Tobit Recursive Filtering for Networked Nonlinear Systems Against Random Man-in-The-Middle Attacks: An Attack Detection Mechanism

In this paper, the problem of the Tobit recursive filtering (TRF) is investigated for a class of networked nonlinear systems, which are subject to random man-in-The-middle attacks (MITMAs) and measurement censoring. The Tobit Type I observation model is adopted to describe the phenomenon of measurement censoring. For the sake of effectively countering the intrusion of malicious attackers, a novel attack detection mechanism (ADM) is designed and integrated into the filter to determine whether the measurement data should be exploited after transmission via the network. The aim of the conducted topic is to propose an innovative ADM-based TRF method by adequately considering the influences of random MITMAs and measurement censoring. An upper bound (UB) of the filtering error covariance can be derived by solving matrix difference equations, and the desired filter gain is further parameterized by minimizing the trace of the obtained UB. Subsequently, the theoretical proof is provided to elaborate on the monotonicity relationship between the trace of the minimized UB and the attack probability. Finally, the validity of the presented ADM-based TRF scheme is demonstrated through simulation experiments. Note to Practitioners-This paper addresses the filtering problem commonly encountered in engineering applications such as intelligent transportation, autonomous driving and aerospace systems. In these contexts, the limitations of sensor hardware frequently give rise to censoring phenomena, leading to distorted measurement data. To overcome this challenge, a Tobit Kalman filtering framework is introduced to effectively characterize measurement censoring and mitigate its effects. In addition, as networked systems become increasingly interconnected, the security of data transmission has emerged as a critical concern. This study considers a scenario where communication channels are subject to random man-in-The-middle attacks and proposes an adaptive threshold-based attack detection mechanism capable of identifying abnormal measurement information and performing appropriate defense actions. The proposed Tobit recursive filtering (TRF) method enhances the reliability of state estimates under both measurement censoring and random cyber-Attacks, providing a secure estimation process suitable for real networked environments. Simulation results illustrate the potential applicability of the developed filtering strategy. Notably, most current TRF methods fundamentally rely on strictly synchronized discrete-Time frameworks. Asynchronous sampling introduces temporal mismatches between state and measurement updates, which can render these filtering schemes structurally inapplicable. Future research will tackle challenges related to sensor energy constraints and asynchronous data sampling within the TRF framework to further improve adaptability in large-scale industrial systems.