| 1. |
- Ferranti, Luca, et al.
(author)
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Homotopy Continuation for Sensor Networks Self-Calibration
- 2021
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In: 29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings. - 2219-5491. - 9789082797060 ; 2021-August, s. 1725-1729
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Conference paper (peer-reviewed)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 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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| 2. |
- Ferranti, Luca, et al.
(author)
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Multiple Offsets Multilateration: : A New Paradigm for Sensor Network Calibration with Unsynchronized Reference Nodes
- 2022
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In: 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings. - 1520-6149. - 9781665405409 ; 2022-May, s. 4958-4962
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Conference paper (peer-reviewed)abstract
- Positioning using wave signal measurements is used in several applications, such as GPS systems, structure from sound and Wifi based positioning. Mathematically, such problems require the computation of the positions of receivers and/or transmitters as well as time offsets if the devices are unsynchronized. In this paper, we expand the previous state-of-the-art on positioning formulations by introducing Multiple Offsets Multilateration (MOM), a new mathematical framework to compute the receivers positions with pseudoranges from unsynchronized reference transmitters at known positions. This could be applied in several scenarios, for example structure from sound and positioning with LEO satellites. We mathematically describe MOM, determining how many receivers and transmitters are needed for the network to be solvable, a study on the number of possible distinct solutions is presented and stable solvers based on homotopy continuation are derived. The solvers are shown to be efficient and robust to noise both for synthetic and real audio data.
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| 3. |
- Ferranti, Luca, et al.
(author)
-
Sensor Networks Tdoa Self-Calibration : 2d Complexity Analysis and Solutions
- 2021
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In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - 1520-6149. - 9781728176062 - 9781728176055 ; 2021-June, s. 4635-4639
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Conference paper (peer-reviewed)abstract
- Given a network of receivers and transmitters, the process of determining their positions from measured pseudoranges is known as network self-calibration. In this paper we consider 2D networks with synchronized receivers but unsynchronized transmitters and the corresponding calibration techniques, known as Time-Difference-Of-Arrival (TDOA) techniques. Despite previous work, TDOA self-calibration is computationally challenging. Iterative algorithms are very sensitive to the initialization, causing convergence issues. In this paper, we present a novel approach, which gives an algebraic solution to two previously unsolved scenarios. We also demonstrate that our solvers produce an excellent initial value for non-linear optimisation algorithms, leading to a full pipeline robust to noise.
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