On the minimum number of active anchors for optimal localization

High-accuracy localization is crucial for numerous location-based applications. In wireless networks, the position information of a node (agent) can be obtained from range measurements with respect to nodes with known positions (anchors). The transmission power allocation among anchors not only affects network lifetime and throughput, but also determines the localization accuracy. In this paper, we formulate the power optimization problem that provides the best location accuracy under a total power constraint. For a given set of anchors, the minimum number of active anchors required for optimal localization in 2-D network is proven to be either two or three, depending on the network parameters. We then derive the closed-form expression for the optimal power allocation in the case of small networks and extend the results to general cases. We also develop a near-optimal strategy that requires less computational complexity, incurring negligible average performance loss. Our results provide a theoretical basis for designing anchor selection and power allocation algorithms for localization.