Distributed Kalman Filter using fast polynomial filter

Distributed estimation algorithms have received a lot of attention in the past few years, particularly in the fusion framework of Wireless Sensor Network (WSN). Distributed Kalman Filter (DKF) for WSN is one of the most fundamental distributed estimation algorithms for scalable wireless sensor fusion. In the literature, most of DKF methods rely on consensus filter algorithms. The convergence rate of such distributed consensus algorithms is slow and typically depends on the network topology and the weights given to the edges between neighboring sensors. In this paper, we propose a DKF based on polynomial filter to accelerate the distributed average consensus in the static network topologies. The main contribution of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate by minimizing its second largest eigenvalue. The simulation results show that the proposed algorithm increases the convergence rate of DKF by 4 times compared to the standard iteration. The proposed methodology can contribute in the real time WSN´s applications.