Discrete Monotonic Optimization Based Sensor Selection for TDOA Localization

This paper investigates the sensor selection problem for time difference of arrival (TDOA) localization in wireless sensor networks. Specifically, a multi-objective optimization problem is formulated in which a Boolean vector is involved to find the best tradeoff between the localization accuracy and the energy consumption. The ε- constraints method is introduced to convert the original multi- objective optimization problem to a tractable single-objective problem. To solve the converted sensor selection problem, we propose the polyblock outer approximation (POA) algorithm based on discrete monotonic optimization (DMO) in order to find the global optimal solution, which however can not be obtained by the traditional semidefinite relaxation (SDR) approach. Further, for the sake of practical implementation, we propose another two suboptimal algorithms, namely, POA-based accelerated cutting (POA-AC) algorithm and POA-based monotonic cutting (POA-MC) algorithm. Simulation results validate that the localization accuracy for sensors selected by the POA-AC algorithm and POA-MC algorithm is greater than the semidefinite relaxation (SDR) solution and achieves the same results as that by the exhaustive search method.