Sparsity-inspired power allocation for network localization

High-accuracy localization is essential for many location-based applications. The position of an object can be obtained from range measurements based on wireless transmissions. Transmitting power allocation not only affects network lifetime and throughput, but also determines localization accuracy. The number of active transmitting nodes is also crucial since it is related to communication load and computation complexity. In this paper, we formulate the power optimization problem that provides the best localization accuracy under power constraints. We first prove the sparsity of the optimal power allocation, i.e., the optimal localization accuracy can be achieved by activating no more than (J) transmitting nodes in d-dimensional networks. Inspired by such sparsity, we derive the expressions of the optimal power allocation in 2-D networks. We also put forth a near-optimal algorithm for the power allocation problem with individual power constraints. Our results provide a theoretical basis for designing transmitting node selection and power allocation algorithms for network localization.