基于联合矩阵对角化的双基地MIMO雷达DOD-DOA估计

针对双基地MIMO雷达收发角(DOD-DOA)估计问题,该文提出一种基于联合矩阵对角化的快速多目标收发角估计算法。该算法首先根据匹配滤波输出的数据结构,利用奇异值分解和秩1矩阵判断定理将收发角度估计问题转化为联合矩阵对角化问题,然后采用单次-扫描迭代算法对其求解,得到收发阵列流型矩阵,最后通过谱分析方法估计收发角。该算法充分利用匹配滤波输出的所有信息,无需2维谱峰搜索,每次迭代均可得到精确的闭式解,且收发角自动配对。与现有算法相比,该算法不仅提高了角度估计精度,而且有效降低了运算量。仿真结果证明了所提算法的有效性。     

多变量矩阵方程异类约束最小二乘解的迭代算法

本文构造迭代算法研究了多变量矩阵方程异类约束问题,给出了算法的相关性质,证明了该算法的收敛性,利用该算法可经有限步得到方程的异类约束最小二乘解。最后,通过数值例子表明算法是有效的。     

基于子空间信道矩阵迭代的阶数估计算法

针对二阶统计量信道盲辨识算法中有效阶数估计问题,该文提出了一种基于子空间信道矩阵迭代的阶数估计(SS-CMR)算法.基于过估计条件下的Q矩阵特殊结构和其解空间向量可等价为真实信道冲激响应与公共零点信道的卷积,该算法首先利用子空间算法获得估计的信道矩阵,然后构建迭代形式的代价函数进行阶数估计.仿真表明,SS-CMR算法较CMR算法性能提升,且明显优于现有其他阶数估计算法;解析分析表明算法复杂度较CMR算法明显降低,对首尾系数很小的信道的阶数估计尤为有效.     

一类非线性矩阵方程对称解的双迭代算法

传统的方程求解办法并不能算出非线性矩阵方程的对称解,故文章给出一类非线性矩阵方程对称解的双迭代算法,先以牛顿迭代算法求解方程对称解,然后,借助MCG,即修正梯度共轭法经由牛顿迭代后算得的每一步线性矩阵方程的对称解进行计算。研究结果表明,文章所提出的非线性矩阵方程的对称解是有效可取的。     

一种新的GNSS快速定位算法

GNSS定位的经典算法Gauss-Newton迭代法对初始位置依赖性强,若初值设置不当则迭代次数增加,而每次迭代涉及矩阵乘法和矩阵求逆,计算量剧增,直接影响系统冷启动首次定位时间。直接解算定位法无需初值和迭代计算,计算量小但定位精度较差。针对上述问题,本文提出了一种两步快速定位法,首先用直接解算法解算出用户的概略位置,然后将距离方程组在该位置处进行泰勒展开,用加权最小二乘算法计算用户位置的修正量,概略位置修正后即为用户位置。新算法与传统Gauss-Newton迭代定位算法相比,在保证相同定位精度前提下大幅降低运算量,具有重要的工程意义。仿真结果证明了新算法的有效性。      

谐波恢复的联合对角化算法

该文构造一组具有对角结构的特征矩阵,提出一种新的迭代算法完成这组特征矩阵的联合对角化,进而恢复出谐波频率。新方法将经典ACDC算法的四次代价函数简化为二次代价函数;且每步迭代具有精确的最小二乘闭式解,消除了ACDC算法的误差积累问题。仿真实验表明该方法估计性能优于TLS-ESPRIT 算法和ACDC算法,尤其在低信噪比下性能显著提高。     

大规模MIMO系统中低复杂度的预编码改进算法

针对大规模MIMO系统中线性预编码包含复杂的大维矩阵求逆运算,从而产生较大系统开销这一问题,提出了一种低复杂度的基于区域选择初始解的RZF-GS预编码算法.该算法是在RZF预编码的基础上,用Gauss-Seidel迭代算法代替矩阵的求逆运算,并将通常的零初始解向量优化为基于区域选择初始解的向量.实验结果表明,该算法使系统整体的复杂度降低一个数量级,同时,与Neumann级数预编码和零初始解的RZF-GS预编码相比,该算法均明显加快了其收敛速率,用较少的迭代次数就能逼近经典RZF预编码的最优误码率性能.     

