Learning Adaptive Parameter Policies for Nonlinear Bayesian Filtering

Abstract

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the approximation's accuracy and computational cost. The parameters include, for example, the number of particles, scaling parameters, and the number of iterations in iterative computations. Typically, these parameters are fixed or adjusted heuristically, although the approximation accuracy can change over time with the local degree of nonlinearity and uncertainty. The approximation errors introduced at a time step propagate through subsequent updates, affecting the accuracy, consistency, and robustness of future estimates. This paper presents adaptive parameter selection in nonlinear Bayesian filtering as a sequential decision-making problem, where parameters influence not only the immediate estimation outcome but also the future estimates. The decision-making problem is addressed using reinforcement learning to learn adaptive parameter policies for nonlinear Bayesian filters. Experiments with the unscented Kalman filter and stochastic integration filter demonstrate that the learned policies improve both estimate quality and consistency.