How to select the best sensors for TDOA and TDOA/AOA localization?

This paper focuses on the sensor subset optimization problem in time difference of arrival (TDOA) passive localization scenario. We seek for the best sensor combination by formulating a non-convex optimization problem, which is to minimize the trace of covariance matrix of localization error under the condition that the number of selected sensors is given. The accuracy metric is described by the localization error covariance matrix of classical closed-form solution, which is introduced to convert the TDOA nonlinear equations into pseudo linear equations. The non-convex optimization problem is relaxed to a standard semi-definite program (SDP) and efficiently solved in a short time. In addition, we extend the sensor selection method to a mixed TDOA and angle of arrival (AOA) localization scenario with the presence of sensor position errors. Simulation results validate that the performance of the proposed sensor selection method is very close to the exhaustive search method.