Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media

Victoria  Blanes-Vidal; Esmaeil S. Nadimi

doi:10.1109/MLSP.2017.8168145

Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media

Victoria Blanes-Vidal, Esmaeil S. Nadimi

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

In this paper, we regarded an absorbing inhomogeneous medium as an assembly of thin layers having different propagation properties. We derived a stochastic model for the refractive index and formulated the localisation problem given noisy distance measurements using graph realisation problem. We relaxed the problem using semi-definite programming (SDP) approach in l ^p realisation domain and derived upper bounds that follow Edmundson-Madansky bound of order 6p (EM _6p) on the SDP objective function to provide an estimation of the techniques' localisation accuracy. Our results showed that the inhomogeneity of the media and the choice of l ^p norm have significant impact on the ratio of the expected value of the localisation error to the upper bound for the expected optimal SDP objective value. The tightest ratio was derived when l ^∞ norm was used.

Original language	English
Title of host publication	Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing
Editors	Naonori Ueda, Jen-Tzung Chien, Tomoko Matsui, Jan Larsen, Shinji Watanabe
Number of pages	6
Publisher	IEEE Press
Publication date	5. Dec 2017
Pages	1-6
ISBN (Print)	978-1-5090-6342-0
ISBN (Electronic)	978-1-5090-6341-3
DOIs	https://doi.org/10.1109/MLSP.2017.8168145
Publication status	Published - 5. Dec 2017
Event	27th International Workshop on Machine Learning for Signal Processing - Tokyo, Japan Duration: 25. Sept 2017 → 28. Sept 2017 Conference number: 27

Workshop

Workshop	27th International Workshop on Machine Learning for Signal Processing
Number	27
Country/Territory	Japan
City	Tokyo
Period	25/09/2017 → 28/09/2017

Series	Machine Learning for Signal Processing
Volume	2017
ISSN	1551-2541

Keywords

Edmundson-Madansky bound
Inhomogeneous media
Localisation
Semi-Definite programming

Documents & Links

10.1109/MLSP.2017.8168145

Cite this

Blanes-Vidal, Victoria ; S. Nadimi, Esmaeil. / Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media. Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing. editor / Naonori Ueda ; Jen-Tzung Chien ; Tomoko Matsui ; Jan Larsen ; Shinji Watanabe. IEEE Press, 2017. pp. 1-6 (Machine Learning for Signal Processing, Vol. 2017).

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title = "Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media",

abstract = "In this paper, we regarded an absorbing inhomogeneous medium as an assembly of thin layers having different propagation properties. We derived a stochastic model for the refractive index and formulated the localisation problem given noisy distance measurements using graph realisation problem. We relaxed the problem using semi-definite programming (SDP) approach in l p realisation domain and derived upper bounds that follow Edmundson-Madansky bound of order 6p (EM 6p) on the SDP objective function to provide an estimation of the techniques' localisation accuracy. Our results showed that the inhomogeneity of the media and the choice of l p norm have significant impact on the ratio of the expected value of the localisation error to the upper bound for the expected optimal SDP objective value. The tightest ratio was derived when l ∞ norm was used. ",

keywords = "Edmundson-Madansky bound, Inhomogeneous media, Localisation, Semi-Definite programming",

author = "Victoria Blanes-Vidal and {S. Nadimi}, Esmaeil",

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doi = "10.1109/MLSP.2017.8168145",

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booktitle = "Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing",

publisher = "IEEE Press",

note = "27th International Workshop on Machine Learning for Signal Processing, MLSP ; Conference date: 25-09-2017 Through 28-09-2017",

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Blanes-Vidal, V & S. Nadimi, E 2017, Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media. in N Ueda, J-T Chien, T Matsui, J Larsen & S Watanabe (eds), Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing. IEEE Press, Machine Learning for Signal Processing, vol. 2017, pp. 1-6, 27th International Workshop on Machine Learning for Signal Processing, Tokyo, Japan, 25/09/2017. https://doi.org/10.1109/MLSP.2017.8168145

Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media. / Blanes-Vidal, Victoria ; S. Nadimi, Esmaeil.
Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing. ed. / Naonori Ueda; Jen-Tzung Chien; Tomoko Matsui; Jan Larsen; Shinji Watanabe. IEEE Press, 2017. p. 1-6 (Machine Learning for Signal Processing, Vol. 2017).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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AU - S. Nadimi, Esmaeil

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N2 - In this paper, we regarded an absorbing inhomogeneous medium as an assembly of thin layers having different propagation properties. We derived a stochastic model for the refractive index and formulated the localisation problem given noisy distance measurements using graph realisation problem. We relaxed the problem using semi-definite programming (SDP) approach in l p realisation domain and derived upper bounds that follow Edmundson-Madansky bound of order 6p (EM 6p) on the SDP objective function to provide an estimation of the techniques' localisation accuracy. Our results showed that the inhomogeneity of the media and the choice of l p norm have significant impact on the ratio of the expected value of the localisation error to the upper bound for the expected optimal SDP objective value. The tightest ratio was derived when l ∞ norm was used.

AB - In this paper, we regarded an absorbing inhomogeneous medium as an assembly of thin layers having different propagation properties. We derived a stochastic model for the refractive index and formulated the localisation problem given noisy distance measurements using graph realisation problem. We relaxed the problem using semi-definite programming (SDP) approach in l p realisation domain and derived upper bounds that follow Edmundson-Madansky bound of order 6p (EM 6p) on the SDP objective function to provide an estimation of the techniques' localisation accuracy. Our results showed that the inhomogeneity of the media and the choice of l p norm have significant impact on the ratio of the expected value of the localisation error to the upper bound for the expected optimal SDP objective value. The tightest ratio was derived when l ∞ norm was used.

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KW - Semi-Definite programming

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Blanes-Vidal V , S. Nadimi E. Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media. In Ueda N, Chien JT, Matsui T, Larsen J, Watanabe S, editors, Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing. IEEE Press. 2017. p. 1-6. (Machine Learning for Signal Processing, Vol. 2017). doi: 10.1109/MLSP.2017.8168145

Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media

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