Passive Source Localization Using Compressive Sensing

This paper presents an underwater passive source localization method by forming an underdetermined linear inversion problem. The signal strength on a specified grid is evaluated using sparse reconstruction algorithms by exploiting the spatial sparsity of the source signals. Our strategy leads to a high ratio of measurements to sparsity (RMS), an increase in the peak sharpness with a low side lobe level, and minimization of the dimensionality of the problem due to the formulation of the system equation of the multiple snapshots based on the data correlation matrix. Furthermore, to reduce the computational burden, pre-locating with Bartlett is presented. Our proposed technique can perform close to Bartlet and white noise gain constraint processes in the single-source scenario, but it can give slightly better results while localizing multiple sources. It exhibits the respective characteristics of traditionally used Bartlett and white noise gain constraint methods, such as robustness to environmental/system mismatch and high resolution. Both the simulated and experimental data are processed to demonstrate the effectiveness of the method for underwater source localization.

[1]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[2]  E. Candès The restricted isometry property and its implications for compressed sensing , 2008 .

[3]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[4]  H. Cox,et al.  Passive sonar limits upon nulling multiple moving ships with large aperture arrays , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).

[5]  Wen Xu,et al.  Sparse-reconstruction-based high resolution beamforming and its application to multi-beam systems , 2012, 2012 Oceans - Yeosu.

[6]  Teng Long,et al.  Underwater Acoustic Matched Field Imaging Based on Compressed Sensing , 2015, Sensors.

[7]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[8]  Wen Xu,et al.  Performance Bounds on Matched-Field Methods for Source Localization and Estimation of Ocean Environmental Parameters , 2001 .

[9]  Wen Xu,et al.  Fast estimation of sparse doubly spread acoustic channels. , 2012, The Journal of the Acoustical Society of America.

[10]  Graeme Pope,et al.  Compressive sensing: a summary of reconstruction algorithms , 2009 .

[11]  Jun Zhang,et al.  On Recovery of Sparse Signals Via $\ell _{1}$ Minimization , 2008, IEEE Transactions on Information Theory.

[12]  Linsheng Li,et al.  Kernel sparse tracking with compressive sensing , 2014, IET Comput. Vis..

[13]  Raffaele Grasso,et al.  Single-snapshot DOA estimation by using Compressed Sensing , 2014, EURASIP Journal on Advances in Signal Processing.

[14]  Y. Pi,et al.  Bayesian compressive sensing in synthetic aperture radar imaging , 2012 .

[15]  Bo Li,et al.  Bayesian Compressive Sensing Based Optimized Node Selection Scheme in Underwater Sensor Networks , 2018, Sensors.

[16]  V. Morozov On the solution of functional equations by the method of regularization , 1966 .

[17]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[18]  P. Stoica,et al.  Robust Adaptive Beamforming , 2013 .

[19]  B. Hassibi,et al.  Compressive sensing for sparse approximations: constructions, algorithms, and analysis , 2010 .

[20]  Wei-Ping Zhu,et al.  Compressive sensing-based speech enhancement in non-sparse noisy environments , 2013, IET Signal Process..

[21]  Daniel E. Quevedo,et al.  Maximum hands-off control and L1 optimality , 2013, 52nd IEEE Conference on Decision and Control.

[22]  Henrik Schmidt,et al.  Parameter Estimation Theory Bounds and the Accuracy of Full Field Inversions , 1995 .

[23]  W. Kuperman,et al.  Matched field processing: source localization in correlated noise as an optimum parameter estimation problem , 1988 .

[24]  Hugo Proença,et al.  Face recognition: handling data misalignments implicitly by fusion of sparse representations , 2015, IET Comput. Vis..

[25]  Richard Bamler,et al.  Super-Resolution Power and Robustness of Compressive Sensing for Spectral Estimation With Application to Spaceborne Tomographic SAR , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[26]  Peter Gerstoft,et al.  Adaptive and compressive matched field processing. , 2017, The Journal of the Acoustical Society of America.

[27]  Bhaskar D. Rao,et al.  Sparse channel estimation via matching pursuit with application to equalization , 2002, IEEE Trans. Commun..

[28]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[29]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[30]  Justin K. Romberg,et al.  Compressive Matched-Field Processing , 2012, The Journal of the Acoustical Society of America.

[31]  Armando Manduca,et al.  Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$ -Minimization , 2009, IEEE Transactions on Medical Imaging.

[32]  Thomas Strohmer,et al.  Compressed Remote Sensing of Sparse Objects , 2009, SIAM J. Imaging Sci..

[33]  A Tolstoy,et al.  Applications of matched-field processing to inverse problems in underwater acoustics , 2000 .

[34]  Chaoyu Wang,et al.  High resolution range profile of compressive sensing radar with low computational complexity , 2015 .

[35]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Daniel E. Quevedo,et al.  Packetized predictive control for rate-limited networks via sparse representation , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[37]  Jun Zhang,et al.  On Recovery of Sparse Signals via ℓ1 Minimization , 2008, ArXiv.

[38]  P. Gerstoft,et al.  Compressive beamforming. , 2014, The Journal of the Acoustical Society of America.

[39]  Qiusheng Lian,et al.  Image Reconstruction for Compressed Sensing Based on the Combined Sparse Image Representation: Image Reconstruction for Compressed Sensing Based on the Combined Sparse Image Representation , 2010 .

[40]  Lian Qiu Image Reconstruction for Compressed Sensing Based on the Combined Sparse Image Representation , 2010 .

[41]  Peter Gerstoft,et al.  Null broadening with snapshot-deficient covariance matrices in passive sonar , 2003 .

[42]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[43]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[44]  Junhao Xie,et al.  High-Resolution Ocean Clutter Spectrum Estimation for Shipborne HFSWR Using Sparse-Representation-Based MUSIC , 2015, IEEE Journal of Oceanic Engineering.

[45]  Wen Xu,et al.  High resolution matched-field source localization based on sparse-reconstruction , 2016, 2016 IEEE/OES China Ocean Acoustics (COA).

[46]  Wen Xu,et al.  Joint Passive Detection and Tracking of Underwater Acoustic Target by Beamforming-Based Bernoulli Filter with Multiple Arrays , 2018, Sensors.

[47]  Ron Jenkins,et al.  Quantitative X-Ray Spectrometry , 1981 .

[48]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[49]  Michael Elad,et al.  Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.

[50]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[51]  R. Spindel,et al.  Overview of results from the Asian Seas International Acoustics Experiment in the East China Sea , 2004, IEEE Journal of Oceanic Engineering.

[52]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[53]  J. Capon High-resolution frequency-wavenumber spectrum analysis , 1969 .

[54]  Michael D. Zoltowski,et al.  Multiply-constrained MVDR matched field processing with a-posteriori constraints for enhanced robustness to mismatch , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[55]  H. Bucker Use of calculated sound fields and matched‐field detection to locate sound sources in shallow water , 1976 .

[56]  Arthur B. Baggeroer,et al.  An overview of matched field methods in ocean acoustics , 1993 .

[57]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[58]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..