Moving Horizon Estimation for Nonlinear Systems Subject to Measurement Outliers

This is the authors' abstract. We don't add key points for this paper.

The accuracy of moving horizon state estimation significantly deteriorates when measurements are contaminated by outliers. Existing moving horizon estimation (MHE) methods that address this issue are restricted to linear systems. This paper proposes an outlier‐robust MHE method to address the state estimation problem for nonlinear systems subject to measurement outliers. Specifically, at each sampling instant, the method solves a set of least‐squares cost functions to eliminate potentially contaminated measurements one by one. The state estimate corresponding to the optimal cost is retained, and the process repeats as new information becomes available. Subsequently, the concept of uniform observability is introduced within this estimation framework. Applying the uniform observability property and choosing appropriate design parameters, the stability of the proposed estimator is proved. Additionally, a robustness condition is derived, ensuring that the estimator remains resilient to outliers, provided they are sufficiently large. Finally, the parameter design method to achieve stability and robustness in the estimator implementation is presented. The simulation results show the effectiveness of the proposed estimation approach in case the measurements are contaminated.