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

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › 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.

Originalsprog	Engelsk
Titel	Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing
Redaktører	Naonori Ueda, Jen-Tzung Chien, Tomoko Matsui, Jan Larsen, Shinji Watanabe
Antal sider	6
Forlag	IEEE Press
Publikationsdato	5. dec. 2017
Sider	1-6
ISBN (Trykt)	978-1-5090-6342-0
ISBN (Elektronisk)	978-1-5090-6341-3
DOI	https://doi.org/10.1109/MLSP.2017.8168145
Status	Udgivet - 5. dec. 2017
Begivenhed	27th International Workshop on Machine Learning for Signal Processing - Tokyo, Japan Varighed: 25. sep. 2017 → 28. sep. 2017 Konferencens nummer: 27

Workshop

Workshop	27th International Workshop on Machine Learning for Signal Processing
Nummer	27
Land/Område	Japan
By	Tokyo
Periode	25/09/2017 → 28/09/2017

Navn	Machine Learning for Signal Processing
Vol/bind	2017
ISSN	1551-2541

Dokumenter og links

10.1109/MLSP.2017.8168145

SDU link

Tjek adgangen til materialet i Syddansk Universitetsbiblioteks søgemaskine

Citationsformater

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. red. / Naonori Ueda ; Jen-Tzung Chien ; Tomoko Matsui ; Jan Larsen ; Shinji Watanabe. IEEE Press, 2017. s. 1-6 (Machine Learning for Signal Processing, Bind 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",

year = "2017",

month = dec,

day = "5",

doi = "10.1109/MLSP.2017.8168145",

language = "English",

isbn = "978-1-5090-6342-0",

series = "Machine Learning for Signal Processing",

pages = "1--6",

editor = "Naonori Ueda and Jen-Tzung Chien and Tomoko Matsui and Jan Larsen and Shinji Watanabe",

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. i N Ueda, J-T Chien, T Matsui, J Larsen & S Watanabe (red), Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing. IEEE Press, Machine Learning for Signal Processing, bind 2017, s. 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. red. / Naonori Ueda; Jen-Tzung Chien; Tomoko Matsui; Jan Larsen; Shinji Watanabe. IEEE Press, 2017. s. 1-6 (Machine Learning for Signal Processing, Bind 2017).

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

TY - GEN

T1 - Upper Bound Performance Of Semi-Definite Programming For Localisation In Inhomogeneous Media

AU - Blanes-Vidal, Victoria

AU - S. Nadimi, Esmaeil

N1 - Conference code: 27

PY - 2017/12/5

Y1 - 2017/12/5

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.

KW - Edmundson-Madansky bound

KW - Inhomogeneous media

KW - Localisation

KW - Semi-Definite programming

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DO - 10.1109/MLSP.2017.8168145

M3 - Article in proceedings

SN - 978-1-5090-6342-0

T3 - Machine Learning for Signal Processing

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BT - Proceedings of the 27th IEEE Workshop on Machine Learning for Signal Processing

A2 - Ueda, Naonori

A2 - Chien, Jen-Tzung

A2 - Matsui, Tomoko

A2 - Larsen, Jan

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PB - IEEE Press

T2 - 27th International Workshop on Machine Learning for Signal Processing

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

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

Abstract

Workshop

Dokumenter og links

SDU link

Fingeraftryk

Citationsformater