Bayesian design for transfer estimation between a pair of state-space models

State estimation often faces significant challenges due to uncertain evolution dynamics. This paper introduces a novel Bayesian transfer filtering algorithm that enhances performance by leveraging knowledge from a similar, previously learned source system. The method incorporates a transfer-prior probability density function of the target state through a cross-domain explicit model. A key feature of this approach is the definition of the similarity measure as the bias and covariance between the target and source states, providing deeper insight into the transferability between domains. To effectively utilize source system information, the expectation–maximization algorithm is employed to adaptively identify the bias and covariance. Theoretical analysis of the error dynamics, along with conditions that prevent negative transfer, ensures the efficacy of the proposed estimator. The method is validated through a numerical example and a navigation experiment, demonstrating its robustness and competitiveness compared to existing techniques in handling unmodeled dynamics.