MDS-Based Localization

MDS-Based Localization

Ahmed A. Ahmed (Texas State University–San Marcos, USA), Xiaoli Li (University of Missouri–Columbia, USA), Yi Shang (University of Missouri–Columbia, USA) and Hongchi Shi (Texas State University–San Marcos, USA)
DOI: 10.4018/978-1-60566-396-8.ch008

Abstract

The authors present several network node localization methods that are based on multidimensional scaling (MDS) techniques. Four algorithms are introduced: MDS-MAP(C), MDS-MAP(P), MDS-Hybrid, and RangeQ-MDS. MDS-MAP(C) is a centralized algorithm that simply applies MDS to estimate node positions. In MDS-MAP(P), a local map is built at each node of the immediate vicinity, then these maps are merged together to form a global map. MDS-Hybrid uses MDS-MAP(C) to relatively localize Nr reference nodes. Then, an absolute localization method uses these Nr nodes as anchors to localize the rest of the network. Finally, RangeQ-MDS assumes the absence of an RSSI-distance mapping function. It uses a quantized RSSI-based distance estimation technique (called RangeQ) to achieve more precise hop distances than other range-free approaches do. While MDS-MAP(C), MDS-MAP(P), and MDSHybrid can be range-aware or range-free, RangeQ-MDS is partially range-aware.
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Problem Formulation

The network is represented as a connected undirected graph G = (V, E), where V is the set of sensor nodes, of which there exist A978-1-60566-396-8.ch008.m01V special nodes (called anchors) with known positions, and E is the set of edges connecting neighboring nodes. For the range-free case, the edges in the graph correspond to the connectivity information. For the range-aware case, the edges are associated with values corresponding to the estimated distances.

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