Distributed secure state estimation with a priori sparsity information

This paper addresses the problem of distributed secure state estimation of a discrete-time linear dynamical system in an adversarial environment. Much of the recent work on this problem has imposed redundancy requirements on measurement and communication networks for state estimation in the presence of attacks. In this paper, the authors aim to relax this redundancy requirement by using prior information about the state to be estimated. A scenario where sparsity information of the state is given is especially considered, and it is shown that the a priori sparsity information alleviates the redundancy requirement. An algorithm for distributed secure state estimation is then derived and a sufficient condition on the convergence of the algorithm is given. Numerical simulations finally illustrate the effectiveness of the algorithm.