Deep Double-Bayesian Filtering

This article investigates the problem of deep learning-based state estimation for dynamic systems with partially known dynamics and unknown noise statistics. We propose a Deep Double-Bayesian Filter (DDBF), which leverages Bayesian deep learning for Bayesian filtering, augmenting state estimation while enabling the quantification of both aleatoric and epistemic uncertainties in a deep learning-based filter. First, we introduce a deep neural network augmented mismatch compensation mechanism into the state-space representation to bridge the gap between the nominal model and the actual system dynamics.We model the aleatoric uncertainty in the compensation terms using Bayesian deep learning tools, resulting in an SSM with explicit uncertainty formulation that establishes the probabilistic propagation model, which defines the evolution of the states and measurements. Second, we present a Bayesian filtering algorithm based on this SSM that enables an approximate Bayesian approach for state estimation under partially unknown system dynamics. In contrast to classical deep learning-based filters, the proposed DDBF learns the posterior predictive distribution of states from an approximate Bayesian perspective. This development allows for a more nuanced consideration of learning-based state estimation by combining input-dependent aleatoric uncertainty together with epistemic uncertainty. Finally, the effectiveness of the proposed DDBF is verified through simulations and real-world datasets.