Abstract:

A new two-step semidefinite relaxation method is proposed to deal with the nonlinear and non-convex problem of acoustic energy-based localization in wireless sensor networks. The proposed algorithm transforms the nonlinear positioning equations into a weighted least squares estimation problem of the unknown source location and signal transmit power, which is then solved in two steps. First, the signal transmit power is eliminated from the cost function by expressing it as a function of the source position in the least square sense. In the second step, the weighted least squares formulation is converted into a semidefinite programming(SDP) optimization problem by using a new convex relaxation technique. The tightness of the semidefinite relaxation method is theoretically proved. Simulation results indicate that compared with the previous methods, the proposed algorithm has a higher localization accuracy, especially when the measurement error is relatively large.

Key words: wireless sensor networks, acoustic energy, source localization, semidefinite programming, weighted leasts quares