Distributed Kalman Filter with Fast Consensus for Wireless Sensor Networks

With the revolution of wireless sensor networks and the advances on microchip technologies the potential of distributed interconnected systems have exploded. Yet, even with great sensing capability and great communication throughput in the wireless links, we encounter fundamental problems: Communication Congestion and Scalability. The scalability issue and communication congestion are closely related in the application of distributed estimation algorithms. The more sensors we add to our system the more communication we will require. In general, in order to share the information gathered by all the sensors, we also get a higher likelihood of running into critical network congestion. Moreover, the scalability problem is not only related to communication issues but also to computation problems, as with higher dimensional measurement vectors it also comes a higher computational demand for the estimation algorithms. Distributed Kalman Filter (DKF) is one of the most fundamental distributed estimation algorithms. Most of the proposed DKF in the literature rely on consensus filters algorithm. The convergence rate of such distributed consensus algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors. This paper proposes a DKF with fast consensus. The idea is to apply a polynomial filter on the network matrix in order to increase the convergence by minimizing its second largest eigenvalue of the polynomial. Fast convergence can contribute to significant energy saving. Moreover we redesigned the DKF to reduce its computational complexity and to reduce the communication traffic between the sensor nodes. Thus, the experimental results show that the TelosB mote can run DKF with up to seven neighbors for real application.