Wireless Sensor Networks Localization Using Progressive Isomap

This paper proposes a progressive Isomap algorithm for node localization. The algorithm is an extension of centralized Isomap and is capable of effectively localizing new nodes progressively, without neglecting preceding computational results. In the initial startup phase, sensor nodes within two hop range of three non-collinear anchor nodes are localized using range (ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document})-Isomap. Afterwards, in the progressive phase, the remaining nodes are localized in a sequential manner, using recently localized nodes. The localization process initiated at different nodes in the network give rise to the overlapping substructures of localized nodes. The overlapped substructures are stitched to form a single coordinate system. Finally, Helmert Transformation is used to obtain the global coordinates of the nodes. The effects of varying various parameters on the accuracy and scalability of the proposed algorithm are studied through the simulation. Results indicate that the proposed algorithm has good positioning accuracy and noise-robustness.