Source localization is widely applied in radar, sonar, wireless communications as well asmany other areas. Its key question is the related algorithms for joint estimation of elevation,azimuth, range and other parameters of interested sources, which is an important researcharea in array signal processing. Classic multi-parametric localization algorithms are usuallybased on the eigen-subspace of observed data, achieving the estimation of multi-parametersby extending algorithms like MUSIC and ESPRIT from linear array to planar array. Thosealgorithms have lower resolution and their accuracy in low SNRs is not enough. The idea ofsparse recovery has been introduced into source localization. By using its potentialadvantages in resolution, robustness to noise and the ability to process coherent signals overclassic method, it provides a new way to solve source localization problems.Current sparse recovery algorithms are mainly applied to one-dimensional DOAestimation, which is difficult to directly extend to multi-dimensional case. So we analyzesthe typical one-dimensional DOA estimation algorithm based on sparse reconstruction, andfurther explore effective method to solve two-dimensional DOA estimation as well as jointtwo-dimensional DOA and range estimation problems based on sparse recovery idea. Themain work and innovations are as follows:(1)2D-DOA estimation is estimating the elevation and azimuth of far-field sources. Spatial sparse representation is the foundation of2D-DOA estimation algorithm based onsparse recovery. If we construct directly the two-dimensional sparse model by oversamplingelevation and azimuth simultaneously, the length of related redundant dictionary will bequite large, which will significantly increase the computational complexity of convexoptimization algorithm. Using the sparsity of spatial angle can reduce the length ofredundant dictionary, but it requires related amplitude information to pairing, which maylead to wrong pairing when the amplitudes of different sources are similar.In this paper, we consider the special structure of the L-shaped array and present a newway to construct the redundant dictionary based on the separation of elevation, whichsignificantly reduce the computation load and achieve automatic pairing at the same time. By substitutingl1norm forl0norm, we extend the one-dimensional sparse DOA estimationalgorithm based on SVD to two-dimensional case.(2) A regularization parameter needs to be chosen when using the convex optimizationalgorithm to estimate DOAs, which affects the performance of the algorithm seriously. Thecurrent selection methods are divided into two categories: when statistical properties of thenoise are known, the problem can be transformed into the constrained SOCP version, thenwe can select the parameter according to the noise characteristics. But it was only anapproximation, which requiring the SNR not too low. When noiseâ€™s statistical properties areunknown, algorithms like L-curve method or CV method are usually used. But thesealgorithms require repeated procedures to verify and determine the parameters, which willincrease the computational complexity.In view of above limitations, we consider the weightedl1norm item instead of the noiseitem and obtain a constraint by the property of Capon spectrum, then propose an equivalentform of optimization problem based on transforming the constrained item, which need notto select the parameter and reduces related computational complexity. Base on these works,we propose an improved two-dimensional DOA estimation algorithm using sparse recovery.Simulation results show that the proposed algorithm improves the resolution and estimationaccuracy under low SNRs.(3) For three-dimensional near-field localization, constructing the redundant dictionaryrequires sparse representations in elevation, azimuth and distance entirely, thecorresponding computation will be greater than2D case. When using the special arraystructure, it is also difficult to achieve the separation of the angle and distance parameters.In order to separate the angle parameter, we seek a fourth-order cumulant of specific arrayoutputs to eliminate the distance parameter. Additionally, we use the sparsity of spatialangles instead of elevations (and azimuths), which is helpful to avoid to construct atwo-dimensional dictionary and correspondingly reduce the amount of calculation. Weconstruct sparse representation model for three-dimensional near-field localization andpropose related algorithm based on fourth-order cumulants. Simulation shows that theproposed algorithm has better estimation accuracy at low SNRs than3D-ESPRIT.Above study is the exploration and development of sparse recovery theory in the field ofarray signal processing, and provides a reference for the further study of source localizationproblem based on sparse recovery. |