正定矩阵的三角分解与线性对称方程组的解算

讨论用正定矩阵三角分解法解线性对称方程组的问题,将具有正定系数阵的线性方程组中的正定矩阵分解为两个互为转置的上、下三角阵之积,用比较法导出三角阵诸元素与原矩阵诸元素之间的关系式,再将分解式代入原方程,从而导出用三角分解法解线性对称方程组的计算公式,此法计算规律中,既适用于手算又适用于电算,可在测量平差等科学计算中广泛应用。     

正定矩阵的三角分解及其在测量平差中的应用

介绍正定矩阵的三角分解方法；讨论利用正定矩阵三角分解，求线性对称方程组中未知数、未知数函数，以及方程组系数矩阵逆阵的方法；给出了相应计算的紧凑格式和在测量平差中的应用实例。     

正定矩阵一维三角分解法及其应用

由文献［１］知,正定矩阵三角分解后,下三角阵中各元素在阵中的位置具有一定的分布规律,为此可将矩阵中用二维形式表示的诸元素利用位置函数表示为一维形式,文献［１］中所有利用下三角阵各元素进行计算的公式也都可表示为一维形式,使程序设计简单易行。     

对称矩阵原位替换解算方法

研究对称矩阵原位替换解算方法,包括矩阵行列式、矩阵方程未知数和矩阵逆阵的解算.利用矩阵三角分解原理和矩阵运算的基本法则导出矩阵元素约化值的计算公式,从而进一步导出利用矩阵元素约化值计算矩阵行列式、矩阵方程未知数和矩阵逆阵元素的原位替换解算公式.解算公式用纯量形式表示,有利于编程计算,且可实现按矩阵元素在矩阵中的存储位置原位替换解算.该解算方法可节省所用内存空间和时间,提高科学计算的效率.     

矩阵原位替换解算方法

研究矩阵原位替换解算方法,包括矩阵行列式、矩阵方程未知数和矩阵逆阵的解算。利用矩阵三角分解原理和矩阵运算的基本法则导出矩阵元素约化值的计算公式,从而进一步导出利用矩阵元素约化值计算矩阵行列式、矩阵方程未知数和矩阵逆阵元素的原位替换解算公式。解算公式用纯量形式表出,有利于编程计算,且可实现按矩阵元素在矩阵中的存储位置原位替换解算。该解算方法可节省计算用内存空间和时间,提高科学计算的效率。     

大型稀疏法方程组的非零结构分解

针对大型法方程和误差方程解算问题,导出了稀疏对称正定矩阵基于Cholesky 分解的非零结构,可以预先确定下三角矩阵中非零元素的位置和个数,从而可预先分配其存储空间.对其后的数值计算,只需按照已安排好的非零元素的位置进行计算,即可得到数值解.     

大型稀疏法方程组的非零结构分解

针对大型法方程和误差方程解算问题，导出了稀疏对称正定矩阵基于Cholesky分解的非零结构，可以预先确定下三角矩阵中非零元素的位置和个数，从而可预先分配其存储空间。对其后的数值计算，只需按照已安排好的非零元素的位置进行计算，即可得到数值解。     

修正的Gram-Schmidt正交化广义逆平差方法

直接从条件方程或误差方程系数阵入手,利用修正的Gram-Schmidt正交化过程对系数阵进行三角分解,实现最小二乘求解,导出了基于修正的Gram-Schmidt正交化过程求解系数阵广义逆的数学公式和计算步骤,给出了通过广义逆表示的未知数解向量及其协因数阵的数学表达式。计算过程不仅避免了对矩阵的求逆,并从理论上解决了Gram-Schmidt正交化方法由于舍入误差的影响表现出的数值不稳定性问题,从而很好地解决了具有秩亏系数阵方程组解的不唯一性。算例结果表明,基于修正的Gram-Schmidt正交化方法可以处理包括秩亏阵在内的任意矩阵;在处理不设起算数据的变形监测网观测数据时,能够方便地获得其经典解、伪逆解或拟稳解,而不需要重复计算。     

基于矩阵分解的可分离非线性最小二乘问题求解方法及其应用EI北大核心CSCD

针对可分离非线性函数模型的特殊结构,本文使用变量投影法(VP)将线性参数与非线性参数分离开来,并分别与矩阵的满秩分解、QR分解、奇异值分解和施密特正交化相结合,对两类参数分别求解,缩短了计算机解算方程组的运算时间,使算法更加高效,同时也使得具有一定病态程度的方程组在解算过程中保持相对较好的稳定性。本文利用Mackey-Glass时间序列拟合试验和空间直角坐标转换参数解算试验对比分析了基于不同矩阵分解方法的算法优劣性。试验结果表明,基于矩阵分解的改进变量投影法具有高效的运算效率与稳定的解算过程,也适用于解算空间直角坐标转换参数问题。     

