Research On Multi-target Location Methods Based On Sparse Array

High-precision multi-target positioning technology is widely used in military and civil fields.The multi-target positioning method based on traditional uniform array is well developed.However,sparse array technology emerging in recent years can break through the half-wavelength limitation of array spacing in order to achieve higher equivalent aperture and degree of freedom(DOF),and high-precision positioning of multi-target sources under underdetermined conditions.It has become one of the new technologies with great application potential,which has attracted wide attention.The research of sparse array mainly focuses on the design of sparse array,the increase of array DOF,the estimation of source number in underdetermined condition and the high-precision DOA estimation of coherent sources.This thesis will concentrate on multi-target positioning problems based on sparse array.The main contents are as follows:1.The design of sparse array with the high DOF.In order to explore the advantages of sparse array and satisfy the application requirements of multi-target positioning,this thesis proposes two sparse array design methods for circular and non-circular signals respectively.For the circular signal model,a sparse array design method based on the nonuniform expansion of subarrays(MSC-DiSA)is proposed.The constraint conditions of subarray spacing for obtaining maximum continuous virtual aperture are analysed theoretically,and the mathematical proof using induction method is provided.As for the noncircular signal model,a new design method based on noncircular characteristic(SANC)is proposed.This method makes full use of the characteristic that the elliptic covariance of the noncircular sources is not zero,expands the difference set of the array sensor locations.The optimal physical sensor location distribution with maximum continuous virtual array aperture is obtained by exhaustive search,and the reconstructed virtual array has a higher DOF.The theoretical analysis and simulation results show that the proposed method can effectively expand the virtual array aperture and improve the DOF under the same number of physical sensors.2.The underdetermined source number estimation based on sparse array.It is difficult for traditional uniform array to achieve multi-target underdetermined estimation when the number of sources is larger than the number of array sensors.In this thesis,an underdetermined source number estimation method based on sparse array is proposed.Firstly,by vectorizing the received covariance matrix of sparse array,and eliminating the redundant information in the covariance matrix,the continuous virtual array response is extracted,which is equivalent to a highdimensional single snapshot response of uniform array.On this basis,spatial smoothing and covariance matrix calculation of virtual array are carried out to sharpen the eigenvalue of the covariance matrix.The source number can be obtainde by the MDL method of uniform array.The theoretical analysis and simulation results show that the proposed method can effectively estimate the source number of underdetermined condition in multi-target positioning applications.3.The multi-target DOA estimation based on sparse array.Compared with the second-order covariance matrix,the fourth-order cumulant matrix contains more array information,which can be used to explore the advantages of the DOF of sparse array.For the independent non-Gaussian source model,this thesis proposes a vectorized fourthorder cumulant DOA estimation method based on sparse array.Firstly,the fourth-order cumulant matrix of the received signals is calculated,and then it is transformed into equivalent array manifold response.On this basis,vectorization processing and spatial smoothing are completed.Then,eigenvalue decomposition of the smoothed subarray is carried out.Combining with the lowcomplexity DOA estimation method of uniform array,high-precision DOA estimation of independent multi-target sources can be achieved.The theoretical analysis and simulation results show that compared with the second-order cumulant method based on parse array,the proposed method effectively improves the DOF and satisfies the multi-target application scenarios.Meanwhile,compared with the traditional fourth-order cumulant method based on sparse array,this method significantly improves the DOA estimation accuracy.For the coherent source model,the most DOA estimation algorithms based on sparse array are invalid.To solve this problem,two DOA estimation methods based on MSC-DiSA array are presented in this thesis.Method 1: the MSC-DiSA array can be divided into several identical physical subarrays,each of which has rotation invariance.Using this property,the decoherent process is carried out by spatial smoothing method.On this basis,the noise subspace can be reconstructed after eigenvalue decomposition,and the nonuniform steering vector can be transformed into the uniform form,which avoides a large number of highly complex calculation of spectrum peak search method.The root MUSIC method is used to achieve DOA estimation,which effectively reduces the complexity.Method 2: Different from the subspace-based method,method 2 starts with sparse reconstruction.Firstly,a two-dimensional sparse model of DOA estimation is constructed,and then the cost function of the sparse model is solved by adopting convex optimization method.The similarity of the search results of two-dimensional independent redundant dictionary is used as the criterion to discriminate the validity of incoming waves,which effectively reduces the angle estimation error cased by coherent sources.The theoretical analysis and simulation experiments show that method 1 has a high estimation accuracy and a low computational complexity.However the spatial smoothing process loses the array aperture,and the DOF is low,which is suitable for positioning scenarios with a few targets.The method 2 has a low estimation accuracy,but the DOF is high.It can achieve the DOF of the LASSO method for independent sources and it is suitable for multi-target positioning scenarios.4.The multi-target location solution method based on DOA parameters.Position ambiguity often occurs in DOA parameter-based location solution,especially for multi-target scenarios.In this thesis,K-means clustering method is introduced into location solution,and a multi-target location solution method based on multiple screening K-means clustering is presented.Firstly,the cost function of target source locations is established according to the observed location coordinates and the azimuth information,and the cost function is calculated to obtain the complete set of source location coordinates.Further,the Euclidean distance between the input sample points and the clustering center is calculated.As a result of multiple iteration screening according to the characteristic that the distribution of real target points is relatively concentrated while the position distribution of ambiguity target is relatively scattered,the clustering degree is improved,and the distance between the clustering center and the real coordinates is gradually reduced.The ambiguity influence of "pseudo-coordinates" is gradually removed,and the high-precision estimation of the location coordinates of multi-target sources is finally achieved.The theoretical analysis and simulation experiments show that the presented method can achieve high-precision position calculation of multi-target sources based on DOA parameters.5.The multi-target direct position determination method based on sparse array.In this thesis,sparse array is introduced into the direct position determination,and a multi-target direct position determination method based on angle information is proposed.Firstly,a direct position determination of multiple sources with a single moving sparse array is established.By making use of the concept of difference set,a virtual array is constructed by matrix mapping.The covariance matrix of sparse array is transformed into a covariance matrix of uniform array,and the dimension of the virtual array covariance matrix is extended.Furthermore,the maximum non-holes sub matrix along the diagonal direction of the virtual array covariance matrix is extracted,and the underdetermined direct position determination of multi-target sources is realized by using subspace data fusion method of uniform array.The theoretical analysis and simulation results show that the proposed method can effectively achieve high-precision direct position determination of multi-target sources under underdetermined conditions.