Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.