ABSTRACT
We present a method for calibration-free, infrastructure-free localization in sensor networks. Our strategy is to estimate node positions and noise distributions of all links in the network simultaneously - a strategy that has not been attempted thus far. In particular, we account for biased, non-line-of-sight (NLOS) range measurements from ultra-wideband (UWB) devices that lead to multi-modal noise distributions, for which few solutions exist to date. Our approach circumvents cumbersome a-priori calibration, allows for rapid deployment in unknown environments, and facilitates adaptation to changing conditions. Our first contribution is a generalization of the classical multidimensional scaling algorithm to account for measurements that have multi-modal error distributions. Our second contribution is an online approach that iterates between node localization and noise parameter estimation. We validate our method in 3-dimensional networks, (i) through simulation to test the sensitivity of the algorithm on its design parameters, and (ii) through physical experimentation in a NLOS environment. Our setup uses UWB devices that provide time-of-flight measurements, which can lead to positively biased distance measurements in NLOS conditions. We show that our algorithm converges to accurate position estimates, even when initial position estimates are very uncertain, initial error models are unknown, and a significant proportion of the network links are in NLOS.
- Nayef A Alsindi, Bardia Alavi, and Kaveh Pahlavan. 2009. Measurement and modeling of ultrawideband TOA-based ranging in indoor multipath environments. IEEE Transactions on Vehicular Technology 58, 3 (2009), 1046--1058.Google ScholarCross Ref
- David Arthur and Sergei Vassilvitskii. 2007. k-means++: The Advantages of Careful Seeding. In ACM-SIAM Symposium on Discrete Algorithms. 1027--1035. Google ScholarDigital Library
- James Aspnes, Tolga Eren, David K Goldenberg, A Stephen Morse, Walter Whiteley, Y Richard Yang, Brian Anderson, and Peter N Belhumeur. 2006. A theory of network localization. Mobile Computing, IEEE Transactions on 5, 12 (2006), 1663--1678. Google ScholarDigital Library
- Christophe Biernacki, Gilles Celeux, and Gerard Govaert. 2003. Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics and Data Analysis 41, 3--4 (2003), 561--575. Google ScholarDigital Library
- Jeff Bilmes. 1998. A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. International Computer Science Institute 4, 510 (1998), 126.Google Scholar
- Johannes Blömer and Kathrin Bujna. 2016. Adaptive Seeding for Gaussian Mixture Models. In Advances in Knowledge Discovery and Data Mining: Pacific-Asia Conference. Springer International Publishing, 296--308. Google ScholarDigital Library
- I. Borg and P.J.F. Groenen. 2005. Modern Multidimensional Scaling: Theory and Applications. Springer.Google Scholar
- Ming Cao, Brian DO Anderson, and A Stephen Morse. 2006. Sensor network localization with imprecise distances. Systems & control letters 55, 11 (2006), 887--893.Google Scholar
- Yiu-Tong Chan, Wing-Yue Tsui, Hing-Cheung So, and Pak-chung Ching. 2006. Time-of-arrival based localization under NLOS conditions. IEEE Transactions on Vehicular Technology 55, 1 (2006), 17--24.Google ScholarCross Ref
- Hongyang Chen, Gang Wang, Zizhuo Wang, Hing-Cheung So, and H Vincent Poor. 2012. Non-line-of-sight node localization based on semi-definite programming in wireless sensor networks. IEEE Transactions on Wireless Communications 11, 1 (2012), 108--116.Google ScholarCross Ref
- Li Cong and Weihua Zhuang. 2005. Nonline-of-sight error mitigation in mobile location. IEEE Transactions on Wireless Communications 4, 2 (2005), 560--573. Google ScholarDigital Library
- Jose Costa, Neal Patwari, and Alfred Hero III. 2006. Distributed weighted-multidimensional scaling for node localization in sensor networks. ACM Transactions on Sensor Networks (TOSN) 2, 1 (2006), 39--64. Google ScholarDigital Library
- Jan De Leeuw. 2005. Applications of convex analysis to multidimensional scaling. Department of Statistics, UCLA (2005).Google Scholar
- Arthur Dempster, Nan Laird, and Donald Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (1977), 1--38.Google Scholar
- Y. Diao, Z. Lin, and M. Fu. 2014. A Barycentric Coordinate Based Distributed Localization Algorithm for Sensor Networks. IEEE Trans. on Signal Processing 62, 18 (2014), 4760--4771.Google ScholarCross Ref
- Bruce Hendrickson. 1992. Conditions for unique graph realizations. SIAM journal on computing 21, 1 (1992), 65--84. Google ScholarDigital Library
- W. Kabsch. 1976. A solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A 32 (1976), 922--923.Google ScholarCross Ref
