利用基本矩阵重构地面影像位姿信息

在地面采集的盲区影像往往缺少位姿信息,进而与空中影像联合处理时造成分层错乱。因此为提高倾斜模型精细度,本文通过约束对极奇异矩阵的方法重构补拍影像的位置姿态。首先进行空地影像特征匹配,得出两者的基本矩阵,规范化空中影像投影矩阵,地面影像投影矩阵则由基本矩阵分解成的反对称矩阵和非奇异矩阵组成;然后利用空中影像POS信息消除该投影矩阵对的多义性,从而得出地面影像位置姿态的准确值。试验结果表明,该方法能够在无像控条件下自动计算出地面盲区补拍影像的位姿信息且与空中影像配准良好,在保证模型精细的前提下提高了作业效率。     

A criterion matrix for the second order design of control networks

This paper proposes an original method of constructing a criterion matrix for the optimal design of control networks by means of the contraction of the eigenvalues and the rotation of the eigenvectors of a covariance matrix. The rotation of the eigenvectors is carried out by two different methods, that is through independent rotations of the pairs of the eigenvector matrix components and through a procrustean transfomation of the same matrix. The required criterion is that the “essential eigenvector components” must be as orthogonal as possible to the predicted direction of deformation. A Second Order Design problem is then resolved, that is the optimization of the precision of the observations of a local free distance network to be constructed for the study of recent crustal movements in the seismogenetic area of Friuli (Italy). The results obtained show a high degree of correspondence for the two proposed methods of rotation if limited rotations of the eigenvectors are considered.     

Design of fundamental gravity networks based on the approximation of the given variance-covariance matrix

Techniques will be presented for the design of one-dimensional gravity nets by means of given variance-covariance matrices. After a critical review of the methods for the solution of the matrix equation , we shall compare different numerical results in order to judge the quality of the designs carried out by means of anSVD criterion matrix, by a criterion matrix created according to an assumed distance-dependence of the mean errors of the grid points, and by means of an iteratively improved criterion matrix respectively.     

大欧拉角的空间直角坐标转换方法探讨

首先指出建立使用大旋转角的空间直角坐标转换模型的必要性，接着推导出以罗德里格矩阵为旋转矩阵的大欧拉角空间直角坐标转换的数学模型，然后以布尔沙模型为例、以Visual C#．NET2003编制了计算软件。该算法具有性能稳定、计算收敛速度快、精确度高、转换参数初始值可以为任意值的优点。     

DEM地表坡向变率的向量几何计算法

作为计算坡向变率的数据基础,坡向矩阵具有方向性,以标量的方式计算带有方向属性的数据,将带来计算方式的误区及计算结果的偏差。本文以数学高斯曲面和不同黄土地貌样区5 m分辨率DEM数据为基础,针对坡向数据具有方向性的特点,设计基于数学向量的坡向变率计算方法。首先针对坡向数据进行极坐标转换,形成坡向矩阵的向量几何表达;然后以该坡向向量数据为基础来计算坡向变率;最后将本文方法的计算结果与传统标量方法的计算结果展开对比分析。试验结果显示,本文方法的坡向变率计算有效地避免了正北方向产生的极大偏差以及坡向差超过180°时的不准确现象,同时其他大部分区域也得出更为合理准确的坡向变率计算结果。在不同分辨率DEM下,本文方法能得到较为稳定的结果。本文所提出的基于向量几何的坡向变率计算方法可为精准数字地形分析提供参考,也是借鉴数学向量几何的方法解决数字地形分析问题的重要实践。     

Analytic tools for investigating the structure of network reliability measures with regard to observation correlations

A global measure of observation correlations in a network is proposed, together with the auxiliary indices related to non-diagonal elements of the correlation matrix. Based on the above global measure, a specific representation of the correlation matrix is presented, being the result of rigorously proven theorem formulated within the present research. According to the theorem, each positive definite correlation matrix can be expressed by a scale factor and a so-called internal weight matrix. Such a representation made it possible to investigate the structure of the basic reliability measures with regard to observation correlations. Numerical examples carried out for two test networks illustrate the structure of those measures that proved to be dependent on global correlation index. Also, the levels of global correlation are proposed. It is shown that one can readily find an approximate value of the global correlation index, and hence the correlation level, for the expected values of auxiliary indices being the only knowledge about a correlation matrix of interest. The paper is an extended continuation of the previous study of authors that was confined to the elementary case termed uniform correlation. The extension covers arbitrary correlation matrices and a structure of correlation effect.     

