Cramer-Rao Bounds for Distributed System Size Estimation Using Consensus Algorithms

System size estimation in distributed wireless sensor networks is important in various applications such as network management and maintenance. One popular method for system size estimation is to use distributed consensus algorithms with randomly generated initial values at nodes. In this paper, the performance of such methods is studied and Fisher information and Cramer-Rao bounds (CRBs) for different consensus algorithms are derived. Errors caused by communication noise and lack of convergence is also considered, and their effect on Fisher information and CRB is given. The results provide a lower bound on the variance of the estimator of system size. This in turn, provides guidelines on how to choose consensus algorithms and initial values at the nodes.