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Source localization and denoising: a perspective from the TDOA space

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Abstract

In this manuscript, we formulate the problem of source localization based on Time Differences of Arrival (TDOAs) in the TDOA space, i.e., the Euclidean space spanned by TDOA measurements. More specifically, we show that source localization can be interpreted as a denoising problem of TDOA measurements. As this denoising problem is difficult to solve in general, our analysis shows that it is possible to resort to a relaxed version of it. The solution of the relaxed problem through linear operations in the TDOA space is then discussed, and its analysis leads to a parallelism with other state-of-the-art TDOA denoising algorithms. Additionally, we extend the proposed solution also to the case where only TDOAs between few pairs of microphones within an array have been computed. The reported denoising algorithms are all analytically justified, and numerically tested through simulative campaign.

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Notes

  1. In order to simplify the presentation, we consider only the case with the microphones in general position on the plane, i.e., they do not lie on a line. The interested reader can find the complete analysis for every scenario and the proofs in the original manuscripts.

  2. With slight abuse of notation, in the proof we identify a matrix with the associated linear map defined through matrix multiplication.

  3. For the sake of compactness, throughout this paragraph we will use the word denoising referring to relaxed denoising.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Marco Compagnoni

  2. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Ponzio 34/5, 20133, Milan, Italy

    Antonio Canclini, Paolo Bestagini, Fabio Antonacci, Augusto Sarti & Stefano Tubaro

Authors
  1. Marco Compagnoni
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  2. Antonio Canclini
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  3. Paolo Bestagini
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  4. Fabio Antonacci
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  5. Augusto Sarti
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  6. Stefano Tubaro
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Correspondence to Antonio Canclini.

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Compagnoni, M., Canclini, A., Bestagini, P. et al. Source localization and denoising: a perspective from the TDOA space. Multidim Syst Sign Process 28, 1283–1308 (2017). https://doi.org/10.1007/s11045-016-0400-9

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  • DOI: https://doi.org/10.1007/s11045-016-0400-9

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