A NUV-Based Adaptive Robust Unscented Kalman Filter for Nonlinear State Estimation Under Cyberattacks

Abstract

Cyberattacks in Cyber-Physical Systems (CPS) can corrupt sensor measurements, significantly degrading nonlinear state estimation accuracy and causing numerical instability during filtering. To address these challenges, this paper proposes a Normal-with-Unknown-Variance-based Robust Derivative Unscented Kalman Filter (NUV-RDUKF). The proposed method integrates NUV-based probabilistic outlier modeling, Alternating Maximization (AM)-based adaptive variance estimation, SVD-based covariance processing, and the Derivative UKF framework into a unified nonlinear filtering algorithm. The NUV-AM framework enables online estimation of unknown outlier variances and adaptive adjustment of the measurement covariance matrix, thereby effectively suppressing the influence of abnormal measurements without relying on manually tuned outlier-related thresholds or weighting parameters. Moreover, SVD-based covariance processing is employed to improve numerical reliability by replacing conventional Cholesky-based covariance factorization and direct matrix inversion operations. Meanwhile, the Derivative UKF framework reduces computational complexity while maintaining estimation accuracy. Simulation results under impulsive attacks, bias attacks, and Denial-of-Service (DoS) attacks demonstrate that the proposed method consistently achieves superior estimation accuracy and robustness compared with several existing nonlinear filtering methods, while ensuring numerical reliability.