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Pascal’s triangle-based range-free localization for anisotropic wireless networks

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Abstract

This paper introduces a Pascal’s triangle model to draw the potential locations and their probabilities for a normal node given the hop counts to the anchors according to the extent of detour of the shortest paths. Based on our proposed model, a Pascal’s triangle-based localization (PTL) algorithm using local connectivity information is presented for anisotropic wireless networks with a small number of anchors. The superiority of the PTL algorithm has been validated over the state-of-the-art algorithms through MATLAB simulations. We have shown that compared to the other algorithms, the PTL algorithm achieves higher localization accuracy with even fewer anchors. We have also validated the performance of the PTL algorithm in a real environment.

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Notes

  1. The shortest paths to an anchor pair from a normal node is referred to as the compound shortest path. We give the exact definition of the compound shortest path in Sect. 5.2.

  2. A \((1-\alpha )\) confidence interval for the true mean \(\mu\) is defined as \(\mu \in (\bar{\mu }- z_{\alpha /2}\frac{\bar{\sigma }}{\sqrt{S}}, \bar{\mu } + z_{\alpha /2}\frac{\bar{\sigma }}{\sqrt{S}})\) with sample mean \(\bar{\mu }\), sample standard deviation \(\bar{\sigma }\), sample size S, and z-score \(z_{\alpha /2}\).

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Acknowledgments

This work has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2013R1A1A2062728) and the ICT R&D program of MSIP/IITP (14-044, Technology Development of GNSS Interference Verification Platform).

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Authors and Affiliations

  1. Department of Electronics and Computer Engineering, Hanyang University, Seoul, Korea

    Sangwoo Lee, Myungjun Jin, Bonhyun Koo & Sunwoo Kim

  2. Department of Satellite Wireless Convergence Research, Electronics and Telecommunications Research Institute, Daejeon, Korea

    Cheonsig Sin

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  1. Sangwoo Lee
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Correspondence to Sunwoo Kim.

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Lee, S., Jin, M., Koo, B. et al. Pascal’s triangle-based range-free localization for anisotropic wireless networks. Wireless Netw 22, 2221–2238 (2016). https://doi.org/10.1007/s11276-015-1095-9

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