In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ...In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.展开更多
An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new al...An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.展开更多
In this paper, we construct one of the forms of totally positive Toeplitz matrices from upper or lower bidiagonal totally nonnegative matrix. In addition, some properties related to this matrix involving its factoriza...In this paper, we construct one of the forms of totally positive Toeplitz matrices from upper or lower bidiagonal totally nonnegative matrix. In addition, some properties related to this matrix involving its factorization are presented.展开更多
In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output(MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovative...In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output(MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure(DOD), Direction of Arrival(DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the TemporalSpatial Nested Sampling Model(TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom(DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window(TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the highdimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound(CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.展开更多
This paper concerns the reconstruction of an hermitian Toeplitz matrix with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformat...This paper concerns the reconstruction of an hermitian Toeplitz matrix with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, the authors first consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. The authors show that the dimension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, and the solution of the reconstruction problem of an hermitian Toeplitz matrix with two given eigenpairs is unique.展开更多
Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are giv...Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.展开更多
针对传统波达方向(Direction of Arrival,DOA)估计方法通过空间平滑对相干信号进行处理损失阵列孔径的问题,文章提出了一种基于协方差矩阵托普利兹(Toeplitz)矩阵重构的多重信号分类(Multiple Signal Classification,MUSIC)算法的波达...针对传统波达方向(Direction of Arrival,DOA)估计方法通过空间平滑对相干信号进行处理损失阵列孔径的问题,文章提出了一种基于协方差矩阵托普利兹(Toeplitz)矩阵重构的多重信号分类(Multiple Signal Classification,MUSIC)算法的波达方位估计方法。该方法首先根据阵列接收数据的协方差矩阵及其翻转矩阵来构造新协方差矩阵,并利用新协方差矩阵构造Toeplitz矩阵,然后对其进行特征值分解,得到Toeplitz矩阵的噪声子空间,利用噪声子空间求出信号空间谱,通过谱峰搜索估计入射信号的方位角。文中方法拓展了阵列孔径,增加了可估计相干信号的数量,提升了方位估计的性能,提高了阵列的空间分辨率。仿真和湖上实验数据处理结果表明,文中方法可估计出更多的相干信号,而且在低信噪比、少快拍以及信号入射角度间隔较小时仍然具有良好的方位估计性能。展开更多
文摘In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.
文摘An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.
文摘In this paper, we construct one of the forms of totally positive Toeplitz matrices from upper or lower bidiagonal totally nonnegative matrix. In addition, some properties related to this matrix involving its factorization are presented.
基金supported in part by the National Natural Science Foundation of China(No.62071476)in part by China Postdoctoral Science Foundation(No.2022M723879)in part by the Science and Technology Innovation Program of Hunan Province,China(No.2021RC3080)。
文摘In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output(MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure(DOD), Direction of Arrival(DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the TemporalSpatial Nested Sampling Model(TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom(DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window(TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the highdimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound(CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos. 10771022 and 10571012, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China under Grant No. 890 [2008], and Major Foundation of Educational Committee of Hunan Province under Grant No. 09A002 [2009] Portuguese Foundation for Science and Technology （FCT） through the Research Programme POCTI, respectively.
文摘This paper concerns the reconstruction of an hermitian Toeplitz matrix with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, the authors first consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. The authors show that the dimension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, and the solution of the reconstruction problem of an hermitian Toeplitz matrix with two given eigenpairs is unique.
基金Supported by the GRRC program of Gyeonggi Province(GRRC SUWON 2015-B4)Development of cloud Computing-based Intelligent Video Security Surveillance System with Active Tracking Technology
文摘Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.
文摘针对传统波达方向(Direction of Arrival,DOA)估计方法通过空间平滑对相干信号进行处理损失阵列孔径的问题,文章提出了一种基于协方差矩阵托普利兹(Toeplitz)矩阵重构的多重信号分类(Multiple Signal Classification,MUSIC)算法的波达方位估计方法。该方法首先根据阵列接收数据的协方差矩阵及其翻转矩阵来构造新协方差矩阵,并利用新协方差矩阵构造Toeplitz矩阵,然后对其进行特征值分解,得到Toeplitz矩阵的噪声子空间,利用噪声子空间求出信号空间谱,通过谱峰搜索估计入射信号的方位角。文中方法拓展了阵列孔径,增加了可估计相干信号的数量,提升了方位估计的性能,提高了阵列的空间分辨率。仿真和湖上实验数据处理结果表明,文中方法可估计出更多的相干信号,而且在低信噪比、少快拍以及信号入射角度间隔较小时仍然具有良好的方位估计性能。
