Automatic Detection of the Number of Raypaths in Colored Noise using short- length samples

National audienceFor ocean study, acoustic tomography is used to image the sound speed variations. A common way to proceed is to take advantage of the multi-path properties of the propagated wavefield. Each path provides information on the variation of sound speed distribution. However, multi-path propagation produces interferences between raypaths (especially in shallow water environment). In order to separate the different paths and extract more observables, high resolution methods are applied for ocean acoustic tomography. Compared with beamforming, it can give more precise separation. If the model order is poorly selected, the same as general situation for array processing, the separation may be hampered. Thus, knowledge of the number of raypaths is a crucial step for inversion algorithm. In this paper, a Noise-Whitening Exponential Fitting Test (NWEFT) is presented in this context for detecting the number of raypaths. Classically, two commonly suggested approaches are the Akaike information criterion (AIC) and the minimum description length (MDL). Based on ideal assumption of ergodic Gaussian random processes and white Gaussion noise, MDL is shown to be asymptotically consistent, whereas the AIC tends to overestimate the order of model. However, these assumptions could not be fulfilled in practical case of OAT. In order to be adapted for real case of OAT, Noise-whitening processing is applied as first step. Then, NWEFT bases on the fact that the profile of the ordered eigenvalues fits an exponential law for short- length samples of white Gaussian noise. We approximate the mean profile of ordered noise eigenvalue with the help of first and second order moments of the eigenvalues. The recursive exponential fitting test is mainly based on the comparison between the ordered profile of the normalized eigenvalues of sample covariance matrix of observation and theoretical profile of the ordered noise eigenvalues. It is started from P = 1. Assuming the P smallest eigenvalues are noise eigenvalues, the previous eigenvalue is tested to see that it corresponds to noise or a raypath. The number of raypaths could be detected when a break-point occurs between them. The fact that NWFET works on short- length samples is very important as a long duration of the received signal in OAT is unavailable. Its performance is studied with synthetic and real data set and compared with classical algorithms