Bayesian Transfer Filtering via UFIR Adaptive Regularization

The Bayesian approach resulting in the Kalman filter (KF), often struggle with model uncertainties, particularly when noise statistics are inaccurate. Inspired by transfer learning, this letter presents a novel Bayesian transfer filtering framework that significantly enhances estimation accuracy by incorporating the unbiased finite impulse response (UFIR) structure for adaptive regularization. To adaptively adjust the UFIR filtering estimate, the statistical significance of the transfer-regularization is learned and the variational Bayesian method is applied to learn the regularization factor directly from the data. It is shown that this adaptive strategy not only improves the interpretability and transferability but also removes the need for heuristic selection, which is a common limitation in traditional regularization-based transfer methods. Numerical simulations and water tank experiments collectively confirm the effectiveness of the proposed framework under uncertain noise statistics.