Recursive Distributed Secure State Estimation for Nonlinear Systems With Amplify-and-Forward Relays and Stochastic Measurement Delays Over Sensor Network

This article takes up for discussion the distributed secure state estimation issue for a specific category of nonlinear systems with random measurement delays and being subject to random deception attacks. To prolong the signal transmission distance, the amplify-and-forward (AF) relays are incorporated. A distinctive recursive state estimation algorithm is formulated, adopting a pattern reminiscent of a Kalman-type filter. Firstly, an upper bound matrix (UBM) for the estimation error (EE) variance is calculated. Then the estimator gain matrices are obtained by minimizing the calculated UBM. Subsequently, the impact of the transmission energies from sensors and relays on estimation performance is analyzed. Finally, the proposed estimation algorithm is confirmed through a simulation example, demonstrating its effectiveness.