部分最小二乘平差的快速多维粗差定位定值法

根据部分最小二乘平差原理把观测值按照是否含有粗差分成两组,对含有粗差和不含粗差组分别实施最小二乘平差,从而实现粗差的定位定值。针对原部分最小二乘平差法在分组时速度慢、效率低的缺点,利用观测值改正数的特点,改进了分组方法,从而加快了分组速度,提高了粗差探测效率。     

抗差估计在粗差探测及平差计算中的应用

常规的粗差深测技术，不仅辅助计算工作量大，而且将粗差探测与平差计算分两步进行。本文根据抗差估计原理，通过对观测值附加粗差的办法，制订不同的方案，分别进行抗差估计和ＬＳ估计。     

基于验后方差估计的稳健整体最小二乘方法

根据整体最小二乘的验后方差估计,求出观测值的验后方差,通过方差检验可找出方差异常大的观测值。然后根据经典权与观测值方差成反比的定义赋予它一个相应小的权进行下一步迭代平差,逐步实现粗差定位。通过坐标转换实验,利用一般最小二乘法(LS)、加权整体最小二乘法(WTLS)以及文中提出的稳健整体最小二乘法(RTLS)分别对待估参数进行求解对比,解算结果表明文中提出的方法能对粗差进行有效的定位,且估计量受粗差影响较小,具有稳健性,估算效果优于其它两种方法。     

基于判断矩阵的观测量粗差发现和定位相关性分析

用布尔矩阵分析、研究判断矩阵,得到观测量粗差发现和定位的相关数以及测量系统的最大可发现粗差和定位粗差数的计算公式.试验证明,当粗差发现和定位相互影响的观测量同时含有粗差时,现行的迭代数据探测法和选权迭代法不可能完全正确定位粗差.通过算例验证了使用布尔矩阵和判断矩阵分析多维粗差发现和定位相关性的有效性和优越性.     

多维平差问题粗差的局部分析法

用一个水准网说明了依据改正数进行粗差处理可能导致错误,而且粗差能够被正确处理与其所处的位置有关。为了解决这个问题,本文提出了局部分析法。局部分析法从多维平差问题的函数模型出发,根据设计矩阵得到一个被观测量的多个独立观测,包括被观测量的观测值和其他观测值的函数,并且给出了根据平差问题的设计矩阵搜索这些函数的方法。根据独立观测的数目即可判断被观测量的观测值能否容忍粗差。在此基础上提出了一种根据真误差判断被观测量的独立观测所涉及到的观测值是否含有粗差的方法。最后用一个测角网说明局部分析法和粗差探测方法的过程。     

A Bayesian approach to the detection of gross errors based on posterior probability

Existing methods for gross error detection, based on the mean shift model or the variance inflation model, have hardly considered or taken advantage of the potential prior information on the unknown parameters. This paper puts forward a Bayesian approach for gross error detection when prior information on the unknown parameters is available. Firstly, based on the basic principle of Bayesian statistical inference, the Bayesian method—posterior probability method—for the detection of gross errors is established. Secondly, considering either non-informative priors or normal-gamma priors on the unknown parameters, the computational formula of the posterior probability is given for both the mean shift model and the variance inflation model, respectively, under the condition of unequal weight and independent observations. Finally, as an example, a triangulation network is computed and analyzed, which shows that the method given here is feasible.     

具有稳健初值的选权迭代法

提出先采用线性规划来确定残差的初值，然后再进行选权迭代这样一种方法，其估计结果既具有线性规划的稳健性，又具有最小二乘的最优性。试验表明，这种基于线性规划的稳健估计具有很强的稳健性和检测粗差的能力，其计算结果与没有粗差时的最小二乘估计结果一致，且方法简单、可靠、实用。     

以三维坐标转换为例解算稳健总体最小二乘方法

稳健最小二乘方法能够有效解决平差计算中观测值存在粗差的情况,因此广泛应用于各种实际问题中。在最小二乘方法中,系数矩阵被认为是不含有误差的。然而在实际情况中,系数矩阵中的变量往往也包含观测值,因此不可避免地会被误差污染。为同时考虑系数矩阵和观测向量中的误差,同时对粗差进行探测和定位,本文提出基于选权迭代的稳健总体最小二乘方法,并以三维相似坐标变换为例展示解算过程。通过模拟计算,证明了采用本文提出的稳健总体最小二乘方法,能够较好地达到粗差探测和定位的目的,获得稳健的参数解。     

