Bayesian Transfer Filtering Using Pseudo Marginal Measurement Likelihood

Abstract

Integrating the advantage of the unbiased finite impulse response (UFIR) filter into the Kalman filter (KF) is a practical yet challenging issue, where how to effectively borrow knowledge across domains is a core issue. Existing methods often fall short in addressing performance degradation arising from noise uncertainties. In this article, we delve into a Bayesian transfer filter (BTF) that seamlessly integrates the UFIR filter into the KF through a knowledge-constrained mechanism. Specifically, the pseudo marginal measurement likelihood of the UFIR filter is reused as a constraint to refine the Bayesian posterior distribution in the KF. To optimize this process, we exploit the Kullback-Leibler (KL) divergence to measure and reduce discrepancies between the proposal and target distributions. This approach overcomes the limitations of traditional weight-based fusion methods and eliminates the need for error covariance. Additionally, a necessary condition based on mean square error criteria is established to prevent negative transfer. Using a moving target tracking example and a quadruple water tank experiment, we demonstrate that the proposed BTF offers superior robustness against noise uncertainties compared to existing methods.