Residual Neural FIR Filtering for Robust State Estimation

Abstract

Finite impulse response (FIR) filters are inherently robust owing to their finite-memory structure and independence from initial state statistics. However, they often lack the adaptivity required for time-varying environments. While recent neural-network-based FIR approaches address this limitation, they typically incur substantial computational costs owing to the online inversion of high-dimensional matrices. To overcome this trade-off between adaptivity and computational efficiency, this paper proposes a residual neural FIR (ResNFIR) framework. Unlike conventional approaches that estimate the full-filter gain, the proposed architecture adopts a hybrid structure in which a precomputed nominal FIR gain serves as a baseline, while a gated recurrent unit network generates a residual gain that compensates for model mismatches. The residual component is constrained through a regularization term in the loss function, ensuring nominal stability under steady-state conditions while enabling adaptive correction subject to model uncertainties. By eliminating real-time matrix inversion, the proposed ResNFIR reduces computational time by approximately 98% compared with existing neural FIR filters, making it suitable for high-speed, real-time applications. Numerical simulations using a linearized F404 aircraft engine model demonstrate that the proposed method achieves an estimation accuracy comparable to that of fully adaptive filters under parameter uncertainty conditions, while considerably improving computational efficiency and preserving structural stability.