Proximity Moving Horizon Estimation for Discrete-Time Nonlinear Systems

In this letter, we address the moving horizon estimation (MHE) problem of constrained discrete-time nonlinear systems. We propose a proximity-based formulation of the underlying optimization problem in which the state estimate is designed to lie in proximity of a stabilizing a priori estimate that is based on the extended Kalman filter (EKF). Using Lyapunov's direct method, we prove exponential stability of the estimation errors under suitable assumptions. For a benchmark example, an improved performance of the proposed estimator in comparison to the EKF and to a common MHE scheme with filtering update is showcased.