GRU-based Adaptive Exponentially Weighted Kalman Filter With Forgetting Factor Learning

This study proposes a Gated Recurrent Unit (GRU)-based Adaptive Exponentially Weighted Kalman Filter (GEWKF) to dynamically estimate the forgetting factor, addressing the limitations of conventional exponentially weighted Kalman filters (EWKFs) relying on fixed parameters. Unlike static EWKFs, the proposed GEWKF adaptively tunes the forgetting factor in real time, enhancing robustness and estimation accuracy during abrupt model changes. In contrast to previous deep learning-based adaptive filters that predict complex covariance matrices or full filter gains often at high computational cost and interpretability, GEWKF learns only a single scalar parameter while preserving the recursive framework of the standard Kalman filter. A GRU-based recurrent neural network leverages time-series data, including state prediction errors and measurement residuals, to compute the optimal forgetting factor efficiently and reliably. Simulations reveal that the GEWKF filter matches the performance of the standard Kalman filter under nominal conditions and significantly outperforms both the standard KF and fixed-parameter EWKF under sudden uncertainties. These results highlight that the GEWKF offers a practical and principled framework for state estimation, balancing adaptability, computational efficiency, real-time applicability, and interpretability.