(Color online) Schematic illustration of the WALF general principle. For simplicity, we consider here three propagation paths with their associated signals: e 1, e 2, and e 3 . The WAF absolute maximum is illustrated with a circle while filtering is represented with dashed lines.
Spectrogram of the received LFM signal transmitted by the towed source. This time-frequency representation shows the effects of the multipath underwater propagation such as the appearance of time-delayed echoes.
Wideband ambiguity plane of a simulated multipath propagation. The circle represents the position of the WAF theoretical absolute maximum while the cross illustrates its estimate.
(Color online) Time-frequency representation of the time warped signal received after underwater propagation. The dashed lines illustrate the bandpass filter used to filter out the sine function.
(Color online) WAF of the signal obtained after the filtering operation of the first iteration (bottom panel) and WAF of the first extracted ray (top panel). The cross illustrates the estimate the first arrival position.
(Color online) WAF of the received signal where the crosses represent the theoretical local maxima and the circles their estimated positions. The solid curve represents the WALF method (one compression factor by delay), the dashed line illustrates the uniform motion compensation (one compression factor for all delays), and the dotted line stands for the IR estimation without including motion compensation in the WAF.
(Color online) IR estimated with different methods. The crosses represent the theoretical time delays and amplitudes of the simulated propagation channel. The solid curve is the motion-compensated IR obtained with the WALF method, the dashed line illustrates the uniform motion compensation, and the dotted line stands for the IR estimated without motion compensation.
Spectrogram of the LFM signal transmitted by the towed source. The effects of the multipath underwater propagation such as the apparition of time-delayed echoes can be seen on this time-frequency representation. The faint and steeper LFM signals present in this time-frequency representation are not part of the transmitted signal and illustrate some saturation effects due to the relatively small source-receiver separation.
(Color online) Towed source and hydrophones’ positions as a function of time and evolution of the source-receiver separation over time for the analyzed day of BASE’07 campaign.
(Color online) Wideband ambiguity function of the received signal. The circles represent the local maxima detected with the WALF, and the solid line illustrates how the IR is computed from the WAF.
(Color online) IR estimations with the WALF method (bottom panel, solid line) and without taking motion into account (top panel, dashed line). The crosses represent the IR simulated with a Pekeris waveguide with parameters close to the one recorded in situ.
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