Parameter Estimation For Distributed Sources Via Low-rank Matrix Recovery

In array signal processing,reflection,dispersion,diffraction,and refraction in complicated environments may result in a certain spatial spreading of source energy.So the array observation signal is more suitable to be described by the distributed source model.The method based on a point source assumption is not applicable for distributed source parameter estimation.The traditional methods are mainly based on a parameterized distributed model,and require that the type of angular distribution(probability density function)is known or that dispersed signals are sparse in space.Moreover,the computational complexity is high because of a multidimensional search or large-scale signal reconstruction.Therefore,it is necessary to study the low complexity distributed source parameter estimation method more suitable for general angular distribution.Distributed source signals often have some characteristics.The signal spread of distributed sources in the parameter observation domain will produce a low-rank matrix structure.There-fore,this paper uses the low-rank property of signal distribution in the parameter observation domain for distributed sources,and carries out the parameter estimation research of distributed sources based on low-rank matrix recovery,to improve the performance of distributed source parameter estimation.The parameter estimation of incoherently distributed wideband(IDW)sources,near-field incoherently distributed(NFID)sources,and coherently distributed sources are mainly studied.The main contributions and innovations are as follows:1).Based on low-rank matrix recovery,we develop a new and low complexity method for the joint angle and frequency estimation of incoherent distributed wideband sources—iteratively reweighted nuclear norm and alternating direction method of multipliers(IRNN-ADMM).For IDW sources,the angular spread and frequency bandwidth reduce the sparsity of the signals in the angle and frequency domains,but the discrete representation of the joint angular-frequency distribution gives rise to a useful low-rank matrix.Exploiting this low-rank matrix,a rank mini-mization problem is formulated.And the IRNN-ADMM method is proposed to estimate the joint angular-frequency distribution.Different from traditional methods based on a param-eterized distribution model,the IRNN-ADMM method directly estimates the joint angular-frequency distribution without knowing the frequency distribution and angular distribution.In addition,the key parameters of angular and frequency distributions are obtained via off-grid es-timators,the Cramer–Rao bound(CRB)of the key parameters is derived,and the computational complexity is analyzed.Compared with the traditional methods that require a multidimension-al search or large-scale signal reconstruction,the IRNN-ADMM method has better parameter estimation performance and much lower computational complexity.2).Based on spatial-temporal sparse sampling and low-rank matrix recovery,we develop a new method for the joint angular-frequency distribution of incoherent distributed wideband sources—spatial-temporal sparse sampling and accelerated iterative singular value threshold-ing algorithm(STSS-AISVTA).For the joint angular-frequency distribution estimation of IDW sources,we first extend the one-dimensional spatial linear array sampling to two-dimensional STSS,which reduces the sampling rate requirement on hardware and increases the degrees of freedom of the measurement system.Secondly,according to the low-rank property of joint angular-frequency distribution matrix for IDW sources,a minimization problem of rank function approximation is formulated,namely the modified Schatten-p norm minimization(MS_pNM)problem.Then the AISVTA method is proposed to estimate the joint angular-frequency dis-tribution.Combining the advantages of the STSS and low-rank matrix recovery algorithm,the STSS-AISVTA method can solve the ambiguity problem between angular and frequency param-eters in the low-rank matrix recovery method using a one-dimensional linear array.Moreover,compared with the low-rank matrix recovery method based on a uniform array and sparse method based on STSS,the STSS-AISVTA method has better parameter estimation performance.3).Based on low-rank matrix recovery,we develop a new and low complexity method for the spatial spectrum estimation of near-field incoherent distribution sources—truncated nuclear norm regularization and accelerated proximal gradient line(TNNR-APGL).In this paper,NFID source signals have angular and range spreads.In this case,the discrete representation of the spatial spectrum in the angle-range domain generates a low-rank matrix.Therefore,exploiting this low-rank matrix,a rank minimization problem is formulated.Then the APGL method is proposed to estimate the spatial spectrum matrix by the TNNR to approximate the rank function.Compared with the traditional subspace-based methods,the proposed TNNR-APGL method di-rectly estimates the spatial spectrum without knowing the type of spatial distribution and is more suitable for general spatial distributions.In addition,off-grid estimators are also used to esti-mate the key parameters of angular and distance distributions according to the obtained spatial spectrum.Compared with the traditional methods based on a parameterized distribution model and requiring a multidimensional search,the TNNR-APGL method achieves better precision with faster computation for the key parameter estimation.4).Based on low-rank matrix recovery,a new high-precision method is proposed for the an-gular distribution estimation of coherent distribution sources.For coherently distributed sources,the angular spread makes the discrete representations of the autocorrelation kernel generate a low-rank matrix.Therefore,we formulate a rank minimization problem and use the nuclear norm to approximate the rank function to estimate the autocorrelation kernel matrix.Then the angular distribution is estimated by the relation between the autocorrelation kernel and the angu-lar distribution.In addition,off-grid estimators are applied to estimate the key parameters of the angular distribution.Compared with the traditional method based on a parameterized distribu-tion model and sparse method,the proposed method does not need to know the type of angular distribution,has higher parameter estimation accuracy,and is more suitable for general angular distributions.Because the low-rank property of the autocorrelation kernel matrix is independent of angular spread,the proposed method is more suitable for a large angular spread case than the traditional methods.