概括平差模型的解法探讨

分析了概括平差模型系数矩阵可能出现非列满秩情况的原因,研究了如何使系数矩阵为列满秩矩阵,避免了系数矩阵为非列满秩时的复杂解算过程。     

密度权稳健估计

利用观测量分布函数作为权函数的计算公式,分析了密度权法的抗差性和收敛速率,证实了用密度权法处理含粗差数据是行之有效的。     

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

Estimation of parameters in a split functional model of geodetic observations (<Emphasis Type="Italic">M</Emphasis><Subscript>split</Subscript> estimation)

The paper presents a method of estimating parameters in two competitive functional models. The models considered here are concerned with the same observation set and are based on the assumption that an observation may result from a realization of either of two different random variables. These variables differ from one another at least in the main characteristic (for example, outliers can be realizations of one variable). A quantity that describes the opportunity of identifying a single observation with one random variable is assumed to be known. That quantity, called the elementary split potential, is strictly referred to the amount of information that an observation can provide about two competitive assumptions concerning the observation distribution. Parameter assessments that maximize the global elementary split potential (concerning all observations), are called M _split estimators. A generalization of M _split estimation presented in the paper refers to the theoretical foundation of M-estimation. An erratum to this article can be found at     

二次平差法在测距仪精度估计中的应用

测距仪标称精度一般是根据基线场上的检测结果确定的,由于仪器检测时的条件与工程现场条件不一致,因而标称精度不能反映观测实际精度,以标称精度定权处理观测数据,影响测量成果的质量;在工程实际中,若多余观测边较多,运用二次平差法进行测距仪精度估计,可正确反映仪器实际观测精度,为仪器性能判别及数据处理提供客观依据。     

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冀鲁豫地区重力场变化与封丘ML4.8地震关系的探讨

利用冀鲁豫测网的流动重力5期观测成果,探讨了重力场变化与封丘地震的关系。研究发现：冀鲁豫交界地区的重力点值在封丘地震前后出现了下降-上升-下降的变化过程,较好地对应了封丘ML4.8地震孕育 发震 震后调整的过程。该重力变化可能是封丘地震的异常反映。     

一种两步抗差估计的设计及其解算

抗差估计的关键是选择适当的权函数和合理的调制因子,针对这两个重要问题,在研究当前调制因子取值方法的基础之上,提出了可动性调制因子这一新概念,并基于可动性调制因子、IGG方案权函数,设计了两步抗差估计。两步抗差估计解决了抗差估计中传统的调制因子、方差因子、初值三者取值时存在的一系列问题,尤其当三者取值不能协调配制时出现的秩亏问题,从而使抗差估计方法更具有实际意义和广泛意义。     

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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...