Abstract
We consider the problem of sound sources localization from acoustical measurements obtained from a set of microphones. We formalize the problem within a statistical framework: the pressure measured by a microphone is interpreted as a mixture of the signals emitted by the sources, pervaded by a Gaussian noise. Maximum-likelihood estimates of the parameters of the model (locations and strengths of the sources) may then be computed via the EM algorithm. In this work, we introduce two sources of uncertainties: the location of the microphones and the wavenumber. First, we show how these uncertainties may be transposed to the data using belief functions. Then, we detail how the localization problem may be studied using a variant of the EM algorithm, known as Evidential EM algorithm. Eventually, we present simulation experiments which illustrate the advantage of using the Evidential EM algorithm when uncertain data are available.
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References
Bevington, P.R., Keith, D.: Data Reduction and Error Analysis for the Physical Sciences, 3rd edn. McGraw-Hill, New York (2003)
Cirpan, H.A., Cekli, E.: Deterministic Maximun Likelihood Approach for Localization of Near-Field Sources. International Journal of Electronics and Communications 56(1), 1–10 (2002)
Cirpan, H.A., Cekli, E.: Unconditional Maximum Likelihood Approach for Localization of Near-Field Sources: Algorithm and Performance Analysis. International Journal of Electronics and Communications 57(1), 9–15 (2003)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B (Methodological) 39(1), 1–38 (1977)
Dempster, A.P.: Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals of Mathematical Statistics 38(2), 325–339 (1967)
Dempster, A.P.: Upper and Lower Probabilities Generated by a Random Closed Interval. Annals of Mathematical Statistics 39(3), 957–966 (1968)
Denoeux, T.: Maximum Likelihood Estimation from Uncertain Data in the Belief Function Framework. IEEE Transactions on Knowledge and Data Engineering 25(1), 119–130 (2013)
Denoeux, T.: Maximum Likelihood Estimation from Fuzzy Data Using the EM Algorithm. Fuzzy Sets and Systems 183(1), 72–91 (2011)
Feder, M., Weinstein, E.: Parameter Estimation of Superimposed Signals Using EM Algorithm. IEEE Transactions on Acoustics, Speech and Signal Processing 36(4) (2005)
Kabaoglu, N., Cirpan, H.A., Cekli, E., Paker, S.: Deterministic Maximum Likelihood Approach for 3-D Near-Field Source Localization. International Journal of Electronics and Communications 57(5), 345–350 (2003)
Quost, B., Denœux, T.: Clustering Fuzzy Data Using the Fuzzy EM algorithm. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS (LNAI), vol. 6379, pp. 333–346. Springer, Heidelberg (2010)
Render, R.A., Walker, H.F.: Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAM Review 26(2), 195–239 (1984)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Smets, P.: Belief Functions on Real Numbers. International Journal of Approximate Reasoning 40(3), 181–223 (2005)
Rhodes, I.B.: A Tutorial Introduction to Estimation and Filtering. IEEE Transaction on Automatic Control AC-16(6), 688–706 (1971)
Williams, E.G.: Fourier Acoustic: Sound Radiation and Nearfield Acoustical Holography. Academic Press (1999)
Wu, J.C.F.: On the Convergence Properties of the EM Algorithm. Annals of Statistics 11(1), 95–103 (1983)
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Wang, X., Quost, B., Chazot, JD., Antoni, J. (2013). Sound Source Localization from Uncertain Information Using the Evidential EM Algorithm. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds) Scalable Uncertainty Management. SUM 2013. Lecture Notes in Computer Science(), vol 8078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40381-1_13
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DOI: https://doi.org/10.1007/978-3-642-40381-1_13
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