모델 불확실성을 고려한 GRU 기반 적응형 유한 임펄스 응답 필터

초록

This paper proposes a gated recurrent unit (GRU)-augmented adaptive finite impulse response (FIR) filter for state estimation of discrete, linear time-invariant (LTI) state–space models subject to model uncertainties. While deep-learning techniques have been extensively incorporated into recursive state estimators, their integration within nonrecursive FIR filtering frameworks remains limited. Conventional FIR filters ensure bounded-input bounded-output stability and divergence-free operations; however, their performance may degrade under model uncertainty conditions owing to fixed noise covariance assumptions. To address this issue, the proposed method employs a GRU network trained in an end-to-end manner to estimate the process and measurement noise covariance matrices from sequential measurement and state information. The inferred noise statistics are incorporated into the analytical FIR gain computation, enabling adaptive covariance adjustment while preserving the intrinsic finite-memory and stability properties of nonrecursive filtering. Numerical simulations indicate that the proposed GRU-based, adaptive FIR filter improves estimation accuracy and robustness compared with fixed-covariance FIR filters and conventional recursive estimators under uncertain conditions. The results suggest that integrating learning-based noise estimation into the FIR framework provides a viable hybrid approach for adaptive state estimation in uncertain dynamical systems.

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