Homotopy Continuation for Sensor Networks Self-Calibration
(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.
(Less)
- author
- Ferranti, Luca
LU
; Aström, Kalle
LU
; Oskarsson, Magnus LU
; Boutellier, Jani and Kannala, Juho
- organization
- publishing date
- 2021
- 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}}, }