Ability to detect and locate gross errors on DEM matching algorithm

Abstract

Digital elevation model (DEM) matching techniques have been extended to DEM deformation detection by substituting a robust estimator for the least squares estimator, in which terrain changes are treated as gross errors. However, all existing methods only emphasise their deformation detecting ability, and neglect another important aspect: only when the gross error can be detected and located, can this system be useful. This paper employs the gross error judgement matrix as a tool to make an in-depth analysis of this problem. The theoretical analyses and experimental results show that observations in the DEM matching algorithm in real applications have the ability to detect and locate gross errors. Therefore, treating the terrain changes as gross errors is theoretically feasible, allowing real DEM deformations to be detected by employing a surface matching technique.     

利用序列平均的高精度GPS基线解算模型

系统分析了改进随机模型和改进函数模型两类GPS基线解算模型的优缺点,在此基础上,提出了一种基于序列平均的高精度GPS基线解算模型,即采用动态单历元技术进行静态基线解算,充分利用多路径效应的低频特性,采用小波变化理论,对坐标序列进行多路径效应的去除,提取低频残差项进行序列平均,得到基线向量解。同时,以动态坐标序列为依据,对出现粗差历元或者卫星进行处理,有效弥补了仅采用残差序列进行粗差判断的不足,提高了基线解算的精度和可靠性。实验表明,新模型可以更为有效地削弱多路径效应的影响,而且对于较短的观测时间尤为突出;结合坐标序列和残差序列,能更为有效地进行粗差的探测和去除,提高基线解的精度和可靠性。     

可降水份的误差分析

分析了由无线电探空数据计算可降水份中逼近误差和观测误差的影响 ,利用香港的无线电探空资料计算出逼近误差和观测误差的影响分别为 0 .5mm和 1 .2mm ,两者的综合影响为 1 .3mm。     

A general framework for error analysis in measurement-based GIS Part 1: The basic measurement-error model and related concepts

This is the first of a four-part series of papers which proposes a general framework for error analysis in measurement-based geographical information systems (MBGIS). The purpose of the series is to investigate the fundamental issues involved in measurement error (ME) analysis in MBGIS, and to provide a unified and effective treatment of errors and their propagation in various interrelated GIS and spatial operations. Part 1 deals with the formulation of the basic ME model together with the law of error propagation. Part 2 investigates the classic point-in-polygon problem under ME. Continuing to Part 3 is the analysis of ME in intersections and polygon overlays. In Part 4, error analyses in length and area measurements are made. In this present part, a simple but general model for ME in MBGIS is introduced. An approximate law of error propagation is then formulated. A simple, unified, and effective treatment of error bands for a line segment is made under the name of covariance-based error band. A new concept, called maximal allowable limit, which guarantees invariance in topology or geometric-property of a polygon under ME is also advanced. To handle errors in indirect measurements, a geodetic model for MBGIS is proposed and its error propagation problem is studied on the basis of the basic ME model as well as the approximate law of error propagation. Simulation experiments all substantiate the effectiveness of the proposed theoretical construct.This project was supported by the earmarked grant CUHK 4362/00H of the Hong Kong Research grants Council.     

部分最小二乘平差方法及在粗差定值与定位中的应用

部分最小二乘平差是把观测值按照是否含有粗差分成两组 ,对不含粗差的那一组实施最小二乘平差。本文推导了在相关观测条件下的最小二乘原理 ,对这种平差方法的一些估计量的统计性质进行了简单分析 ,结果表明 ,这种方法能够用于粗差估算。本文还详细叙述了用这种方法进行粗差的定值定位的过程 ,即首先根据单位权中误差进行分组 ,然后实施部分最小二乘平差 ,估算粗差的大小。算例表明这种方法的有效性     

A note on observation decorrelation,variances of residuals,and redundancy numbers

A technique for processing correlated observations suitable for large, sparse, least-squares adjustments is reviewed. Correlated coordinate differences derived from the Global Positioning System are used as illustrative examples. However, the methods examined are suitable for all types of correlated observations. The computation of variances of residuals, redundancy numbers, and marginally detectable errors is considered for sparse systems.     

