Robust Bayesian inference for moving horizon estimation

The accuracy of moving horizon estimation (MHE) suffers significantly in the presence of measurement outliers. Existing methods address this issue by treating measurements leading to large MHE cost function values as outliers and subsequently discarding them, which may lead to undesirable removal of uncontaminated data. Also, these methods are solved by combinatorial optimization problems, restricted to linear systems to guarantee computational tractability and stability. Contrasting these heuristic approaches, our work reexamines MHE from a Bayesian perspective, revealing that MHE's sensitivity to outliers results from its reliance on the Kullback–Leibler (KL) divergence, where both outliers and inliers are equally considered. To tackle this problem, we propose a robust Bayesian inference framework for MHE, integrating a robust divergence measure to reduce the impact of outliers. Specifically, the proposed approach prioritizes the fitting of uncontaminated data and lowers the weight of outliers, instead of directly discarding all potential outliers. A tuning parameter is incorporated into the framework to adjust the degree of robustness, and the classical MHE can be regarded as a special case of the proposed approach as the parameter converges to zero. Our method involves only minor modification to the classical MHE stage cost, thus avoiding the high computational complexity associated with previous outlier-robust methods, making it inherently suitable for nonlinear systems. Additionally, it is proven to have robustness and stability guarantees, which are often missing in other outlier-robust Bayes filters. The effectiveness of the proposed method is finally demonstrated in a vehicle localization experiment.