利用矩阵值域的极化干涉SAR相干性的研究

极化SAR干涉测量 (PolInSAR)的相干性是反演植被参数的重要信息来源,极化空间中不同极化状态对应的相干性分布与复极化相干矩阵的值域相关。本文讨论了不同结构的复极化相干矩阵值域的特点,分析了不同极化状态下干涉相干性与复极化相干矩阵的值域的关系。利用模拟数据和真实全极化SAR数据分析了滑动窗口大小和不同散射体对复极化干涉矩阵值域的影响,以及复极化干涉矩阵的结构对极化干涉SAR相干性分布空间的影响,有助于更加准确地获取极化干涉SAR最优极化基和估计最优相干性。     

基于波士顿矩阵的夜光遥感电力消费估算方法

针对夜光遥感影像估算社会经济参数在局部区域精度不足的问题,提出了基于波士顿矩阵的灯光指数法。该方法在传统灯光指数法的基础上引入波士顿矩阵,将社会经济参量中的电力消费量作为研究对象,以2015年可见光红外成像辐射仪（visible infrared imaging radiometer,VIIRS）年产品为主要数据源,选择中国大陆区域182个城市作为研究区域,利用波士顿矩阵将全部城市分为4类:明星城市、现金牛城市、问题城市与瘦狗城市。结果显示,基于波士顿矩阵的灯光指数法的平均相对误差为34.04%,小于传统灯光指数法的平均相对误差41.69%;且分类后的各类城市,除明星城市外,基于波士顿矩阵的灯光指数法的平均相对误差均小于传统灯光指数法,而两种方法对于明星城市电力消费估算的结果相差不大;将估算结果按照相对误差的大小分为高精度、中等精度与低精度3种,基于波士顿矩阵的灯光指数法高精度与中等精度的估算结果比例均高于传统灯光指数法,而低精度结果的比例则低于传统灯光指数法。由此可见,基于波士顿矩阵法的灯光指数法对于电力消费量的估算结果优于传统灯光指数法。     

近景摄影测量中旋转矩阵构成方法的研究

本文简明扼要地叙述了近景摄影测量中构成旋转矩阵的常用方法,分析了各种矩阵的结构形式及存在缺点;为了解决这个问题,文章介绍了一种利用四维代数(又称四元数)构成旋转矩阵的方法,并详细说明其原理及应用。通过推导四维代数构成的旋转矩阵在相对定向中的实际应用情况,以及它与其他几种矩阵在运算过程中收敛性的实例比较,说明利用四维代数构成旋转矩阵在近景摄影测量中是一种很有实用意义的方法。     

粗差发现和定位能力与相关系数的关系

根据粗差判断方程中的判断矩阵和两个统计检验量之间相关系数的函数式,论证了两种不同的研究方法所确定的粗差不能定位的数学模型实际上是相等的。通过算例,不仅说明两种研究方法对观测量不能定位粗差的判断是一致的,而且使用判断矩阵研究观测量的粗差发现和定位能力会更加方便简单。     

On the foundation of collocation in physical geodesy

The boundary value problem in physical geodesy is nowadays mostly presented with the use of an advanced stochastic model by Krarup-Moritz. This model includes a primary Gauss-Markov model and an adjoining Wiener-Hopf model. Degenerations of the Wiener-Hopf section are found in thesingular auto-covariance matrix of the residuals. The non-singular inverse of the auto-covariance matrix of the signal is proved to be a generalized inverse of the singular auto-covariance matrix of the residuals. The joint model is given a non-stochastic evaluation for a case with spherical external surface (using a non-singular inverse). These findings will not prevent a successful application of the model, which has important merits, specially when using suitablea priori values for the stochastic parameters in the covariance functions. A method for quadratic unbiased estimation ofa priori variances is presented in an introductory section. It is meant to be of value when using a solution of the boundary value problem with the collocation technique based on the classical Gauss-Markov solution. (Bjerhammar (1963).)     

Stochastic significance of peaks in the least-squares spectrum

The least-squares spectral analysis method is reviewed, with emphasis on its remarkable property to accept time series with an associated, fully populated covariance matrix. Two distinct cases for the input covariance matrix are examined: (a) it is known absolutely (a-priori variance factor known); and (b) it is known up to a scale factor (a-priori variance factor unknown), thus the estimated covariance matrix is used. For each case, the probability density function that underlines the least-squares spectrum is derived and criteria for the statistical significance of the least-squares spectral peaks are formulated. It is shown that for short series (up to about 150 values) with an estimated covariance matrix (case b), the spectral peaks must be stronger to be statistically significant than in the case of a known covariance matrix (case a): the shorter the series and the lower the significance level, the higher the difference becomes. For long series (more than about 150 values), case (b) converges to case (a) and the least-squares spectrum follows the beta distribution. The results of this investigation are formulated in two new theorems. Received: 27 May 1997/Accepted: 30 September 1998     

