# Geomtric Sound Source Localization @ EUSIPCO, WASPAA & TASLP

#### Xavier Alameda-Pineda and Radu Horaud

Keywords: multivariate optimization, hyperbolic constraints, log-barrier interior point, branch & bound.

We address the problem of sound-source localization from time-delay estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel geometric formulation is proposed, together with a thorough algebraic analysis and a global optimization solver. The proposed model is thoroughly described and evaluated. The geometric analysis, stemming from the direct acoustic propagation model, leads to necessary and sufficient conditions for a set of time delays to correspond to a unique position in the source space. Such sets of time delays are referred to as {\em feasible sets}. We formally prove that every feasible set corresponds to exactly one position in the source space, whose value can be recovered using a closed-form localization mapping. Therefore we seek for the optimal feasible set of time delays given, as input, the received microphone signals. This time delay estimation problem is naturally cast into a programming task, constrained by the feasibility conditions derived from the geometric analysis. A global branch-and-bound optimization technique is proposed to solve the problem at hand, hence estimating the best set of feasible time delays and, subsequently, localizing the sound source. Extensive experiments with both simulated and real data are reported; we compare our methodology to four state-of-the-art techniques. This comparison shows that the proposed method combined with the branch-and-bound algorithm outperforms existing methods. These in-depth geometric understanding, practical algorithms, and encouraging results, open several opportunities for future work.

Pieces of this work were published in [1], [2], and finally consolidated in [3].

### Publications

1. X. Alameda-Pineda and R. Horaud, “Geometrically-constrained Robust Time Delay Estimation Using Non-coplanar Microphone Arrays,” in European Signal Processing Conference, Bucarest, Romania, 2012, pp. 1309-1313. [ bib pdf code ]
@InProceedings{Alameda-EUSIPCO-2012,
author       = "Alameda-Pineda, Xavier and Horaud, Radu",
title        = "Geometrically-constrained Robust Time Delay Estimation Using Non-coplanar Microphone Arrays",
booktitle    = "European Signal Processing Conference",
year         = "2012",
pages = {1309--1313},
address = {Bucarest, Romania},
soft = {https://team.inria.fr/perception/the-gtde-matlab-toolbox/},
pdf={http://xavirema.eu/wp-content/papercite-data/pdf/Alameda-EUSIPCO-2012.pdf}
}
2. X. Alameda-Pineda, R. Horaud, and B. Mourrain, “The Geometry of Sound Source Localization Using Non-Coplanar Microphone Arrays,” in IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, USA, 2013, pp. 1-4. [ bib pdf code ]
@inproceedings{Alameda-WASPAA-2013,
author = {Xavier Alameda-Pineda and Radu Horaud and Bernard Mourrain},
title = {The Geometry of Sound Source Localization Using Non-Coplanar Microphone Arrays},
booktitle = {IEEE Workshop on Applications of Signal Processing to Audio and Acoustics},
year = {2013},
pages = {1--4},
address = {New Paltz, USA},
soft = {https://team.inria.fr/perception/the-gtde-matlab-toolbox/},
pdf={http://xavirema.eu/wp-content/papercite-data/pdf/Alameda-WASPAA-2013.pdf}
}
3. X. Alameda-Pineda and R. Horaud, “A Geometric Approach to Sound Source Localization from Time-Delay Estimates,” IEEE Transactions on Audio, Speech and Language Processing, vol. 22, iss. 6, pp. 1082-1095, 2014. [ bib pdf code arxiv ]
@article{Alameda-TASLP-2014,
author    = {Xavier Alameda-Pineda and Radu Horaud},
title     = {A Geometric Approach to Sound Source Localization from Time-Delay Estimates},
journal   = {{IEEE Transactions on Audio, Speech and Language Processing}},
year      = {2014},
volume   = {22},
number   = {6},
pages   = {1082-1095},
arxiv = {http://arxiv.org/abs/1311.1047},
soft = {https://team.inria.fr/perception/the-gtde-matlab-toolbox/},
doi={10.1109/TASLP.2014.2317989},
pdf={http://xavirema.eu/wp-content/papercite-data/pdf/Alameda-TASLP-2014.pdf}
}