A Koopman Operator-Based Finite Impulse Response Filter for Nonlinear Systems

This paper proposes a novel Koopman operator-based finite impulse response (KFIR) filter for nonlinear dynamic systems. This filter is generalized from the minimum variance unbiased (MVU) FIR filter for linear systems by using a global linear approximation of the nonlinear dynamics obtained from Koopman operator theory and the extended dynamic mode decomposition (EDMD) algorithm. Based on the recursive linear model, a reduced-order FIR filtering structure is proposed, and the optimal gain is derived to minimize the trace of the estimation error covariance. Unlike traditional methods, the KFIR filter requires no prior knowledge of the initial state and fully utilizes the data of a moving horizon. Simulation results show that the proposed filter has excellent robustness against unexpected modeling uncertainties and inaccurate noise information, making it suitable for real applications.