使用价值分析优化方法在功能—技术矩阵求解中的应用

功能—技术矩阵,经众多工作者的努力研究,已渐趋成熟与实用。但如何利用功能—技术矩阵构造在广义现代设计领域中适用的科学模式,解决多学科设计方案的组成与评价问题,还存在薄弱环节。本文利用“使用价值分析优化”的概念,从设计方案技术先进性和经济合理性的协调统一的角度出发,较好地实现了功能—技术矩阵可行优化组合链的组成与评价,弥补了以往的缺陷。     

航空重力测量数据向下延拓基于信噪比的正则化方法的研究

本文研究了正则化方法在航空重力测量数据向下延拓问题中的应用。首先对这种不适定问题的线性模型,分析了设计阵的复共线性结构与其对参数估计危害之间的关系,利用参数LS估计的信噪比提取了各个参数是否受到复共线性严重危害的信息,从而在一定程度上揭示了设计阵复共线性结构的特征。然后提出了基于信噪比的正则化方法（SNR）,以信噪比为依据构造正则化矩阵,以极小化均方误差为目标选取正则化参数。本文构造正则化矩阵无需利用附加物理或先验信息,这对于在缺乏此类信息的情况下运用正则化方法提供了新的手段。最后进行了数值试验,结果表明,本文提出的新方法（SNR）比普通的正则化方法（OR）在滤噪和保真方面表现更佳。     

约束秩亏间接平差模型的虚拟观测算法

约束秩亏间接平差模型的法方程系数矩阵为分块矩阵,其左上角的子块矩阵秩亏,因此无法直接计算分块矩阵的凯利逆矩阵.利用矩阵运算,构建一个能直接求凯利逆的分块矩阵,进而推算出约束秩亏间接平差模型法方程系数矩阵的凯利逆的直接显性表达式.提出将约束条件看作虚拟观测,和原有的秩亏间接平差模型组合成新的误差方程,再和约束条件组成约束...     

Modified compressive sensing approach for GNSS signal reception in the presence of interference

Pre-processing traditional navigation signals in global navigation satellite system (GNSS) receivers includes the conversion of an analog-to-digital sample and acquisition following the basic principle of Nyquist sampling theory. This condition inevitably increases the system computation time and cost of a modern wideband receiver. In recent years, the compressive sensing (CS) approach has been proven to effectively reduce the number of measurement samples required for digital signal acquisition systems. This method gives new potential to this modern design. In this study, a modified compressive sensing algorithm for the acquisition of a GNSS signal that is contaminated by an interfering signal is presented. The proposed method attempts to combine CS demodulation and the subspace projecting method to enhance GNSS signal acquisition performance with interference present. First, the received signal is sub-sampled and aliased from a compressive sampling process. This operation maintains the restricted isometry property (RIP) condition of the second sampling process using a Toeplitz-structured sensing matrix, which replaces a conventional random sensing matrix. The matrix ensures that distances between desired signals on the set of sparse space are not influenced by the sampling process. Next, the interference is eliminated through the orthogonal feature between the interference signal and the desired signal using the subspace projecting method. This also preserves the RIP of the projecting matrix to ensure that the original structure of the linear projection of the signal is preserved. After this, an iterative least-square method is utilized to recover the correlator output from the reception samples taken by the CS demodulator. In addition, the signal detection performance in the presence of co-channel interference using a CS demodulator is analyzed and evaluated. Finally, the relationships between signal detection probability, compressive factor and signal bandwidth are also illustrated. Several numerical results are presented to verify the theory.     

顾及系数矩阵常数列的总体最小二乘迭代解法

介绍总体最小二乘的奇异值分解法(SVD)和混合总体最小二乘法(LS-TLS),基于间接平差原理推导一种总体最小二乘迭代解法,可以用来解决系数矩阵含常数列的总体最小二乘平差问题。最后分别对系数矩阵不含常数列和系数矩阵含常数列的算例进行验证,得到的结果与采用奇异值分解法和混合总体最小二乘法计算的结果相同,表明算法的有效性。     

测量平差矩阵类C#实现

面对测量平差大量的矩阵数据运算,用计算机来处理成为必然。针对矩阵运算,介绍了用C#实现测量平差矩阵类,不仅具有矩阵的基本运算,而且加入了测量平差中矩阵运算的特殊情况。矩阵类可以在测量平差计算、研究及其它涉及矩阵运算的领域得到广泛应用。     

A four-component decomposition of POLSAR images based on the coherency matrix

A four-component decomposition scheme of the coherency matrix is presented here for the analysis of polarimetric synthetic aperture radar (SAR) images. The coherency matrix is used to deal with nonreflection symmetric scattering case, which is an extension of covariance matrix approach. The same decomposition results have been obtained. The advantage of this approach is explicit expressions of four scattering powers in terms of scattering matrix elements, which serve the interpretation of polarimetric SAR data quantitatively.     

On the sensitivity of the location, size and shape of the GPS ambiguity search space to certain changes in the stochastic model

In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean, the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points inside the search space. Received: 11 November 1996 / Accepted: 21 March 1997