BP Neural Network–Based Kalman Filtering Method Under Multiple Cyberattacks

This paper proposes a Kalman-gain-driven neural Kalman filtering (KF) defense framework, termed KFDBP, for secure state estimation in cyber–physical systems (CPSs) under denial-of-service (DoS), spoofing, and replay attacks. Unlike end-to-end neural filtering approaches such as KalmanNet that directly learn state estimators or implicitly approximate the Kalman gain using deep recurrent architectures, the proposed method employs a lightweight back-propagation (BP) neural network to adaptively regulate the Kalman gain online, while strictly preserving the classical Kalman filter prediction–correction recursion. By formulating an innovation-oriented Kalman gain learning objective, KFDBP explicitly addresses attack-induced observation uncertainty and non-Gaussian measurement corruption without requiring prior knowledge of attack timing, attack type, or attack probability during online estimation. The bounded gain regulation mechanism enhances estimation stability and interpretability, which are critical for safety-sensitive CPS applications, while significantly reducing computational complexity compared with deep neural network–based filters. Extensive Monte Carlo simulations under single and hybrid attack scenarios demonstrate that KFDBP consistently achieves lower estimation error and improved robustness than the conventional Kalman filter and KalmanNet under different attack probabilities, making it suitable for real-time and resource-constrained CPS applications.