Data-Driven Dynamic State Estimation Framework Using a Koopman Operator-Based Linear Predictor

Abstract

Dynamic state estimation (DSE) is a fundamental task in many fields, including control systems, robotics, and signal processing. Traditional DSE methods, which rely on mathematical models to describe system dynamics, are often limited in their applicability to real-world scenarios due to inaccuracies and assumptions. In this paper, we propose a purely data-driven DSE framework based on a Koopman operator-based linear predictor. The Koopman operator is a powerful tool in dynamical systems theory that allows us to analyze and predict the behavior of nonlinear systems. By leveraging the Koopman operator extracted solely from measured input-output data through the extended dynamic mode decomposition with control (EDMDc) method, a linear predictor that can accurately estimate the state variables of a dynamic system is developed. Introducing the extended Kalman filter (EKF) as an estimation method, the learned Koopman operator-based linear predictor is then used to estimate the current state of the system given only the past and present input-output measurements. To evaluate the effectiveness of the proposed framework, we conduct experiments on both simulated and real-world datasets of complex power systems. The results demonstrate that the proposed data-driven approach outperforms traditional model-based approaches in terms of accuracy and robustness. Moreover, the proposed framework is capable of handling nonlinear and time-varying systems, making it applicable to a wide range of practical cases.