Sparse-reconstruction-based High Resolution Matched-Fidld Source Localization

Matched-field processing (MFP) plays a critical role in passive source localization, and the current research effort includes achieving high resolution, robustness and better handling the snapshot deficient case. Conventional MFP suffers from some fundamental limitations:the resolution is low and the side lobe level is high. Many high resolution methods are limited to the case of enough snapshots and are typically sensitive to environmental mismatch. Those methods mainly utilize the sound propagation channel information and the pressure data. On that basis, we utilize the spatial sparsity feature of the underwater source signals, and investigate a high resolution MFP method based on sparse reconstruction algorithms.Starting with narrow band MFP, we discretize the region containing the sources with a specified grid, then the MFP problem is represented as solving a linear matrix equation, in which the signal strength or power on each grid forms the unknown vector to be solved. For the grids are often densely specified to obtain a high resolution, the matrix is always underdetermined. Besides, the source signal is sparse in spatial domain in many practical situations. Thus the equation can be solved through sparse reconstruction algorithms, which are attracting lots of interests recently for its relationship to compressive sensing. We investigate a method which is based on Compressive Sensing and the correlation matrix is used as the measurements (CS-R). Its system equation is based on data correlation matrix, which aims to increase the ratio of measurements to sparsity (RMS) and reduce the problem’s dimensionality to the minimum. Besides, the system equation is equivalent to the objective function of Bartlett MFP, meaning that CS-R can provide robust estimation as the Bartlett one. The11-norm is used for the penalty of spatial sparsity, which ensures that CS-R can achieve high resolution and suppress grating lobe and side lobe effectively. In addition, CS-R does not require the cross spectral density matrix to be full rank, thus it does not rely on a large number of snapshots. For the broadband case, by extending the research of narrow band case, we investigate broadband MFP based on model-based compressive sensing. The sparse representations of source signals at different frequencies are combined to form an extended vector, which has the structure of block sparsity. Therefore, it translates the broadband MFP problem into solving an extended system equation, and block sparse reconstruction algorithms are used to solve it. For block sparsity is much smaller than the conventional sparsity and the signal at multi-frequencies are processed jointly, it can achieve better estimation.Furthermore, for the case of narrowband MFP, performance analysis with perfectly known environment and environmental uncertainly are conducted. The results demonstrate some advantages of our proposed CS-R method over other methods, including high resolution, effective side lobe suppression, environmental robustness, and applicable to snapshot deficient cases. Through simulations, the influence of the grid size on the performance of CS-R is analyzed. Finally, experimental data are processed to demonstrate the effectiveness of CS-R MFP.