Robust Rauch--Tung--Striebel Smoothers Based on Generalized Statistical Measure Under Cyberattacks

Accurate state estimation (SE) for systems affected by unknown non-Gaussian (NG) noise is significantly challenging, especially when compounded by hybrid cyberattacks. In this article, we investigate the fixed-interval smoothing problem for NG systems under such attacks. Since most attack detectors are susceptible to failure in these scenarios, we propose the flag-bit-based detection mechanism by expanding the measurement equation with a marking signal dedicated to identifying attacks exclusively. To improve the estimation accuracy of NG systems at risk of undetected attacks, the robust forward filtering and backward smoothing are derived by solving the new cost functions defined based on the proposed generalized statistical measure (GSM) with enhanced flexibility, based on which we obtain the new robust Rauch-Tung-Striebel smoother. The sufficient conditions for the convergence of both forward and backward passes are rigorously established, which provides the theoretical support of the proposed estimator in terms of optimality and uniqueness. Extensive simulations validate the lower false detection rate of the proposed detector and the improved estimation accuracy of the proposed smoother compared to related works under various noise and attack conditions.