Localization from Mere Connectivity

Localization from Mere Connectivity

June 1–3, 2003 | Yi Shang, Wheeler Ruml, Ying Zhang, Markus P. J. Fromherz
This paper presents MDS-MAP, a node localization algorithm that uses connectivity information to determine the positions of nodes in a network. The algorithm is based on multidimensional scaling (MDS), a data analysis technique that takes O(n³) time for a network of n nodes. MDS-MAP consists of three steps: first, it computes shortest paths between all pairs of nodes to estimate distances; second, it applies MDS to derive node locations that fit these estimated distances; and third, it transforms the relative map into absolute positions using known anchor nodes. The algorithm is robust to measurement errors and can achieve comparable results with fewer anchor nodes than previous methods. It can also provide relative coordinates when no anchor nodes are available. The method works well with low ratios of anchor nodes and performs better on regular networks. The algorithm is centralized, but it can be applied to sub-networks and combined to form an overall map. Experimental results show that MDS-MAP performs well in both random and grid layouts, with position errors decreasing as connectivity increases and as the number of anchor nodes increases. The method is particularly effective when the number of anchor nodes is small and the node distribution is uniform. MDS-MAP is more robust to range errors than previous methods and can handle non-uniform radio propagation and ranging errors. The algorithm can be extended by applying more advanced MDS techniques and by combining it with other methods for improved performance. The paper concludes that MDS-MAP is a promising approach for node localization in ad-hoc networks, especially when anchor nodes are limited.This paper presents MDS-MAP, a node localization algorithm that uses connectivity information to determine the positions of nodes in a network. The algorithm is based on multidimensional scaling (MDS), a data analysis technique that takes O(n³) time for a network of n nodes. MDS-MAP consists of three steps: first, it computes shortest paths between all pairs of nodes to estimate distances; second, it applies MDS to derive node locations that fit these estimated distances; and third, it transforms the relative map into absolute positions using known anchor nodes. The algorithm is robust to measurement errors and can achieve comparable results with fewer anchor nodes than previous methods. It can also provide relative coordinates when no anchor nodes are available. The method works well with low ratios of anchor nodes and performs better on regular networks. The algorithm is centralized, but it can be applied to sub-networks and combined to form an overall map. Experimental results show that MDS-MAP performs well in both random and grid layouts, with position errors decreasing as connectivity increases and as the number of anchor nodes increases. The method is particularly effective when the number of anchor nodes is small and the node distribution is uniform. MDS-MAP is more robust to range errors than previous methods and can handle non-uniform radio propagation and ranging errors. The algorithm can be extended by applying more advanced MDS techniques and by combining it with other methods for improved performance. The paper concludes that MDS-MAP is a promising approach for node localization in ad-hoc networks, especially when anchor nodes are limited.
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Understanding Localization from mere connectivity