Data-Driven Moving Horizon Estimators for Linear Systems with Sample Complexity Analysis
This addresses state estimation in control systems where model parameters are unknown, offering a data-driven approach with theoretical guarantees, but it is incremental as it builds on traditional moving horizon estimators.
The paper tackles state estimation for linear systems with unknown parameters and Gaussian noise by designing a data-driven moving horizon estimator (DDMHE) that uses offline and online data, proving the estimation error is ultimately bounded and analyzing sample complexity to relate offline data length to error.
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.