Nearly Optimal Sensor Selection for TDOA-Based Source Localization in Wireless Sensor Networks

In a large-scale wireless sensor network, it is typically impossible to use all the sensors to localize a source due to the limited communication range and battery power of the sensor nodes, thereby a sensor selection procedure is required. In this paper, the sensor selection problem for time-difference-of-arrival (TDOA) based localization is addressed. We propose two nearly optimal sensor selection methods: one is based on the original TDOA model and the other is based on the transformed time-of-arrival (TOA) model. Both methods aim to minimize the trace of the Cramér-Rao lower bound (CRLB) under the condition of fixed number of selected sensors. For the first method, we introduce a special vector to distinguish the reference sensor with the non-reference sensors. We then formulate a non-convex optimization problem with a Boolean vector as the optimization variable. For the second method, we first prove that the CRLB for TDOA-based localization is exactly the same with that for TOA-based localization where the start transmission time is unknown. We then formulate a non-convex optimization problem to minimize the CRLB for TOA-based localization. Both non-convex optimization problems are relaxed as convex semidefinite programs (SDPs) by applying semidefinite relaxation, followed by the Gaussian randomization procedure to improve the quality of the SDP solutions if necessary. Simulation results show that the performance of proposed methods approaches that of the exhaustive search method.