基于BFGS拟牛顿法的压缩感知SL0重构算法

平滑l₀范数(SL0)算法是一种基于近似l₀范数的压缩感知信号重构算法,采用最速下降法和梯度投影原理,通过选择一个递减序列来逐步逼近最优解,具有匹配度高、计算量低、不需要已知信号稀疏度等优点。但是,其迭代方向为负梯度方向,使得在迭代过程中产生“锯齿现象”,导致在最优解附近收敛速度较慢。牛顿法具有较快的收敛速度,但是对初值的要求较高,并且需要计算Hesse矩阵。拟牛顿法则克服了这个缺点,利用BFGS公式计算Hesse矩阵的近似矩阵,只需要计算1阶导数信息。该文在SL0算法的基础上,结合BFGS拟牛顿法,提出一种改进的压缩感知信号重构算法。首先采用最速下降法迭代得到信号的某个估计值,然后将此估计值作为拟牛顿法的初值继续迭代,直至得到最优解。计算机仿真结果表明,在相同的条件下,该算法在重构精度、峰值信噪比和重建匹配度等方面均有较大提高。     

一种车载毫米波FMCW MIMO雷达快速成像方法

针对车载毫米波FMCW MIMO雷达现有的常规波束形成算法的旁瓣效应造成的方位向分辨率低以及高分辨算法的工程实时性低的问题,提出了一种迭代自适应算法（IAA）高分辨成像的快速实现方法。该方法首先利用快速傅里叶变换（FFT）获取目标一维距离像,然后对每一距离单元利用FFT算子和Gohberg-Semencul（GS）因子分解计算迭代自适应算法（IAA）的数据协方差矩阵和其逆矩阵,利用快速Toeplitz矩阵向量乘法计算IAA迭代值,从整体上提升了IAA估计各角度散射系数的实时性。仿真和实验结果验证了该方法的可行性和有效性。     

用于自适应阵列处理的一种改进的梯度技术

本文提出了一种改进的自适应算法,适用于天线阵列的实时数据处理。该算法用来确定一个副瓣抵消系统中的滤波器的权集。本算法以采用取样矩阵估计的梯度下降技术为基础,来解Wiener滤波器方程。因此,这种取样矩阵梯度技术算法在某种程度上兼有直接取样矩阵求逆技术的收敛特性和迭代方法在数值计算上的得益。迭代方法的数值计算的稳定性和不大的计算工作量使我们得出如下结论:该算法在大的天线阵列的应用方面特别有用。     

MLFMA/VIE-MoM大型矩阵方程的快速迭代求解方法

 本文针对体积分方程矩量法(VIE-MoM)分析三维非均匀介质电磁散射问题所导出的大型矩阵方程的求解问题, 基于多层快速极子技术(MLFMA)算法研究了快速近似迭代方法.提出了一种基于MLFMA分组方案对系数矩阵进行重组并提取强耦合元素的近场预条件器的构造方法,有效地提高了广义最小余量法(GMRES)的迭代收敛速度.提出了一种在迭代计算过程中的近似矩阵向量乘积方案,明显降低了单步计算过程中MLFMA远区耦合作用的计算时间.计算实例表明,采用本文的迭代加速技术可使计算速度提高3至5倍,有效地提高了VIE-MoM大型矩阵方程的迭代求解速度.     

Stationary, nonstationary, and hybrid iterative method of momentssolution schemes

The purpose of this paper is to report on the convergence rates of two iterative matrix solution methods individually and then to combine the two methods into a hybrid scheme to achieve additional convergence rate benefits. One iterative matrix solver investigated is the sparse iterative method (SIM) which is a stationary, Jacobi-like solver but uses a sparse and not a banded matrix, with matrix elements corresponding to strong interactions, rather than position in the matrix. In this paper, the SIM is modified to include an adaptive relaxation scheme to improve its convergence speed and numerical stability. Another iterative scheme investigated is the nonstationary biconjugate gradient stabilized (BiCGSTAB) method. It is shown that the BiCGSTAB is considerably improved when the method is preconditioned by the sparse matrix used in the SIM method. Finally, a hybrid scheme is proposed which combines both SIM-AR and BiCGSTAB-precon and it is shown that the hybrid gives best results on the problems considered. Examples giving convergence time versus accuracy are presented for two problems: a wire-grid plate, and a wire-grid partial helicopter     

Adaptive multiscale moment method (AMMM) for analysis of scatteringfrom perfectly conducting plates

Adaptive multiscale moment method (AMMM) is presented for the analysis of scattering from a thin perfectly conducting plate. This algorithm employs the conventional moment method and a special matrix transformation, which is derived from the tensor products of the two one-dimensional (1-D) multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method. The special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales. From one scale to another scale, the initial estimate for the solution can be predicted using this multiscale technique. Hence, the compression is applied directly to the solution and the size of the linear equations to be solved is reduced, thereby improving the efficiency of the conventional moment method. The basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix, but to the solution itself directly using an iterative solution methodology. The extrapolated results at the higher scale thus provide a good initial guess for the iterative method. Typically, when the number of unknowns exceeds a few thousand unknowns, the matrix solution time exceeds generally the matrix fill time. Hence, the goal of this method is directed in solving electrically larger problems, where the matrix solution time is of concern. Two numerical results are presented, which demonstrate that the AMMM is a useful method to analyze scattering from perfectly conducting plates     

