Persymmetric adaptive polarimetric detection of subspace range-spread targets in compound Gaussian sea clutter

This paper focuses on the adaptive detection of range and Doppler dual-spread targets in non-homogeneous and nonGaussian sea clutter.The sea clutter from two polarimetric channels is modeled as a compound-Gaussian model with different parameters,and the target is modeled as a subspace rangespread target model.The persymmetric structure is used to model the clutter covariance matrix,in order to reduce the reliance on secondary data of the designed detectors.Three adaptive polarimetric persymmetric detectors are designed based on the generalized likelihood ratio test(GLRT),Rao test,and Wald test.All the proposed detectors have constant falsealarm rate property with respect to the clutter texture,the speckle covariance matrix.Experimental results on simulated and measured data show that three adaptive detectors outperform the competitors in different clutter environments,and the proposed GLRT detector has the best detection performance under different parameters.

Separable Symmetric Tensors and Separable Anti-symmetric Tensors

In this paper,we first initialize the S-product of tensors to unify the outer product,contractive product,and the inner product of tensors.Then,we introduce the separable symmetry tensors and separable anti-symmetry tensors,which are defined,respectively,as the sum and the algebraic sum of rank-one tensors generated by the tensor product of some vectors.We offer a class of tensors to achieve the upper bound for rank(A)≤6 for all tensors of size 3×3×3.We also show that each 3×3×3 anti-symmetric tensor is separable.

Robust Space-Time Adaptive Track-Before-Detect Algorithm Based on Persymmetry and Symmetric Spectrum

Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.

Acoustic band pinning in the phononic crystal plates of anti-symmetric structure

Acoustic bands are studied numerically for a Lamb wave propagating in an anti-symmetric structure of a one- dimensional periodic plate by using the method of supercell plane-wave expansion. The results show that all the bands are pinned in pairs at the Brillouin zone boundary as long as the anti-symmetry remains and acoustic band gaps （ABGs） only appear between certain bands. In order to reveal the relationship between the band pinning and the anti-symmetry, the method of eigenmode analysis is introduced to calculate the displacement fields of different plate structures. Further, the method of harmony response analysis is employed to calculate the reference spectra to verify the accuracy of numerical calculations of acoustic band map, and both the locations and widths of ABGs in the acoustic band map are in good agreement with those of the reference spectra. The investigations show that the pinning effect is very sensitive to the anti-symmetry of periodic plates, and by introducing different types of breakages, more ABGs or narrow pass bands will appear, which is meaningful in band gap engineering.

A UNIFIED APPROACH FOR DEALING WITH THE EM SCATTERING FROM SYMMETRIC AND ANTI-SYMMETRIC STRUCTURES

It is of both the theoretical and practical importance to reduce the storage andCPU time of moment methods by utilizing the geometrical and physical features of the scatterer.An unified approach based on the group theory is presented to deal with the EM scattering fromsymmetric and anti-symmetric structures.

Least-square Solutions of Inverse Problems for Anti-symmetric and Skew-symmetric Matrices

The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.

Subspace detection for range-spread target to suppress interference:exploiting persymmetry in non-homogeneous scenario

This paper deals with subspace detection for rangespread target in non-homogeneous clutter with unknown covariance matrix where structured interference is presented in the received data.Through exploiting the persymmetry of the clutter covariance matrix,we propose two adaptive target detectors,which are referred to as persymmetric subspace Rao to suppress interference and persymmetric subspace Wald to suppress interference("PS-Rao-I"and"PS-Wald-I"),respectively.The persymmetry-based design brings in the advantage of easy implementation for small training sample support.The signal flow analysis of the two detectors shows that the PS-Rao-I rejects interference and integrates signals successively through separated matrix projection,while the PS-Wald-I jointly achieves interference elimination and signal combination via oblique projection.In addition,both detectors are shown to be constant false alarm rate detectors,significantly improving the detection performance with other competing detectors under the condition of limited training.

复合高斯杂波下距离扩展目标斜对称自适应子空间检测器

针对非高斯杂波背景中距离维扩展的多秩线性子空间信号自适应检测问题,本文基于两步法设计了广义似然比(GLRT)、Rao、Wald检测器。为解决训练样本有限情况下自适应检测器性能急剧下降的问题,本文在检测器设计阶段利用了协方差矩阵的斜对称结构特征。考虑到高分辨率雷达目标回波除了具有沿雷达径向的平动分量之外,还能观测到偏航、横滚、俯仰等转动分量,将目标信号建模为距离扩展子空间信号,以充分利用多普勒信息;为弱化纹理分量先验分布选择的困难,减小模型失配导致的检测性能损失,将杂波建模为纹理分量为未知常数且散斑协方差矩阵具有斜对称结构的复合高斯杂波模型。经过蒙特卡洛仿真实验验证,在训练样本数量受限的情况下,本文所提三种斜对称检测器检测概率达到0.5所需的信杂比相比传统检测器平均低20 dB。同时,分析表明提出的三个斜对称自适应检测器均对散斑协方差矩阵具有恒虚警特性。