基于坐标归一化和奇异值分解的直接线性变换解法

直接线性变换方法是数字摄影测量和计算机视觉领域最常用的解析处理方法之一,特别适用于未检校数码相机的三维测量,但直接线性参数间的相关性、物方控制的约束和设计矩阵元素数量级的较大差异,均可导致法矩阵严重病态,从而影响解的稳定性。本文借鉴改进的八点基本矩阵估计算法,采用基于坐标归一化和奇异值分解的解法,即首先将像点和物点坐标进行相似变换得到归一化坐标后组成法矩阵,其次利用矩阵奇异值分解方法代替常规的最小二乘方法,模拟和真实数据表明,此方法可以有效提高解算精度和稳定性。     

Improvement of a Doppler-Radiometer Using a Sparse Array

A 2-D Doppler-radiometer has been proposed to improve the poor angular resolution of microwave radiometers, using aperture synthesis on a moving platform. In this letter, we investigate drawbacks of the Doppler-radiometer, which have not been discussed previously in detail. The imaging method is revised to be suitable for imaging of distributed sources, which is the more common situation than a point source, and then the specklelike sidelobes in the point source response are discussed. In distributed source imaging, the specklelike sidelobes in the point source response of the Doppler-radiometer severely degrade the imaging performance, so it is necessary to reduce them. The cause of specklelike sidelobes is discussed, and a sparse array is proposed to improve the imaging performance of the Doppler-radiometer. The improvement is demonstrated by simulation of the point source response, showing reduced speckle.     

空中点到直线距离的测定

结合实际需要,研究空中点到直线距离的测量方法。     

The need for a new definition of a conventional international origin

The conventional international origin (CIO), established from observations made a century ago, is not directly related to observations by modern space-geodetic techniques. Both the greater precision of these techniques and improved knowledge of the structure of the Earth justify the need for a new CIO. We analyze recent polar motion time-series (VLBI, SLR, and GPS) to test estimators that might be used to establish such a new conventional origin. This new origin would be defined as the barycenter of the motion of the pole for a specific epoch. Consistency among the series examined is of the order of 2 milli-arc-seconds. A drift model can be employed in the analysis of specific series to establish an origin as the barycenter at a specific epoch, rather than the midpoint of the series. As an example, we estimate a “Conventional International Reference Origin” for the year 2000.0, using polar motion series that began in 1984.     

GPS信号FFT捕获的GPU实现

缩短GPS接收机冷启动时间一直是GPS领域的热点问题,而决定冷启动时间的关键是捕获速度。针对快速付里叶变换（FFT）捕获算法的并行运算特点和图形处理单元（GPU）适合于进行并行的优势,简单介绍了FFT捕获算法原理和对比了GPU与FPGA的特点,重点设计了各通道和各频点均进行并行计算的FFT捕获算法的GPU实现方案。利用实测的GPS中频数据初步验证了本文捕获方案的正确性和运行时间。试验结果表明：与基于CPU的捕获方案相比,本文的捕获方案对卫星PRN和CA码相位的捕获结果完全正确,而捕获时间大幅度缩短了。     

Designing a geodetic-geodynamic network: a comparative study of data processing tools

The geodetic-geodynamic network (G1) was established with the intention of monitoring recent crustal deformation and serving as the major control network in Israel. In 1996 the network was measured for the first time using GPS. This paper presents the second GPS measurement campaign of the G1 network, held in 2002. It presents the network configuration design and the data processing procedures by commercial and scientific post-processing GPS software, as well as a comparison of the results. Long session duration and medium vector length with strict analysis by the commercial GPS processing software TTC (Trimble Total Control) were found to achieve results that are equivalent to those obtained when using the BERNESE scientific software.     

求某点坐标

注：１本成果,经多年工作实践研究而形成;２属专利成果,简便易算,只会简单算术即可。&&求某点坐标@于忠$七台河市规划局!黑龙江七台河154600 @于晓佳$七台河市规划局!黑龙江七台河154600     

Computing Transient Electromagnetic Responses of a Metallic Object Using a Spheroidal Excitation Approach

The model-based spheroidal excitation approach is extended to accurately compute the transient electromagnetic response of a highly conducting and permeable object. The complete formulation is presented in the convolution form. The method is applicable to data from various sensors that measure the transient field or voltage in either the on- or off-time regime and for an arbitrary transmitter waveform. The technique is tested against state-of-the-art time-domain electromagnetic induction sensor data. The results show good agreements between modeled and measured data. In addition, numerical studies demonstrate the importance of accounting for the transmitter waveform.