Distributed Center and Coverage Region Estimation in Wireless Sensor Networks Using Diffusion Adaptation

A fully distributed algorithm for estimating the center and coverage region of a wireless sensor network (WSN) is proposed. The proposed algorithm is useful in many applications, such as finding the required power for a certain level of connectivity in WSNs and localizing a service center in a network. The network coverage region is defined to be the smallest sphere that covers all the sensor nodes. The center and radius of the smallest covering sphere are estimated. The center estimation is formulated as a convex optimization problem using soft-max approximation. Then, diffusion adaptation is used for distributed optimization to estimate the center. After all the sensors obtain the center estimates, max consensus is used to calculate the radius distributively. The performance analysis of the proposed algorithm is provided, as a function of a design parameter controls the trade-off between the center estimation error and the convergence speed of the algorithm. Simulation results are provided.