Data-Driven Moving Horizon Estimators for Linear Systems with Sample Complexity Analysis

Abstract

This paper investigates the state estimation problem for linear systems subject to Gaussian noise, where the model parameters are unknown. By formulating and solving an optimization problem that incorporates both offline and online system data, a novel data-driven moving horizon estimator (DDMHE) is designed. We prove that the expected 2-norm of the estimation error of the proposed DDMHE is ultimately bounded. Further, we establish an explicit relationship between the system noise covariances and the estimation error of the proposed DDMHE. Moreover, through a sample complexity analysis, we show how the length of the offline data affects the estimation error of the proposed DDMHE. We also quantify the performance gap between the proposed DDMHE using noisy data and the traditional moving horizon estimator with known system matrices. Finally, the theoretical results are validated through numerical simulations.