Unbiased Kalman Filters for Consensus of Continuous-Time Sensor Networks with Switching Topology

This paper considers the consensus problem of continuous-time sensor network in a noisy environment, in which both fixed topology case and switching topology case are considered. The main idea is based on the fact that the state of each agent has twofold identity, i.e., the state of itself and the control input of agents that take it as a neighbor. With this in mind, we first solely design unbiased Kalman filters for each agent such that the sensor network solves consensus problem when all information is contaminated by noises. Then, the convergence of the proposed algorithms is proved. All the proposed algorithms are fully distributed, unbiased, and use the least information. The validity of them is illustrated by the included numerical examples.