Optimal Trilateration Is an Eigenvalue Problem

Martin Larsson; Viktor Larsson; Kalle Astrom; Magnus Oskarsson

doi:10.1109/ICASSP.2019.8683355

Optimal Trilateration Is an Eigenvalue Problem

Martin Larsson, Viktor Larsson, Kalle Astrom, Magnus Oskarsson

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

Abstract

The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.

Original language	English
Title of host publication	2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	5586-5590
Number of pages	5
Volume	2019-May
ISBN (Electronic)	9781479981311
DOIs	https://doi.org/10.1109/ICASSP.2019.8683355
Publication status	Published - 2019 May
Event	44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom Duration: 2019 May 12 → 2019 May 17

Conference

Conference	44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
Country/Territory	United Kingdom
City	Brighton
Period	2019/05/12 → 2019/05/17

Subject classification (UKÄ)

Signal Processing
Computational Mathematics

Keywords

Calibration
Multilateration
Optimal estimation
Trilateration

Access to Document

10.1109/ICASSP.2019.8683355

Cite this

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title = "Optimal Trilateration Is an Eigenvalue Problem",

abstract = "The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.",

keywords = "Calibration, Multilateration, Optimal estimation, Trilateration",

author = "Martin Larsson and Viktor Larsson and Kalle Astrom and Magnus Oskarsson",

year = "2019",

month = may,

doi = "10.1109/ICASSP.2019.8683355",

language = "English",

volume = "2019-May",

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booktitle = "2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings",

publisher = "IEEE - Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

note = "44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 ; Conference date: 12-05-2019 Through 17-05-2019",

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Larsson, M , Larsson, V , Astrom, K & Oskarsson, M 2019, Optimal Trilateration Is an Eigenvalue Problem. in 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. vol. 2019-May, 8683355, IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 5586-5590, 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019, Brighton, United Kingdom, 2019/05/12. https://doi.org/10.1109/ICASSP.2019.8683355

Optimal Trilateration Is an Eigenvalue Problem. / Larsson, Martin ; Larsson, Viktor ; Astrom, Kalle et al.

2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Vol. 2019-May IEEE - Institute of Electrical and Electronics Engineers Inc., 2019. p. 5586-5590 8683355.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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T1 - Optimal Trilateration Is an Eigenvalue Problem

AU - Larsson, Martin

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AU - Astrom, Kalle

AU - Oskarsson, Magnus

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N2 - The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.

AB - The problem of estimating receiver or sender node positions from measured receiver-sender distances is a key issue in different applications such as microphone array calibration, radio antenna array calibration, mapping and positioning using UWB or using round-trip-time measurements between mobile phones and WiFi-units. In this paper we address the problem of optimally estimating a receiver position given a number of distance measurements to known sender positions, so called trilateration. We show that this problem can be rephrased as an eigenvalue problem. We also address different error models and the multilateration setting where an additional offset is also unknown, and show that these problems can be modeled using the same framework.

KW - Calibration

KW - Multilateration

KW - Optimal estimation

KW - Trilateration

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M3 - Paper in conference proceeding

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VL - 2019-May

SP - 5586

EP - 5590

BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings

PB - IEEE - Institute of Electrical and Electronics Engineers Inc.

T2 - 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019

Y2 - 12 May 2019 through 17 May 2019

ER -

Optimal Trilateration Is an Eigenvalue Problem

Abstract

Conference

Subject classification (UKÄ)

Keywords

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Localization using Distance Geometry: Minimal Solvers and Robust Methods for Sensor Network Self-Calibration

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