Homotopy Continuation for Sensor Networks Self-Calibration

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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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.
Original languageEnglish
Title of host publicationProceedings of 29th European Signal Processing Conference, EUSIPCO
Number of pages5
ISBN (Electronic)978-9-0827-9706-0
ISBN (Print)978-1-6654-0900-1
Publication statusPublished - 8 Dec 2021
MoE publication typeA4 Article in a conference publication
EventEuropean Signal Processing Conference - Dublin, Ireland, Dublin, Ireland
Duration: 23 Aug 202127 Aug 2021
Conference number: 29

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491
ISSN (Electronic)2076-1465


ConferenceEuropean Signal Processing Conference
Abbreviated titleEUSIPCO


  • Location awareness
  • Transmitters
  • Signal processing algorithms
  • Europe
  • Receivers
  • Tools
  • Signal processing


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