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Homotopy Continuation for Sensor Networks Self-Calibration

Ferranti, Luca LU ; Aström, Kalle LU orcid ; Oskarsson, Magnus LU orcid ; Boutellier, Jani and Kannala, Juho (2021) 29th European Signal Processing Conference, EUSIPCO 2021 In European Signal Processing Conference 2021-August. p.1725-1729
Abstract

Given a sensor network, TDOA self-calibration aims at simultaneously estimating the positions of receivers and transmitters, and transmitters time offsets. This can be formulated as a system of polynomial equations. Due to the elevated number of unknowns and the nonlinearity of the problem, obtaining an accurate solution efficiently is nontrivial. Previous work has shown that iterative algorithms are sensitive to initialization and little noise can lead to failure in convergence. Hence, research has focused on algebraic techniques. Stable and efficient algebraic solvers have been proposed for some network configurations, but they do not work for smaller networks. In this paper, we use homotopy continuation to solve four previously... (More)

Given a sensor network, TDOA self-calibration aims at simultaneously estimating the positions of receivers and transmitters, and transmitters time offsets. This can be formulated as a system of polynomial equations. Due to the elevated number of unknowns and the nonlinearity of the problem, obtaining an accurate solution efficiently is nontrivial. Previous work has shown that iterative algorithms are sensitive to initialization and little noise can lead to failure in convergence. Hence, research has focused on algebraic techniques. Stable and efficient algebraic solvers have been proposed for some network configurations, but they do not work for smaller networks. In this paper, we use homotopy continuation to solve four previously unsolved configurations in 2D TDOA self-calibration, including a minimal one. As a theoretical contribution, we investigate the number of solutions of the new minimal configuration, showing this is much lower than previous estimates. As a more practical contribution, we also present new subminimal solvers, which can be used to achieve unique accurate solutions in previously unsolvable configurations. We demonstrate our solvers are stable both with clean and noisy data, even without nonlinear refinement afterwards. Moreover, we demonstrate the suitability of homotopy continuation for sensor network calibration problems, opening prospects to new applications.

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Please use this url to cite or link to this publication:
author
; ; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Homotopy continuation, Minimal problems, Sensor networks calibration, TDOA
host publication
29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings
series title
European Signal Processing Conference
volume
2021-August
pages
5 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
29th European Signal Processing Conference, EUSIPCO 2021
conference location
Dublin, Ireland
conference dates
2021-08-23 - 2021-08-27
external identifiers
  • scopus:85123190038
ISSN
2219-5491
ISBN
9789082797060
DOI
10.23919/EUSIPCO54536.2021.9616184
language
English
LU publication?
yes
id
80074729-1c3d-46dd-88aa-174cf2dffa71
date added to LUP
2022-03-24 15:28:07
date last changed
2022-05-02 18:15:07
@inproceedings{80074729-1c3d-46dd-88aa-174cf2dffa71,
  abstract     = {{<p>Given a sensor network, TDOA self-calibration aims at simultaneously estimating the positions of receivers and transmitters, and transmitters time offsets. This can be formulated as a system of polynomial equations. Due to the elevated number of unknowns and the nonlinearity of the problem, obtaining an accurate solution efficiently is nontrivial. Previous work has shown that iterative algorithms are sensitive to initialization and little noise can lead to failure in convergence. Hence, research has focused on algebraic techniques. Stable and efficient algebraic solvers have been proposed for some network configurations, but they do not work for smaller networks. In this paper, we use homotopy continuation to solve four previously unsolved configurations in 2D TDOA self-calibration, including a minimal one. As a theoretical contribution, we investigate the number of solutions of the new minimal configuration, showing this is much lower than previous estimates. As a more practical contribution, we also present new subminimal solvers, which can be used to achieve unique accurate solutions in previously unsolvable configurations. We demonstrate our solvers are stable both with clean and noisy data, even without nonlinear refinement afterwards. Moreover, we demonstrate the suitability of homotopy continuation for sensor network calibration problems, opening prospects to new applications.</p>}},
  author       = {{Ferranti, Luca and Aström, Kalle and Oskarsson, Magnus and Boutellier, Jani and Kannala, Juho}},
  booktitle    = {{29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings}},
  isbn         = {{9789082797060}},
  issn         = {{2219-5491}},
  keywords     = {{Homotopy continuation; Minimal problems; Sensor networks calibration; TDOA}},
  language     = {{eng}},
  pages        = {{1725--1729}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{European Signal Processing Conference}},
  title        = {{Homotopy Continuation for Sensor Networks Self-Calibration}},
  url          = {{http://dx.doi.org/10.23919/EUSIPCO54536.2021.9616184}},
  doi          = {{10.23919/EUSIPCO54536.2021.9616184}},
  volume       = {{2021-August}},
  year         = {{2021}},
}