LZD模型多维粗差发现和定位能力分析

不借助地面控制点的DEM匹配差异探测算法是多时相DEM分析的最新发展方向。现有的算法大多把DEM表面差异作为粗差进行处理,算法性能得到了较大的提高,但忽略了对DEM匹配模型多维粗差的可发现和可定位能力进行分析,而这是DEM差异探测算法的理论基础。本文采用测量误差和可靠性理论中的判断矩阵法,通过理论分析和模拟试验验证了对于实际DEM而言,LZD模型具备多维粗差发现和定位能力。基于LZD模型的DEM差异探测算法能够正确地探测表面变形,这就完善了DEM差异探测研究的理论基础。     

稳健估计方法提高数据处理精度

介绍了近代平差理论的稳健估计方法,编制稳健估计方法的程序,并通过实例验证,与最小二乘估计进行比较,表明稳健估计在水准网粗差探测和平差计算中优于最小二乘估计方法,并且能够定位粗差,从而进行消除或者减弱,得到较为干净的观测值。因此,稳健估计方法应用于测量平差具有一定的抵抗粗差的能力,从而可以提高数据处理的精度。     

Adjustment of geodetic measurements with mixed multiplicative and additive random errors

Adjustment has been based on the assumption that random errors of measurements are added to functional models. In geodetic practice, we know that accuracy formulae of modern geodetic measurements often consist of two parts: one proportional to the measured quantity and the other constant. From the statistical point of view, such measurements are of mixed multiplicative and additive random errors. However, almost no adjustment has been developed to strictly address geodetic data contaminated by mixed multiplicative and additive random errors from the statistical point of view. We systematically develop adjustment methods for geodetic data contaminated with multiplicative and additive errors. More precisely, we discuss the ordinary least squares (LS) and weighted LS methods and extend the bias-corrected weighted LS method of Xu and Shimada (Commun Stat B29:83–96, 2000) to the case of mixed multiplicative and additive random errors. The first order approximation of accuracy for all these three methods is derived. We derive the biases of weighted LS estimates. The three methods are then demonstrated and compared with a synthetic example of surface interpolation. The bias-corrected weighted LS estimate is unbiased up to the second order approximation and is of the best accuracy. Although the LS method can warrant an unbiased estimate for a linear model with multiplicative and additive errors, it is less accurate and always produces a very poor estimate of the variance of unit weight.     

基于方差膨胀模型的多个粗差的探测

本文将粗差归入随机模型,提出了基于方差膨胀模型的粗差探测方法。首先针对测量平差实际给出了非等权独立观测条件下的单个粗差的Score检验统计量,然后提出了基于方差膨胀模型的两种定位多个粗差的方案,最后对一边角网进行了计算和分析。大量试验表明,用本文给出的定位多个粗差的方法是切实可行的,它不仅有效地发现了粗差,而且计算简便、快捷,结果比较理想。     

基于部分最小二乘岭估计的粗差定值定位

在利用部分最小二乘原理进行粗差定值定位时,模型的法方程矩阵可能存在病态性,使得到的粗差定值定位结果不可靠。文中针对观测数据包含多个粗差且法方程病态问题,利用岭估计处理病态问题,建立部分最小二乘岭估计的粗差定值定位方法,给出粗差搜索步骤,利用迭代算法实现多个粗差的定值和定位。通过模拟算例分析部分最小二乘法、部分最小二乘岭估计在粗差搜索方面的效果,从另一个角度探讨粗差处理方法,推广现有的误差理论,证明文中方法的有效性。     

L1范数探测粗差失效的观测量识别方法

粗差发生时,L_1范数估计求得的条件方程闭合差较最小二乘估计(LS)的残差更能集中反映粗差,从而有助于粗差的发现与定位。然而,存在一类观测值,虽然其具有粗差发现和定位能力,但在采用L_1范数估计解决粗差探测问题时,无论含有多大量级粗差都不能准确定位,为叙述方便,称其为L_1抗差性失效点(robustness failpoint in L_1-norm estimation,RFP-L_1)。显然,只有判定测量系统不存在RFP-L_1,或存在时能够准确判断其是否含有粗差,才能保证基于L_1的粗差探测结果的准确、可靠,此过程中,RFP-L_1的识别是问题解决的基础。本文由条件方程,推导出观测值粗差对条件方程闭合差绝对值和的影响系数计算式,得到了最小影响系数大小与观测值是否为RFP-L_1的判别关系,并探讨了存在RFP-L_1的测量系统设计矩阵数值特点,提出了判断RFP-L_1观测值的方法。仿真试验表明,最小影响系数反映了观测值粗差对L_1范数估计目标函数的影响大小,非RFP-L_1和RFP-L_1的最小影响系数具有分别等于1和小于1的规律性,同时得出,若观测方程中系数矩阵只有±1和0,对应的观测量均不属于RFP-L_1。