迭代二次规划遮挡点恢复

为了有效地的恢复遮挡点,本文提出一种迭代二次规划遮挡点恢复方法,该方法首先分别利用图像矩阵的行向量和列向量在图像矩阵生成的正交补空间上的投影为0的特性,构造行和列余差函数,同时,对遮挡点分别按行为主序和列为主序进行排列,利用排列后这两者之间存在一个变换关系,将行和列余差函数统一表示为一个二次优化目标函数.该方法同时考虑了遮挡点在行和列两个方向的约束,而且将遮挡点求解转化为迭代求解一个二次规划问题.实验结果表明,本文方法具有收敛速度快,恢复精度高等优点.     

Matrix method for relating base current ratios to field ratios ofAM directional stations

A matrix method for relating the field ratios to the voltage sources is presented. As a moment-method program is running, the field and base current for each tower is recorded. Matrices that relate base currents to field ratios, can be extracted from this data or by inverting a matrix. This method is an exact solution and requires only one run of the moment-method program. For this reason, it is superior to other iterative processes     

Coupled canonical grid/discrete dipole approach for computingscattering from objects above or below a rough interface

A numerical model for computing scattering from a three-dimensional (3D) dielectric object above or below a rough interface is described. The model is based on an iterative method of moments solution for equivalent electric and magnetic surface current densities on the rough interface and equivalent volumetric electric currents in the penetrable object. To improve computational efficiency, the canonical grid method and the discrete dipole approach (DDA) are used to compute surface to surface and object to object point couplings, respectively, in O(N log N), where N is the number of surface or object sampling points. Two distinct iterative approaches and a preconditioning method for the resulting matrix equation are discussed, and the solution is verified through comparison with a Sommerfeld integral-based solution in the flat surface limit. Results are illustrated for a sample landmine detection problem and show that a slight surface roughness can modify object backscattering returns     

An Iterative Moment Method for Analyzing the Electromagnetic Field Distribution Inside Inhomogeneous Lossy Dielectric Objects (Short Papers)

An iterative method is proposed for solving the electromagnetic deposition inside lossy inhomogeneous dielectric bodies. The technique uses the conventional method of moments to formulate the problem in matrix form. The resulting system of linear equations is solved iteratively by the method of conjugate gradients. The main advantage of the method is that the iterative procedure does not require the storage of any matrix, thus offering the possibility of solving larger problems compared to conventional inversion or Gaussian elimination schemes. Another important advantage is that monotonic convergence to a solution is ensured and accomplished within a fixed number of iterations, not exceeding the total number of basis functions, independently of the initial guess for the solution. Preliminary examples involving two-dimensional cylinders of fat and muscle are illustrated. The iterative method is expendable and applicable to the three-dimensional case.     

A spectral iteration technique for analyzing scattering fromcircuit analog absorbers

An iterative technique is described for solving for the current and field distributions in a structure composed of a periodic array of sheet conductors, deposited on a dielectric layered substrate, whether or not backed by a conductor. The incident field must be a plane wave but can be oblique. The periods array is taken into account by use of a Floquet mode field formalism, and an iterative method has been chosen that permits a numerical solution on personal computers by avoiding matrix inversions     

A technique for organizing large moment calculations for use with iterative solution methods

Through a specific choice of evenly spaced basis and testing functions, one can construct a moment matrix formulation wherein significant redundancy is embodied in the matrix. A scheme that exploits this redundancy to effect substantial computer storage reduction in an iterative field solution, such as the conjugate-gradient method is described. The expense incurred is a modest increase in computation time. The redundancy results from translational similarity features of specific classes of geometries and leads to matrix equations that may be interpreted as discrete convolutions. For illustration, the analysis here is carried out on a planar scatterer, but the strategy can be applied to spherical or cylindrical scatterers.     

Sparsification of the Impedance Matrix in the Solution of the Integral Equation by Using the Maximally Orthogonalized Basis Functions

The higher order vector basis functions defined in large patches have been utilized in the numerical solution of integral equations in this paper to sparsify the impedance matrix and relieve the memory pressure. The physical explanation for the sparsification of the impedance matrix is also elucidated. Furthermore, the maximally orthogonalized bases have been applied to improve the condition number of the impedance matrix. The scaling factor was reformed to speed up the iteration convergence in the numerical solution. Finally, the iterative method for sparse matrix equations is applied to improve the solution efficiency. Some numerical results are provided to illustrate the excellent performance both in the sparsification of the impedance matrix and solution efficiency for numerical analysis of the scattering problem.