Distributed Consensus Estimation of Wireless Sensor Networks

Average consensus develops with multi-agent systems where consensus is a vital aspect in coordination and cooperation [5]. It is a linear iteration scheme where each node updates its value as a linear weighted combination of the values received from neighbors and its own. Consensus can be guaranteed by appropriately designing the weights used in the linear schemes. However, the characteristics of WSNs introduce several challenges for average consensus as summarized below: (1) The nodes are always supplied by portable batteries whose energies are also constrained by limited physical sizes. As a result, efficiency is a vital aspect in average consensus. (2) Nodes need to exchange messages through unreliable wireless communication. The unreliability can introduce noise, dynamic topology, time delays, and other problems. How to obtain robust estimation is another issue should be concerned with. (3) The nodes are easy to be compromised and the security problem in estimation is also important. Plenty of research work have been reported to tackle these challenges and they are classified in Table 2.1 . On the aspect of efficiency, designing protocols for reaching consensus with fast convergence rate is a choice. Matrix optimization is utilized to design the weight coefficients in [6]. The increased convergence time based on matrix optimization is limited by network connectivity. It can be slowed down even if the weights are optimized. A local prediction component is added to the update protocol in [7] and [8] which propose theoretical analysis to demonstrate the improvement of the convergence time. Lower bounds for iteration steps in average consensus and a minimum-time consensus scheme are also proposed in [9]. [10] couples the