Homotopy Continuation for Sensor Networks Self-Calibration

Luca Ferranti, Kalle Aström, Magnus Oskarsson, Jani Boutellier, Juho Kannala

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceedingPeer review


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.

Titel på värdpublikation29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Antal sidor5
ISBN (elektroniskt)9789082797060
StatusPublished - 2021
Evenemang29th European Signal Processing Conference, EUSIPCO 2021 - Dublin, Irland
Varaktighet: 2021 aug. 232021 aug. 27


NamnEuropean Signal Processing Conference
ISSN (tryckt)2219-5491


Konferens29th European Signal Processing Conference, EUSIPCO 2021

Ämnesklassifikation (UKÄ)

  • Datorseende och robotik (autonoma system)


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