Sensor Network Localization, A Localized Algorithm Based On Semi-definite Programming

Given a subset of pairwise distance, there may be some fixed points (anchor) ofthe absolute position, whether we can estimate all unknown point position accuratelywithin a given dimensional space involves in the solution of a non-strictly convexoptimization problem. This problem is known as the Euclidean distance geometry, orgraph realization problem. Semi-definite programming will lead to high-dimensionalsolution when partial distance information contains noise. Under the application ofsensor localization background, over a three-dimensional solution has no real meaning,so we need to limit the dimension of solutions using soft‘methods.In this paper, the main work:1. Introducing the new framework of semi-definite programming in graphrealization. Euclidean matrix completion and graph embedding condition areincluded.2. In the framework of semi-definite programming in graph realization. We usethe idea of trace-norm regularization in machine learning to deal with lowrank matrix completion. Our algorithm is applied to the sensor realizationproblem, we can obtain better results in networks with very few anchors,smaller communication radius case than GPS triangulation.3. With the growth of the number of unknown point, semi-definite programmingsolution becomes calculated unsolvable. We discuss a local method forpositioning sensor nodes, and then these patches stitching into a whole, as amethod for the overall positioning result. Local graph algorithm is not only incomputational efficiency and accuracy better than global graph realizationalgorithm.It should be pointed out that the proposed method is a universal solution,molecular models can also be applied to build. It is not limited to the sensorpositioning problems.