Robust Nonlinear FIR Filtering via Koopman Operator Framework With Combined Bounded-Gaussian Noise Characterization

State estimation for nonlinear systems using Finite Impulse Response (FIR) filters presents two key challenges: constructing effective filter structures and deriving optimal solutions. This paper introduces a novel nonlinear FIR filtering approach that addresses these challenges through the Koopman operator framework. The Koopman operator, a prominent data-driven method, provides intrinsic coordinates that enable global linearization of nonlinear dynamics. This transformation yields a linearized system that accurately represents the original non-linear behavior, offering new possibilities for nonlinear FIR filter design. To enhance robustness, we model the linearization error as bounded noise, enabling the filter to accommodate significant modeling mismatches within defined limits. Combined with the system’s Gaussian noise, this hybrid uncertainty description leverages the FIR structure’s inherent high degree of freedom. The optimal filter gain is then determined through multi-objective optimization. Simulation results demonstrate the proposed filter’s exceptional robustness against both modeling uncertainties and noise characterization errors, confirming its practical applicability.