Multiobjective Optimization Based Sensor Selection for TDOA Tracking in Wireless Sensor Network

This paper investigates the sensor selection problem in time difference of arrival (TDOA) tracking scenario to find the optimal sensor activation strategy for the upcoming time step. We propose a multiobjective optimization framework to minimize two conflicting objectives, i.e., tracking accuracy and quantity budget, which are represented by the trace of the conditional posterior Cramér Rao lower bound (CPCRLB) and the number of selected sensors, respectively. Due to the reduced measurement dimension and correlated noise caused by the common reference sensor (CRS), sensor selection algorithms for the general nonlinear model in existing literature cannot be applied to the TDOA tracking directly as they mostly assume that each sensor produces an independent measurement. Therefore, we introduce two Boolean vectors to indicate the CRS and ordinary sensors respectively. The sensor selection problem is then formulated as a multiobjective optimization problem (MOP), which can be further transformed as a single objective optimization problem (SOOP) using the linear weighted-sum method. We prove that the SOOP satisfies the rules of discrete monotonic optimization (DMO), and propose the polyblock outer approximation (POA)-based algorithms to seek for a globally optimal solution. For comparison, we introduce the conventional semidefinite program (SDP)-based algorithm to solve the SOOP with multi-step relaxation. Simulation results demonstrate that the proposed POA-based algorithms can considerably outperform the SDP-based ones in solving the optimization problem.