Automatic determination of the number of targets present when using the time reversal operator

The Journal of the Acoustical Society of America
Angela QuinlanPascal Larzabal

Abstract

Acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources. The DORT method is a derivation of the time reversal process, which allows for focusing on multiple targets. An important step in this process is the determination of the number of targets or sources present. This is achieved by examining the eigenvalues of the time reversal operator (TRO). The number of significant eigenvalues is then chosen as the number of sources present. However, as mentioned in [N. Mordant, C. Prada, and M. Fink, J. Acoust. Soc. Am. 105, 2634-2642 (1999) and C. Prada, M. Tanter, and M. Fink, in Proceedings of the IEEE Symposium, 1997, pp. 679-683], factors such as low signal to noise ratio (SNR), small data sample, array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues. This paper proposes a robust method of automatically determining the number of targets even in the presence of a small number of snapshots. For white Gaussian noise, the profile of the ordered eigenvalues is seen to fit an exponential law. The observed eigenvalues are then compared to this mode...Continue Reading

References

Mar 27, 2003·The Journal of the Acoustical Society of America·E KerbratM Fink
Mar 27, 2003·The Journal of the Acoustical Society of America·Sylvain YonMathias Fink
Jun 26, 2003·The Journal of the Acoustical Society of America·Thomas FolégotMathias Fink
Jul 26, 2003·The Journal of the Acoustical Society of America·Claire Prada, Jean-Louis Thomas
Jul 16, 2005·The Journal of the Acoustical Society of America·Thomas FolegotMathias Fink
Jan 1, 1992·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·M Fink
Jan 1, 1992·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·F WuM Fink

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