. Finally, we assess SF-based tracking of the time-varying rate parameter (state) in data modelled as a mixture of exponential components.