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

TL;DR

This paper introduces a data-driven moving horizon estimator for linear systems with unknown parameters, providing theoretical guarantees and analyzing how data length influences estimation accuracy.

Contribution

It develops a novel estimator that leverages offline and online data, with proven error bounds and explicit sample complexity analysis for unknown linear systems.

Findings

Expected 2-norm of estimation error is ultimately bounded.

Explicit relationship between noise covariances and estimation error.

Sample complexity affects the estimator's accuracy, with validation through simulations.

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.