动态系统的抗差Kaliman滤波

离散历元的动态观测量及其相应的动态模型可能存在异常，若数据处理模型不考虑对这些异常的特别处理，则动态模型参数估值及其所提供的动态信息将极不可靠。基于贝叶斯统计和抗差估计原理，我们构造了一种抗差滤波算法。该算法考虑观测分布和参数验前分布均为污染分布。并利用一个实测网验算该算法和模型的可靠性。     

The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

Changes of spheroid and of datum

Summary A datum change between two geodetic systems with points in common may be derived in three stages; slight adjustments of coordinates to make the networks of common points geometrically similar in the two systems; a scale factor to make them geometrically congruent; finally, an orthogonal transformation to swing them into coincidence. The geometrical concept is developed of a “datum screw”, not arbitrarily chosen as is the “origin” or “datum point” of a geodetic survey, but intrinsic to the geometry. The conditions under which it degenerates to a simple “datum shift” are discussed. Differential and other formulae for changes of spheroid and of datum are given, together with a set of tables of coefficients.     

Boundary-value problems in the complex world of geodetic measurements

A review of recent progress and current activities towards an improved formulation and solution of geodetic boundary value problems is given. Improvements stimulated and required by the dramatic changes of the real world of geodetic measurements are focused upon. Altimetry–gravimetry problems taking into account various scenarios of non-homogeneous data coverage are discussed in detail. Other problems are related to free geodetic datum parameters, most of all the vertical datum, overdetermination or additional constraints imposed by satellite geodetic observations or models. Some brief remarks are made on pseudo-boundary value problems for geoid determination and on purely gravitational boundary-value problems. Received: 17 March 1999 / Accepted: 19 April 1999     

Robust estimation of systematic errors of satellite laser range

Methods for analyzing laser-ranging residuals to estimate station-dependent systematic errors and to eliminate outliers in satellite laser ranges are discussed. A robust estimator based on an M-estimation principle is introduced. A practical calculation procedure which provides a robust criterion with high breakdown point and produces robust initial residuals for following iterative robust estimation is presented. Comparison of the results from the least-squares method with those of the robust method shows that the results of the station systematic errors from the robust estimator are more reliable. Received: 18 March 1997 / Accepted: 17 March 1999     

Transformation of coordinates between two horizontal geodetic datums

The following topics are discussed in this paper: the geocentric coordinate system and its different realizations used in geodetic practice; the definition of a horizontal geodetic datum (reference ellipsoid) and its positioning and orientation with respect to the geocentric coordinate system; positions on a horizontal datum and errors inherent in the process of positioning; and distortions of geodetic networks referred to a horizontal datum. The problem of determining transformation parameters between a horizontal datum and the geocentric coordinate system from known positions is then analysed. It is often found necessary to transform positions from one horizontal datum to another. These transformations are normally accomplished through the geocentric coordinate system and they include the transformation parameters of the two datums as well as the representation of the respective network distortions. Problems encountered in putting these transformations together are pointed out.     

Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks

The robustness of an outlier detection method strongly depends on the weights of observations, i.e., the type of the stochastic model applied (homoscedasticity, heteroscedasticity and heterogeneousness). In this paper, we have investigated how the reliability of the robust methods and tests for outliers changes depending on the weights of the observations in geodetic networks. Furthermore, the contribution of the directions and distances to horizontal control network with regard to reliability are investigated separately. The concept of a breakdown point is used as a global measure of robustness against outliers. The mean success rate (MSR) is found to be a practical tool for confirming the breakdown point. Many different “good” data samples are generated for each network and then deliberately contaminated using a Monte-Carlo simulation. Six robust methods and Baarda’s test are applied to the corrupted samples and the degree of corruption is varied. The performance of each method is measured using both local and global MSRs. Our research shows: (1) The MSRs of Baarda’s test change depending on the strength of the heteroscedasticity, but do not change for trilateration and leveling networks, (2) the global MSRs of robust methods do not differ considerably from the local ones     

大旋转角坐标变换非迭代公式

针对求解7参数的过程中,经典的线性化最小二乘法因需线性化、迭代及初值以及存在算法耗时出现不收敛现象的问题,该文对无须迭代的7参数坐标变换公式进行了研究。为避免各类参数间的相关性,采用消去法并按照依次求解旋转参数、比例系数和平移参数的顺序解得坐标变换参数。先利用最小二乘法求解旋转参数,然后通过构建目标函数的方式求解比例系数与平移参数,最终得到无须线性化、无须迭代、无须初值的,可用于大旋转角的7参数坐标变换公式。与线性化最小二乘方法进行相比,该方法具有相当的精度及更高的运算效率,可在一定程度上丰富坐标变换理论。     

