Singular Value Thresholding Algorithm for Wireless Sensor Network Localization

Abstract

Wireless Sensor Networks (WSN) are of great current interest in the proliferation of technologies. Since the location of the sensors is one of the most interesting issues in WSN, the process of node localization is crucial for any WSN-based applications. Subsequently, WSN’s node estimation deals with a low-rank matrix which gives rise to the application of the Nuclear Norm Minimization (NNM) method. This paper will focus on the localization of 2-dimensional WSN with objects (obstacles). Recent studies introduce Nuclear Norm Minimization (NNM) for node estimation instead of formulating the rank minimization problem. Common way to tackle this problem is by implementing the Semidefinite Programming (SDP). However, SDP can only handle matrices with a size of less than 100 × 100. Therefore, we introduce the method of Singular Value Thresholding (SVT) which is an iterative algorithm to solve the NNM problem that produces a sequence of matrices { X k , Y k } and executes a soft-thresholding operation on the singular value of the matrix Y k . This algorithm is a user-friendly algorithm which produces a low computational cost with low storage capacity required to give the lowest-rank minimum nuclear norm solution.