Robust data-driven Kalman filtering for unknown linear systems using maximum likelihood optimization

• Published in: Automatica (Oxford) Vol. 180; p. 112474
• Main Authors: Duan, Peihu, Liu, Tao, Xing, Yu, Johansson, Karl Henrik
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2025
• Subjects: Performance analysis; Robust data-driven Kalman filter; Sample complexity; Unknown system matrices; Unknown system matrices; Sample complexity; Performance analysis; Robust data-driven Kalman filter
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2025.112474

This paper investigates the state estimation problem for unknown linear systems subject to both process and measurement noise. Based on a prior input–output trajectory sampled at a higher frequency and a prior state trajectory sampled at a lower frequency, we propose a novel robust data-driven Kalman filter (RDKF) that integrates model identification with state estimation for the unknown system. Specifically, the state estimation problem is formulated as a non-convex maximum likelihood optimization problem. Then, we slightly modify the optimization problem to get a problem solvable with a recursive algorithm. Based on the optimal solution to this new problem, the RDKF is designed, which can estimate the state of a given but unknown state-space model. The performance gap between the RDKF and the optimal Kalman filter based on known system matrices is quantified through a sample complexity bound. In particular, when the number of the pre-collected states tends to infinity, this gap converges to zero. Finally, the effectiveness of the theoretical results is illustrated by numerical simulations.