Design of Bayesian Transfer Filter for Systems with Inequality Constraints

This paper introduces a novel filtering algorithm that integrates inequality state constraints into a Bayesian transfer learning (TL) framework. The proposed method interprets inequality constraints as pseudo-measurements and combines them with transferred knowledge from the source domain to condition the posterior distribution of the target state. This design mitigates the adverse effects of noisy and low-quality target data on estimation performance. To optimize the transfer of source information, the Kullback-Leibler (KL) divergence between the target and source domains is minimized. Additionally, a transfer weight matrix is introduced to balance information utilization between the domains, reducing the risk of negative transfer caused by biased source data. Simulation experiments demonstrate that the proposed weighted Bayesian transfer filter (WBTF) significantly enhances estimation accuracy, particularly under high-noise conditions in the source domain.