Secure State Estimation for Linear Time-varying Processes via Local Estimators

Abstract

This paper studies the secure state estimation problem of linear time-varying Gaussian processes in the presence of stochastic noises based on measurements from a set of sensors, a subset of which can be compromised by an attacker. The measurement of the compromised sensors can be arbitrarily manipulated by the attacker. We first show that in the absence of attacks, the Kalman filter can be decomposed into m local estimators and the Kalman estimate can be obtained by summing up the local estimates. We further show a least square interpretation to the fusion process and based on which, a convex optimization based secure state estimation scheme is proposed. The secure state estimation algorithm guarantees that when all the sensors are benign, the secure estimate coincides with the Kalman estimate. When less than half of the sensors are compromised, the secure state estimation scheme can still generate an estimate with bounded estimation error. Moreover, we demonstrate how to formulate the convex optimization problem to a conic programming problem to facilitate the application of the proposed secure state estimation algorithm in embedded systems. In the end, numerical simulations are conducted to verify the effectiveness of the proposed algorithm.