Modal Analysis And Source Localization Using Compressive Sensing

The underwater acoustic array processing is an important part of the underwater acoustic signal processing,which is used for detection,recognition,and positioning.To get accurate results,it often requires a long array and the number of sensors is large enough which are impractical.Therefore,in recent years,the method of compressive sensing has been widely applied to array processing.When the information that needs to be estimated is sparse,compressive sensing can be proposed to solve these problems where the number of sensors is small or the array aperture is limited.In this paper,compressive sensing is applied to normal mode amplitude estimation and wavenumber estimation.Compressive sensing is expected to reduce the requirements of array aperture and number of sensors,and can improve the performance of modal analysis,that is,the source localization performance.On the basis of known sound speed profiles,we estimate the mode amplitudes using data from a vertical line array(VLA).A compressive sensing approach has been used which formulat-ing mode decomposition as a convex optimization(CVX)problem based on the l1 norm.In this paper,sampled-mode shapes,least-squares method and convex optimization method are studied in the case of well-sampled and short aperture.Least-squares method is determined by minimizing the data misfit to yield an unbiased estimate of the true solution.In the presence of ill-conditioned matrix,the inversion can be unstable.Therefore,the singular value decomposition method is used to solve unstable inversions based on least-squares,where small singular values characterizing an ill-conditioned matrix can be omitted,however the resolution is degraded.The convex optimiza-tion(CVX)method based on the l1 norm introduces a equalization factor ? to balance the relative tolerance which leads to high robustness.On the basis of unknown sound speed profiles,we estimate the horizontal wavenumber us-ing data from a Horizontal line array(HLA).The projection method,multiple signal classification method(MUSIC),autoregressive(AR)method and convex optimization(CVX)were studied.The projection method performs a spatial Fourier transform of the pressure field,however requires a large aperture of the HLA and the main lobe width and the number of sidelobes are large.The MU-SIC method amounts to finding the noise space of the auto-correlation function of the data,forming the noise-space correlation function and identifying the smallest local minima of the noise-space correlation as the wavenumber set.The convex optimization(CVX)method based on the li nor-m introduces a equalization factor ? to balance the estimation error and solution sparsity which requiring a shorter aperture and leading to a smaller mainlobe width and fewer sidelobes.Furthermore,we study the SW06 experiment data using the method above.On basis of the VLA pressure data,we study the effects of source velocity and bottom bathymetry on auto-correlation and cross-correlation of normal modes.The auto-correlation and cross-correlation of normal modes are related to source moving speed and has little relationship with bottom bathymetry.On basis of the HLA data,we study the effects of array aperture on the estimation of horizontal wavenumber.The SW06 experiment data shows that CVX method needs a shorter aperture and the mainlobe width is smaller.Finally,the paper discusses the effect of random noise and range-dependent sound speed profile and bottom bathymetry on CVX method.