A Distributed Gradient Descent Method for Node Localization on Large-Scale Wireless Sensor Network

A distributed iterative method is proposed to solve the problem of node (sensor) localization for large-scale wireless sensor network (WSN), by leveraging the graph topology decomposition and gradient descent method. First, the undirected graph representing the WSN is divided into several overlapping subgraphs. Based on the decomposition subgraphs, the localization problem is splitting into a series of subproblems each of which resides on one subgraph. The iterative procedure is proceeded on the subgraphs and each iteration consists of two operators. The first operator is solving the subproblem in every subgraph by using the gradient descent method which possesses light computational cost, and the second operator is to fuse and average the local positions of nodes in the overlapping region of adjacent subgraphs. In order to enrich the available information of localization, the positions of the target nodes with high localization accuracy are used as the (pseudo) anchor nodes for the subsequent iteration. Owing to that the operators are accomplished on subgraphs with small sizes, the proposed distributed iterative method possesses low computational cost, making it suitable for large-scale WSN. Numerical results are included to demonstrate the effectiveness of the proposed localization method.