Towards invariant extended Kalman filter-based resilient distributed state estimation for moving robots over mobile sensor networks under deception attacks

Abstract

This paper studies the resilient distributed state estimation problem for moving robots over wireless sensor networks (WSNs) under deception attacks. The state of a moving robot consists of its position and orientation, evolving according to a nonlinear motion model, and the WSNs are mobile. These settings make the problem more challenging than most existing researches on the resilient distributed state estimation which recover stationary or linear states by static WSNs. To achieve the resilient distributed state estimation for the robot over a mobile sensor network (MSN), we propose a novel invariant extended Kalman filter-based resilient distributed state estimation approach. Specifically, based on the mappings between a Lie group and its Lie algebra, we first define a new type of estimation errors and linearize it. Utilizing the linearization results, the calculation of the current prior estimate based on the last posterior one is achieved by each sensor, which avoids the estimation biases induced by the computation of Jacobian matrices. Then, sensors in the MSN fuse the local prior estimates of their neighbors according to the covariance intersection fusion rule, obtaining more accurate estimates than their local prior ones. Finally, measurements collected by the sensors are used to correct the estimates. In the correction process, an adaptive gain is designed for each sensor to restrict the negative effects of the attacks on the estimates, which is crucial for the accomplishment of the resilient estimation task. We illustrate the performance of the approach by convergence analysis of the estimation errors based on the boundedness of the covariance matrix estimates computed in the state estimation process and verify it by simulation and experimental results.