An Affine Scaling Steepest Descent Algorithm for Target Localization in Wireless Sensor Networks

Target localization is one of the essential tasks in the applications of wireless sensor networks (WSNs). The traditional target localization based on received signal strength may fail to obtain satisfactory localization performance, especially when the number of the RSS measurements is limited. Compressed sensing (CS) has been shown to be an effective technique for target localization due to the intrinsic sparse nature of target localization in WSNs. The CS-based target localization can be formulated to a sparse recovery problem based on l(0)-norm or l(1)-norm minimization. Compared to l(0)-norm and l(1)-norm, l(p)-norm (0 < p < 1) can provide the most effective sparsity measurement of a vector. Some traditional sparse recovery algorithms for l(p)-norm minimization, however, usually obtain suboptimal sparse solutions when the initial point is not in the convergence domain of the globally optimal sparse solution. In this paper, we propose a novel affine scaling steepest descent (ASSD) algorithm to find a satisfying sparse solution of l(p)-norm minimization. By setting an optimal stepsize at each iteration, our ASSD algorithm can avoid the iterative solutions concentrating on the attraction basin of the suboptimal sparse solution and move to the attraction basin of a sparser solution, so it has high opportunity to obtain the globally optimal sparse solution, and then accurately determine the locations of targets. The experimental results show that our ASSD algorithm performs much better than the traditional BP, OMP, GMP, ASM, IRL1, and ITM algorithms, especially when the number of measurements is insufficient.