Ordinal MDS-Based Localization for Wireless Sensor Networks

Abstract

There are various applications in wireless sensor networks which require knowing the relative or actual position of the sensor nodes. Recently, there have been different localization algorithms proposed in the literature. The algorithms based on classical Multidimensional Scaling (MDS) only require 3 or 4 anchor nodes and can provide higher accuracy than some other schemes. In this paper, we propose and analyze another type of MDS (called <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ordinal</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MDS</i> ) for localization in wireless sensor networks. Ordinal MDS differs from classical MDS by that it only requires a monotonicity constraint between the shortest path distance and the Euclidean distance for each pair of nodes. We conduct simulation studies under square and C-shaped topologies with different connectivity levels and number of anchors. Results show that ordinal MDS provides a lower position estimation error than classical MDS.