Multi-parameter Estimation For Array Signals Based On Sparse Reconstruction

Source parameter estimation is one of the most important issues in array signalprocessing. Thus it has played a fundamental role in many applications involving radar,sonar, wireless communication, medical imaging，electronic surveillance and seismicexploration, etc. Among the traditional source parameter estimation methods, a classof the most representative one is subspace-based method. However, the common andpeculiar drawbacks of this class of methods cannot be completely overcome since thelimitation of the subspace framework. Recently, the sparse signal reconstruction hasattracted wide attention of scholars with the emergence and continuous improvementof compressed sensing theory. Source parameter estimation from sparse signalreconstruction perspective can bring many potential advantages, such as highresolution, good robustness to noise and without knowing the prior knowledge of thesource number. It can be regarded that the sparse signal reconstruction theory andmethod provide a possible way to solve or circumvent the problems existed in thetraditional source parameter estimation methods.The existing sparse-reconstruction-based source parameter methods mainlyconcentrate on estimating far-field DOA parameter，and most of them either sufferfrom estimation bias or cannot guarantee the global optimality. This paper focuses onresearching robust array signal multi-parameter estimation problems utilizing sparsesignal reconstruction. We first analyze and evaluate the suitability of classical sparsesignal reconstruction algorithms on source parameter estimation, and successivelypropose far-field DOA and power estimation, mixed far-field and near-field DOA andrange estimation, as well as polarized far-field DOA, power and polarizationestimation algorithms by proceeding in an orderly way and step by step. Our aim isto provide a series of new and effective ideas for array signal multi-parameterestimation problem in sparse signal reconstruction framework.The main contributions and innovative points of this dissertation are listed asfollows:1. We propose a new DOA and power estimation algorithm using a sparserepresentation of second-order statistics vector andl0-norm approximation inGaussian white noise and unknown nonuniform noise, based on TLP, DC decomposition and sum-average arithmetic. Theoretically, we prove that theproposedl0-norm approximation algorithm is not only convergent, but also stableand asymptotic unbiased. The regularization parameter and tunning parameter areselected properly by discrepancy principle and cross-validation, respectively. Theproposed algorithm, in addition to eliminating the influence of Gaussian white noiseand unknown nonuniform noise effectively, and overcoming the estimation biasinvolved in the existingl1-norm constraint reconstruction algorithms (such asLASSO、BPDN or Group LASSO), gains an improved resolution, estimationaccuracy and robustness to noise. Meanwhile, it can estimate the source parameterswithout the need of an accurate initialization.2. Exploiting the characteristic that covariance differencing can eliminate thesymmetric Toeplitz colored noise effectively, we propose a novel DOA and powerestimation algorithm jointly using Adaptive LASSO and covariance differencing inunknown colored noise. We use a special case of cross-validation to select theregularization parameter properly on the basis of the special structure ofovercomplete basis matrix. The proposed algorithm can not only eliminate theinfluence of colored noise effectively and gain improved DOA and power estimationaccuracy, but also avoid the pre-estimation of noise covariance matrix. Meanwhile, itcan estimate DOA and power parameters without knowing the prior knowledge ofsource number, and the false peaks brought by covariance differencing can be easilydistinguished by judging the sign of spatial spectrum.3. By utilizing symmetric uniform linear array, we construct two kinds of sparseobservation models in second-order statistics and fourth-order cumulant domainrespecitvely. Sequentially, we propose two new mixed source localization algorithms,namely mixed far-field and near-field source parameter estimation based on a sparserepresentation of cumulant vectors and reweightedl1-norm constraint, mixedfar-field and near-field source parameter estimation jointly using weightedl1-normconstraint and MUSIC, using the idea that transforming multidimensional parametersolution into multiple one-dimensional parameter. The proposed two kinds of newalgorithms not only decrease the computational complexity effectively, avoid theunnecessary grid division and parameter-pairing process, but also suitable forfar-field and near-field source parameter estimation. Meanwhile, the estimationaccuracy can also be guaranteed. In a word, they can be regarded as a class ofcommon algorithm.4. We extend the sparse signal reconstruction to polarized sensitive array for thefirst time in source parameter estimation field, and further propose a new DOA、power and polarization estimation algorithm. We discuss in depth on how to obtainaccurate multi-parameter estimation using sparse signal reconstruction with polarized sensitive array, and also demonstrate how to exploit polarized information to improvethe suitability and estimation performance of the algorithm. Simulation results showthat the proposed algorithm can not only estimate DOA, power and polarizationparameters simultaneously, but also achieve an improved resolution and robustness tonoise. Moreover, the proposed algorithm can distinguish two sources with same DOAsuccessfully by utilizing polarized information.The multi-parameter estimation for array signals with scalar and vector array isstudied deeply in this paper from sparse signal reconstruction perspective. Comparedwith the existing methods, the proposed several algorithms provided an improvedperformance on estimation accuracy, robustness to noise, resolution and sensitivity tothe number of sources, etc. The research results of this paper will provide referencefor further study on array signal processing issues based on sparse signalreconstruction.