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Time of flight estimation in multi-path dispersive configuration using compressive sensing reconstruction in the warped domain

In this paper, we present a new approach of time of flight (TOF) estimation using wide band signals, based on compressive sensing (CS) reconstruction in warped domain. In real conditions, constraints related to signal's transmitting/receiving (such as the transducers configuration or the experimental setup) can affect the informational content of the signal. Thus, the received signals need content reconstruction before the parameters estimation (generally based on matched filtering). In the current study, we are interested to improve such waves TOF estimation between two transducers (a transmitter and a receiver) that are not perfectly aligned, due either to the initial experimental setup or to the vibrations in operational conditions. The misalignments of transmitter-receiver transducers introduce interferences since the propagation environment will have several propagation dispersive paths in terms of the received signals. This multipath propagation environment will conduct to interferences and, then, to the partial samples loss. In order to recover the missing samples, the proposed signal reconstruction method uses firstly a time axis (warping) transformation of the signal. The aim of time axis transformation is to turn any non-linear frequency modulation into a stationary signal in the warped domain. In this transformed domain, the CS concept is used to recover the missing spectral components. Then, an unwrapping function enables to express the recovered signal into the original time domain. We prove that the matched filter-based acoustic wave TOF estimation from the reconstructed signal is more accurate than using the original received signal.