- W. Kabsch. 1978. A discussion of the solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A 34 (1978), 827--828.Google ScholarCross Ref
- Anushiya Kannan, Baris Fidan, Guoqiang Mao, and Brian Anderson. 2007. Analysis of flip ambiguities in distributed network localization. Information, Decision and Control (IDC) (2007), 193--198.Google Scholar
- Soummya Kar, J. Moura, and Kavita Ramanan. 2012. Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication. Trans. on Information Theory 58, 6 (2012), 3575--3605. Google ScholarDigital Library
- Benjamin Kempke, Pat Pannuto, Bradford Campbell, and Prabal Dutta. 2016. SurePoint: Exploiting Ultra Wideband Flooding and Diversity to Provide Robust, Scalable, High-Fidelity Indoor Localization. In Proceedings of the 14th ACM Conference on Embedded Network Sensor Systems CD-ROM. ACM, 137--149. Google ScholarDigital Library
- Benjamin Kempke, Pat Pannuto, and Prabal Dutta. 2016. Harmonium: Asymmetric, Bandstitched UWB for Fast, Accurate, and Robust Indoor Localization. In 2016 15th ACM/IEEE International Conference on Information Processing in Sensor Networks (IPSN). IEEE, 1--12. Google ScholarDigital Library
- U. Khan, S. Kar, and J. Moura. 2010. DILAND: An Algorithm for Distributed Sensor Localization With Noisy Distance Measurements. IEEE Transactions on Signal Processing 58, 3 (2010), 1940--1947. Google ScholarDigital Library
- Usman A Khan, Soummya Kar, and José MF Moura. 2009. Distributed sensor localization in random environments using minimal number of anchor nodes. IEEE Transactions on Signal Processing 57, 5 (2009), 2000--2016. Google ScholarDigital Library
- Joseph B Kruskal. 1964. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29, 1 (1964), 1--27.Google ScholarCross Ref
- Josef Kulmer, Erik Leitinger, Paul Meissner, and Klaus Witrisal. 2015. Cooperative Multipath-assisted Navigation and Tracking: A Low-Complexity Approach. In Future Access Enablers of Ubiquitous and Intelligent Infrastructures. Springer, 159--165.Google Scholar
- Duke Lee. 2005. Localization using multidimensional scaling (LMDS). Ph.D. Dissertation. UNIVERSITY OF CALIFORNIA.Google Scholar
- Julia Letchner, Dieter Fox, and Anthony LaMarca. 2005. Large-scale Localization from Wireless Signal Strength. In National Conference on Artificial Intelligence, Vol. 1. AAAI Press, 15--20. Google ScholarDigital Library
- Volodymyr Melnykov and Igor Melnykov. 2012. Initializing the EM algorithm in Gaussian mixture models with an unknown number of components. Computational Statistics and Data Analysis 56, 6 (2012), 1381--1395. Google ScholarDigital Library
- David Moore, John Leonard, Daniela Rus, and Seth Teller. 2004. Robust distributed network localization with noisy range measurements. In Proceedings of the 2nd ACM International Conference on Embedded Networked Sensor Systems. 50--61. Google ScholarDigital Library
- Amanda Prorok. 2013. Models and Algorithms for Ultra-Wideband Localization in Single-and Multi-Robot Systems. Ph.D. Dissertation. École Polytechnique Fédérale de Lausanne.Google Scholar
- Amanda Prorok and Alcherio Martinoli. 2014. Accurate indoor localization with ultra-wideband using spatial models and collaboration. The International Journal of Robotics Research 33, 4 (2014), 547--568. Google ScholarDigital Library
- Yihong Qi. 2003. Wireless geolocation in a non-line-of-sight environment. Ph.D. Dissertation. Ph. D. dissertation, Princeton Univ., Princeton, NJ.Google Scholar
- Zafer Sahinoglu, Sinan Gezici, and Ismail Guvenc. 2008. Ultra-wideband positioning systems. Cambridge, New York (2008).Google Scholar
- Yi Shang, W Rumi, Ying Zhang, and Markus Fromherz. 2004. Localization from connectivity in sensor networks. Parallel and Distributed Systems, IEEE Transactions on 15, 11 (2004), 961--974. Google ScholarDigital Library
- Yi Shang and Wheeler Ruml. 2004. Improved MDS-based localization. In INFOCOM 2004. Twenty-third AnnualJoint Conference of the IEEE Computer and Communications Societies, Vol. 4. IEEE, 2640--2651.Google ScholarCross Ref
- Saipradeep Venkatraman, James Caffery, and Heung-Ryeol You. 2004. A novel TOA location algorithm using LOS range estimation for NLOS environments. IEEE Transactions on Vehicular Technology 53, 5 (2004), 1515--1524.Google ScholarCross Ref
- Radim Zemek, Shinsuke Hara, Kentaro Yanagihara, and Ken-ichi Kitayama. 2007. A joint estimation of target location and channel model parameters in an IEEE 802.15. 4-based wireless sensor network. In IEEE Int. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC). 1--5.Google Scholar
Index Terms
Calibration-free network localization using non-line-of-sight ultra-wideband measurements
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