Research On Sparse Arrays For Direction Finding Of Radiation Sources

With the continuous development of complex electromagnetic environment in modern battlefield,the number of airspace radiation sources has increased significantly.The ability of radar system and passive reconnaissance system to estimate the radiation angles is facing a severe test.Super-resolution estimation of emitter angles based on array signal processing is a hot issue in the field of spatial spectrum estimation.In the framework of classical signal processing theory,the radiant angle estimation algorithm based on the conventional uniform array is based on the uniform Nyquist sampling theorem in the spatial domain.Therefore,the number of estimable radiation sources of a uniform array is limited by the number of elements.How to break through this limitation and improve the performance of the traditional subspace class angle estimation algorithm is the research goal of many scholars.The proposed sparse array provides a way to break through this bottleneck.Sparse array is an array system whose array element spacing is greater than the signal half wavelength.Sparse arrays can provide larger array apertures and more degrees of freedom for signal source estimation than conventional uniform arrays.Therefore,the performance of sparse array direction finding is superior,and its advantages are mainly manifested in three aspects: higher direction finding accuracy,larger number of estimable signal sources,and higher direction finding resolution.In this thesis,the nested array in sparse arrays is taken as the research object.How to further improve the performance of the angle estimation of nested array and the nested array structure is studied in this thesis.The main works of the thesis are as follows:1.Aiming at the phase ambiguity problem of multi-baseline phase interferometer direction finding in sparse array,a robust residual theorem algorithm is proposed.The algorithm utilizes the idea of total least squares.The fuzzy number estimation function is established and the closed expression of the fuzzy number estimation is obtained by deriving this function.The algorithm solves the problem that the traditional residual theorem is not robust under the condition of measurement noise,and greatly reduces the search times and computational complexity of the original residual theorem.Aiming at the harsh condition that the ratio of signal wavelength to baseline in phase interferometer must be prime number,a nearest lattice unwrapping phase ambiguity algorithm is proposed.According to the least square method,the nearest lattice function of the fuzzy number estimation is established,and the fuzzy number is estimated by the basis subtraction and Babai algorithm.2.In order to overcome the shortcomings that it is necessary to know the number of signals for spatial smoothing MUSIC algorithms of nested arrays.Under the condition that the number of signals is unknown,the maximum likelihood estimation function based on direction finding model of the nested array is derived.The steepest descent method is used to obtain the set of potential radiation source angle estimation.The false redundant angles are removed by the multiple hypothesis test method.The active radiation source angles and the number of radiation sources are estimated jointly.3.Aiming at the problem that the direction finding accuracy of spatial smoothing MUSIC algorithm in nested array is not high enough,the sparse Bayesian learning estimation model of single measurement vector is established based on the direction finding model of nested array,and the iterative formula of unknown parameters is solved by EM algorithm.To solve the problem of high computational complexity of sparse Bayesian learning for single measurement vector model,a sparse Bayesian learning algorithm based on smooth reconstruction is proposed.By using the method of smooth reconstruction,the single observation vector corresponding to the nested array is transformed into a smoothly overlapped multiple measurement vector matrix.That reduces the size of over-complete dictionary matrices.Singular value decomposition(SVD)is applied to the transformed observation matrix.By this way,the size of over complete dictionary matrix is further reduced,and the influence of data noise is reduced.On the basis of single measurement vector sparse Bayesian learning method,sparse Bayesian learning estimation model of multiple measurement vectors is derived,and the iterative formula of hyperparameter is obtained by EM algorithm to estimate the signal angles.In order to estimate the angle of broadband radiation source based on nested array,a broadband smoothing reconstruction block sparse Bayesian learning algorithm is proposed.Firstly,the output of array in time domain is segmented into discrete Fourier transform(DFT)to form a broadband angle estimation model of nested array,and then the covariance matrix of array output in frequency domain is obtained.The covariance matrix is vectorized and the redundancy is removed.The single measurement vector model is transformed into the multiple measurement vector block sparse model by using the smoothing reconstruction method.The sparse Bayesian learning method of the multi-frequency block sparse model is derived to estimate the angles of the broadband radiation source.4.To solve the problem of two-dimensional angle estimation of nested arrays,L-shaped nested arrays and two parallel nested arrays are proposed.Based on the L-shaped nested array structure,an angle estimation algorithm based on spatial spectral decomposition is proposed.First,the algorithm constructs two dimensional separable and unwrapping angle estimation models.For one dimension of the two dimensions,the smooth reconstruction sparse Bayesian learning algorithm is used to obtain the angle estimation value.Based on the steering vector matrix of the known angle estimation value and the spatial spectral decomposition of the two-dimensional joint covariance matrix,the closed form expression of the steering vector matrix of the other dimension angle estimation is derived.Then the corresponding angle values are estimated,and the two dimensional angles can be automatically paired through the joint covariance matrix.A sparse reconstruction algorithm based on triple mixed norm is proposed to solve the problem of transitivity of angle estimation error in the spatial spectral decomposition algorithm.The algorithm uses the joint covariance matrix of two-dimensional piecewise data to construct the sparse reconstruction model of angle estimation.The triple mixed norm is defined,and the sparse reconstruction model is solved by triple mixed norm.The gradient function used for alternating iteration of unknown parameters is derived.Two dimensional angles that can be automatically matched are estimated.A two parallel nested array structure is proposed.The joint covariance matrix of inverted subarray 1 data and subarray 2 data is calculated by inverted processing of subarray 1 sampled data.By vectorizing the joint covariance matrix,the angles of two dimensions are separated and unwrapped.The sparse Bayesian learning algorithm based on smoothing reconstruction is used to estimate one dimension angle.The known angle estimators form a steering vector matrix,and another dimension angle is calculated by spatial spectral decomposition method.The two dimension angles can be automatically matched.5.To solve the problem of mutual coupling in angle estimation of nested arrays,two different translational nested arrays are proposed.These two structures not only improve the sparsity of the first-order nested arrays,but also reduce the mutual coupling effect between the array elements.These two structures improve the aperture of nested array and the number of virtual elements,and increase the degree of freedom of angle estimation.Based on the translational nested array structure,the angle estimation model under the condition of mutual coupling is established,and the mutual coupling matrix estimation algorithm is proposed.Firstly,the element estimation function of the mutual coupling matrix is deduced,and the initial angle is estimated by smoothing reconstruction sparse Bayesian learning algorithm.The mutual coupling matrix is estimated by using the estimated initial value of the angles.The mutual coupling matrix is alternately iterated with the radiation source angles,and finally the radiation source angles and mutual coupling matrix are estimated.