Probability-Guaranteed Distributed Secure Estimation for Nonlinear Systems Over Sensor Networks Under Deception Attacks on Innovations

This paper studies the distributed secure state estimation problem for a class of general nonlinear systems over sensor networks under unknown deception attacks on innovations. At each sensing node, an estimator is designed to generate the state estimate by making use of the local measurements in combination with the neighbours' information shared via the communication network. During the transmission of innovations among nodes, the data are maliciously falsified by adversaries in a random way. A neural-network-based mechanism is put forward to approximate the unknown falsified innovations with the aim to mitigate the effects on the estimation performance. The objective of the addressed problem is to develop a distributed estimation approach to jointly estimate the system states as well as the unknow deception attacks, ensuring that the state estimation errors at each sensing node reside within required ellipsoidal regions with a pre-specified probability. With the help of certain convex optimization methods, we obtain sufficient conditions for the solvability of the addressed problem and the desired estimator gains can be iteratively computed by solving a series of matrix inequalities. On basis of the proposed framework, some optimization problems are presented to determine sub-optimal estimator parameters from different perspectives. Finally, the applicability of the developed algorithms is validated via a numerical simulation example.