基于几何方法的结构化协方差矩阵估计

针对雷达在非均匀环境下难以获得足够数量样本估计协方差矩阵,致使干扰抑制性能下降的问题,遵循几何范式,本文提出了两种结构化干扰协方差矩阵(ICM)估计算法。具体而言,算法从一组训练数据出发,考虑不同的协方差矩阵结构信息(Persymmetric或Toeplitz结构),构造了两种结构样本协方差矩阵(SSCMs),通过利用正定矩阵空间特性并施加条件数上限约束,以ICM和SSCMs之间的Frobenius范数作为目标函数建立极小化问题,并对该问题进行转化,最终得到估计器的闭式解。在两种场景下的仿真结果表明了所提算法可更加精确地估计ICM,有效地提高了干扰抑制性能,且在小样本情况下的优化效果更为显著。

复合高斯杂波条件下存在干扰时的反对称贝叶斯检测器

该文对复合高斯杂波条件下存在干扰时的目标检测问题进行研究。针对自适应检测器需要一定数目独立同分布训练样本才能保证较好的检测性能,利用接收天线的反对称结构以及引入杂波协方差矩阵的先验信息的方法,利用两步广义似然比检验准则提出了该背景下的贝叶斯检测器。仿真结果表明,该文提出的检测器在训练样本数较少时具有较好的目标检测性能。

广义α-对角占优矩阵与非奇异H-矩阵的判别

设A=(aij)∈Cijn,若存在a∈(0,1),使i∈N={1,2,…,n},有|aij|>aRi(A)+(1-a)Si(A),则称A为严格α-对角占优矩阵。首先推广严格α-对角占优矩阵的概念到广义严格α-对角占优矩阵;然后得到了判别广义α-对角占优矩阵的两个新的充分条件,改进和推广了已有的结论,进一步丰富和完善了α-对角占优矩阵和H-矩阵的理论。最后举例说明了所给结果的优越性。为相关领域如矩阵论、控制论、经济数学等提供了理论研究基础。

广对称矩阵及其次对角化问题

在定义次转置矩阵及其运算性质的基础上,给出了广对称矩阵及其相关的概念,进而讨论了它的主要性质,最后得到次对角化的方法。

零训练样本的集中式MIMO雷达斜对称检测器

传统集中式多输入多输出(MIMO)雷达自适应检测器虽然不需要训练样本即可实现目标检测,但在波形采样数较少时检测性能下降明显。该文利用集中式MIMO雷达噪声协方差矩阵的斜对称结构,基于广义似然比(Generalized Likelihood Ratio Test,GLRT)准则和Wald准则,提出了相应的斜对称检测器,并给出了统计分布特性及检测概率和虚警概率的解析表达式。仿真结果表明所提检测器在波形采样数较少时仍可获得较好的检测性能,同时证明了理论分析的正确性。

次对称三对角阵的逆特征值问题

给出了存在惟一的次对称(persymmetric)矩阵,使给定的两个数和两个不同维的向量成为它和它的主子阵的特征对的充分必要条件,并给出了惟一解的表达式和两个数值例子.

反对称次对称的线性方程组的缩减算法

充分利用反对称次对称矩阵的性质,研究了反对称次对称的线性方程组Ax=b的缩减算法,给出求该类解方程的缩减算法.2个数值例子说明算法是可行有效的.

矩阵方程A^TXA=D的反对称次对称最小二乘解

该文研究的问题为:给定A∈Rn×m,D∈Rm×m求X∈ASRn×n,使得‖ATXA-D‖F=min。这里ASRn×n表示全体n×n阶反对称次对称矩阵的集合,‖·‖表示Frobinius范数;利用矩阵对的标准相关分解(CCD),得到了该问题的通解表达式及矩阵方程ATXA=D有反对称次对称解的充分必要条件。

复广对称矩阵

在广对称矩阵理论讨论的基础上,对复广对称矩阵作了进一步讨论,由此给出了复广对称矩阵的充要条件、基本性质及其可次对角化的一系列理论基础。

反对称次对称的线性方程组的缩减算法

充分利用反对称次对称矩阵的性质,解反对称次对称线性方程组Ax=b,并给出求该类方程解的缩减算法.该算法可节省计算量,提高计算效率.两个数值例子说明算法是有效的.

反对称次对称矩阵的广义特征值反问题

.已知矩阵及对角阵,讨论反对称次对称矩阵矩阵广义特征值反问题的解,给出其解的一般表达式。

次对称阵的逆特征值问题

讨论了3种次对称阵的逆特征值问题,其中一种是由部分特征值与部分特征向量来构造次对称阵并给出解存在的充要条件与解的表达式;另外两种是次对称阵的最佳逼近问题,分别给出其解的表达式;在每个问题证明求解过程中,本文充分利用特殊变换矩阵S,使比较复杂的次对称矩阵问题转化成熟悉对称矩阵问题来解决.