不同大地坐标系间相互转换的病态解决及抗差算法

不同大地坐标系间进行坐标转换是利用具有两个坐标系下坐标的公共点,求取转换参数 经常会遇到系数矩阵病态导致转换精度差的问题,且公共点的坐标精度直接影响转换参数的求解精度,也就是影响坐标转换的精度.本文探讨利用LC曲线法、截断奇异值法及广义交叉检验准则法解决病态问题,同时采用抗差估计理论进行不同大地坐标间的转换.当公共点...     

株洲市2000国家大地坐标联测及控制网的改造升级

株洲市基于CGCS2000的城市控制网升级改造,获取了株洲市2000国家大地坐标系的大地基准和原有城市控制点及升级改造后控制点的2000国家大地坐标,并通过了检测验收;改造升级了的株洲城市控制网,更新了株洲市控制网的1954坐标,建立了与2000国家大地坐标系、1980坐标的转换关系,实现了基于CZTCORS网络RTK技术的似大地水准面成果的应用.     

THEORETIC RESEARCH ON ROBUSTIFIED LEAST SQUARES ESTIMATOR BASED ON EQUIVALENT VARIANCE-COVARIANCE

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A Quaternion-based Geodetic Datum Transformation Algorithm

This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa–Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae.     

STABILITY OF SOLUTION FOR DYNAMIC GEODETIC NETWORK ADJUSTMENT

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Stability of solution for dynamic geodetic network adjustment

This paper discusses theoretically the stability of solutions for dynamic geodetic network adjustment, Kalman filtering and sequence adjustment, and two examples are given. The solution for dynamic geodetic network adjustment is stable if the dynamic geodetic network is a classical network. There is not rank deficit in datum, or else the solution is not stable, which will depend on the initial value.     

自适应抗差最小二乘估计

抗差估计与最小二乘估计在相应条件下各具优点。特定的抗差估计极值函数只在特定的污染分布条件下显示其抗差性和优效性。本文研究最小二乘估计，抗差估计以及抗差估计类之间的自适应估计问题。重点讨论了适于测量平差计算的误差分布检验量以及自适应抗差极值函数和权函数的构造与选择，最后人出了自适应抗差最小二科解算积式。     

基于抗差估计的地表移动观测站GPS控制网坐标系统转换

为监测潘一东区1252（1）首采面开采引起的地表移动变形规律,布设了由1条全走向线和一条全倾向观测线、12个控制点和186个监测点构成的地表移动观测站.在采用GPS定位技术实施观测站平面连接测量过程中,为克服转换基准点中存在的位移对求解的转换参数的影响,采用了抗差估计理论,并建立转换后GPS网的质量评价模型.根据对GPS连接测量平面控制网的处理结果分析,采用抗差估计求参,有利于保留GPS技术高精度的特点.     

Robust bayesian estimation

Classical least squares Bayesian estimation consists of minimizing the sum of the squared residuals of observations and the corrections to prior estimates of parameters.Many authors have produced more robust versions of this estimation by replacing the square by something else, such as the absolute value. In this article, three robust (M-LS, LS-M and M-M) estimators for three corresponding error models are described based on the principle of maximum likelihood type estimates (M-estimates). The influence functions of the three robust Bayesian estimators are given. The algorithm implementation problems are discussed and the expressions for the posterior variance-covariance are derived.     

动态大地测量的平差基准

从平差基准的基本概念出发 ,说明动态大地测量的平差基准的意义和基准的数量 ,讨论动态高程系统的转换关系 ,建立等价于原观测值的坐标差与速率差的观测方程及基准方程 ,并通过分析说明 ,四维大地测量平差必须恰当地选取平差基准 ,才能得到具有参考价值的结果。     

Global height datum unification: a new approach in gravity potential space

The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential. The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector (from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of the offset of the zero point of the Iranian height datum from the geoid’s potential value W ₀=62636855.8 m²/s². According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid.     

Nonlinear analysis of the three-dimensional datum transformation [conformal group ℂ7(3)]

 The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates, also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ₇(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are given. Received: 7 January 2002 / Accepted: 9 September 2002 Correspondence to: E. W. Grafarend