Sensor Selection for TDOA-Based Source Localization Using Angle and Range Information

Sensor selection for time-difference-of-arrival (TDOA)-based localization can be fulfilled by minimizing the Cramér-Rao lower bound (CRLB). With an identical range measurement noise variance for different sensors, the CRLB involves the angle information only between the sensors and source. An issue caused by this is that the state-of-the-art sensor selection methods using semidefinite relaxation (SDR) may incorrectly select sensors owing to the ambiguity caused by relaxation, and Gaussian randomization (GR) is usually required to help select the correct sensors, which would cause an additional cost in the implementation. In this article, we develop a sensor selection method for TDOA-based source localization by explicitly incorporating both the angle and the range information between the sensors and the source to resolve the ambiguity caused by SDR. Specifically, the sensor selection problems for the cases of the known and unknown numbers of selected sensors are investigated and formulated as the nonconvex optimization problems. SDR is then utilized to relax the nonconvex problems as the convex semidefinite programs. Simulation results show that the proposed method works well without performing the additional GR procedure.