Sensor Selection for TDOA-Based Localization in Wireless Sensor Networks With Non-Line-of-Sight Condition

This paper investigates the selection of a subset of sensors for time difference of arrival (TDOA) localization under the non-line-of-sight (NLOS) condition in wireless sensor networks (WSN). Specifically, we aim to optimize the sensor activation for the sake of minimizing the localization error when considering NLOS condition subject to energy constraints. In contrast to existing sensor selection strategies, two independent Boolean selection vectors are utilized to determine the reference sensor and other sensors simultaneously in TDOA localization. Upon presenting expressions of the Cramer-Rao lower bound (CRLB) under three different scenarios, including: 1) line-of-sight (LOS), 2) Prior statistics unknown NLOS (PSU-NLOS), 3) Prior statistics known NLOS (PSK-NLOS), the optimization problems for sensor selection are formulated to minimize the CRLB based on two independent Boolean selection vectors. Analytical scheme is developed by solving the tractable semidefinite program (SDP) problems which are converted from the original nonconvex problem. Furthermore, two low-complexity heuristic algorithms, namely best option filling (BOF) algorithm and iterative swapping greedy (ISG) algorithm, are proposed for the sake of practical implementation. Simulation results validate that the localization accuracy for sensors selected by the SDP with randomization algorithm and the ISG algorithm achieves the exhaustive search method. Additionally, these two algorithms are stable under several random sensor network geometries.