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Journal of the Acoustical Society of America

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Tracking radar -- Mathematics, Kalman filtering, Boats and boating -- Electronic equipment, Image processing -- Digital techniques


The waveguide invariant in shallow water environments has been widely studied in the context of passive sonar. The invariant provides a relationship between the frequency content of a moving broadband source and the distance to the receiver, and this relationship is not strongly affected by small perturbations in environment parameters such as sound speed or bottom features. Recent experiments in shallow water suggest that a similar range-frequency structure manifested as striations in the spectrogram exists for active sonar, and this property has the potential to enhance the performance of target tracking algorithms. Nevertheless, field experiments with active sonar have not been conclusive on how the invariant is affected by the scattering kernel of the target and the sonar configuration monostatic vs bistatic . The experimental work presented in this paper addresses those issues by showing the active invariance for known scatterers under controlled conditions of bathymetry, sound speed profile and high SNR. Quantification of the results is achieved by introducing an automatic image processing approach inspired on the Hough transform for extraction of the invariant from spectrograms. Normal mode simulations are shown to be in agreement with the experimental results.


Copyright 2010 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in Journal of the Acoustical Society Of America, 128(2), 611-618 and may be found at (



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