Abstract

This work proposes a novel connectivity-based localization algorithm, well suitable for large-scale sensor networks with complex shapes and a non-uniform nodal distribution. In contrast to current state-of-the-art connectivity-based localization methods, the proposed algorithm is highly scalable with linear computation and communication costs with respect to the size of the network; and fully distributed where each node only needs the information of its neighbors without cumbersome partitioning and merging process. The algorithm is theoretically guaranteed and numerically stable. Moreover, the algorithm can be readily extended to the localization of networks with a one-hop transmission range distance measurement, and the propagation of the measurement error at one sensor node is limited within a small area of the network around the node. Extensive simulations and comparison with other methods under various representative network settings are carried out, showing the superior performance of the proposed algorithm.

Highlights

  • Geographic location information is imperative to a variety of applications in wireless sensor networks, ranging from position-aware sensing to distributed data storage and processing, geographic routing and nodal deployment

  • Previous localization methods with mere connectivity have mainly focused on dimension reduction of multidimensional datasets based on the input distance matrix, which is approximated by hop counts between each possible pair of nodes

  • Several approaches have been proposed to increase the possibility to escape from local minima of the minimized energy, the selection of initial values is still crucial for the final localization results [5]

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Summary

Introduction

Geographic location information is imperative to a variety of applications in wireless sensor networks, ranging from position-aware sensing to distributed data storage and processing, geographic routing and nodal deployment. Some application scenarios prohibit the reception of satellite signals by part or all of the sensors, rendering it impossible to solely rely on global navigation systems. Even for those ranging information-based localization schemes, extra equipment installed to measure the distance or the angle between nodes can lead to a dramatic increase of network cost. To this end, many interesting approaches have been proposed for localization with mere connectivity information. Each node only knows which nodes are nearby within its one-hop communication radio range, but does not know how far away and in what direction its neighbors are

Challenges of Previous Approaches
Our Approach
Related Works
Optimal Flat Metric
Discrete Metric and Gaussian Curvature
Discrete Surface Ricci Flow
Localization with Mere Connectivity
Computing Optimal Flat Metric with Mere Connectivity
Isometric Embedding
Time Complexity and Communication Cost
Discussions
Localization with Distance Measurement
Constructing Triangulation
Computing the Optimal Flat Metric with Distance Measurement
Error Propagation
Simulations and Comparison
Networks with Variant Nodal Densities
Networks with Different Transmission Models
Networks with Non-Uniform Nodal Distribution
Comparison with Other Methods on Networks with Mere Connectivity
Comparison with Other Methods on Networks with Range Distance Measurements
Computing Time
Findings
Conclusions
Full Text
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