测量平差模型误差对平差结果的影响

测量平差模型不仅包括函数模型还包括随机模型,因此要研究测量平差模型误差对平差结果的影响就要研究函数模型误差和随机模型误差二者同时的影响。本文以间接平差模型为例,随机模型误差、函数模型误差和随机模型误差三个层次研究了测量平差模型误差对平差结果影响的公式,论证了不同平差模型误差情况下的平差结果,并推导和论证了同时考虑函数模型误差和随机模型误差对平差结果影响的公式。     

GPS网参数约束平差法研究

简要介绍了参数约束平差的模型,与常规平差方法比较,参数约束平差数据处理简单,易于程序实现,以一GPS网为算例,用参数约束平差法获得了经典自由网平差、秩亏自由网平差、符合网平差的结果。     

论三种平差模型的统一性

本文从吉洪诺夫正则化方法出发,推导出经典平差、自由网平差、广义岭估计的数学模型;分析了它们与系数阵复共线性的关系,证明它们分别是不同条件数下吉洪诺夫正则化方法的具体形式,从而三种平差模型有机地统一成一种数学模型。     

On the least-squares adjustment of a straight line

The linear regression of one variable on the other is reviwed, together with its statistical analysis. The adjustment of both variables is reduced to the previous regression. The mathematical form of the straight line is independent of the relative weight of the two variables. Only the adjusted coordinates vary, along the line, in proportion to that weight.     

联合平差中的方差分量估计问题的探讨

天文大地网与GPS空间网联合平差从大的方面分为空间网与地面网两部分。空间网主要是GPS点的三维地心坐标及协方差阵 ;而地面网又涉及到多类观测值 ,主要包括方向观测、导线边、天文方位角三类观测值 ,且各类观测值又分为不同等级的观测。空间网与地面网之间、地面网不同类观测之间及同一类不同观测等级之间的权比不正确将直接影响平差结果 ,因此 ,各类观测值的最佳权匹配就成为联合平差的一个关键。本文就Helmert方差分量简化算法及Baumker简化公式用于联合平差中方差分量估计问题进行讨论 ,并用我国天文大地网 1万点的地面观测数据进行实算、比较、分析 ,以确定联合平差中方差分量估计的方法     

On the choice of inverse in the adjustment of coordinates

The usefulness of the generalized inverse of a matrix in the adjustment of coordinates by least squares is investigated. It is found that by imposing suitable conditions upon the coordinate corrections a virtually identical variance-covariance matrix can be obtained with considerably less computation.     

Rational adjustment of gyro-theodolite observations

Formulae for the reduction of gyro-theodolite observations using the reversal point method are reviewed and relative precisions are compared. The significance of theoretical and practical comparison models is discussed and the flexibility and stability of different reduction proposals are considered. More stable formulae than are currently available are derived for five, seven and nine observations for moderate damping. The optimum number of observations to be taken for any spin-up of the gyroscope is also examined.     

参数有界约束下的最小二乘平差算法

文中基于测量不确定度理论,建立参数有界约束下的平差模型及其解算方法。顾及变形监测网特点,将该平差模型及算法应用到沉降监测网实例中,即利用已知先验信息,建立相应约束模型,求得有界条件下的参数最优估值。通过与经典最小二乘平差法比较,结果证明模型的有效性,估计的参数值控制在给定范围内且不"失真",其沉降量更接近实际情况。     

Refinement of the short arc satellite altimetry adjustment model

The short arc adjustment mode makes a determination of the geoid surface possible without the requirement of highly precise reference orbits. In this mode, the state vector components are subject to adjustment and represent in fact a set of independent weighted parameters. In a most elementary approach, the radial distance to a satellite point is differentiated with respect to these parameters and a radial distance to the geoid (r) is differentiated with respect to the earth potential coefficients. The observed satellite altimetry value (H) is approximately equal to the difference between these two radial distances. In the present study, a correction is introduced that makes it possible to express the mathematical model for H as accurately as practicable, good to a few centimeters. With regard to the partial differentiation, it is argued that r, in addition to being differentiated with respect to the potential coefficients, has to be differentiated also with respect to the state vector components. This gives rise to a second type of correction. It is shown that for most practical purposes, the ellipsoidal approximation to the geoid used to compute the above two kinds of corrections is satisfactory. The final results indicate that actual computation of these corrections is a very simple matter; an eventual upgrading of satellite altimetry computer programs can thus be accomplished with almost no additional effort. A practical benefit of the presented analysis is faster convergence in the adjustment which, in some cases, may remove the need for iterated solutions altogether.     

经典平差函数模型的概括形式分析

对经典平差函数模型的两种概括形式进行回顾和总结,基于零空间投影算子导出经典平差函数模型的第三种概括形式-等价条件平差模型,教授学生理解该概括形式平差模型的作用及特点。提出在本科教学实践中以不同的平差模型概括形式开展课堂讨论,有利于启发学生对平差模型内在联系的自觉发现。     

测量平差课程教学改革探讨

测量平差课程作为测绘类本专科生的一门专业必修课程,只有通过教学改革,才能满足科学技术发展和社会对本学科提出的新要求。本文作者结合自身教学实践,从课程的教学体系、教学内容和方法、实践教学、如何培养学生科研能力等几个方面探讨了测量平差课程教学改革中的一些问题。     

机载LiDAR数据逐航带平差与航带区域网平差对比

机载LiDAR系统获取的点云数据在经过预处理解算后仍会残余部分系统误差,因此,在利用点云数据生成DEM等相关数字产品之前,必须检查并改正这部分系统误差。以此为主要目标,本文对机载LiDAR数据的逐航带平差与航带区域网平差展开研究,并以Microsoft Visual Studio 2008 C++为开发平台、基于实测数据对比了两者在完成多航带构成的测区平差时的精度,结果表明:机载LiDAR数据的航带区域网平差方法相较于LZD算法可有效降低逐航带平差导致的误差累积,精度更高。     

Matlab软件在测量平差教学中的应用

从测量平差课程的特点出发,阐述如何利用Matlab软件处理平差模型中的观测数据,给出一个水准网间接平差算例及其源程序,对软件的进一步使用提出建议。     

平差数学模型教学改革的探讨

在测量平差概述的教学过程中,通过对必要量、观测量、必要观测量、多余观测量、必要起算数据、多余起算数据等几个概念之间关系的分析,有助于学生理解与掌握平差数学模型的建立,教学效果较好。     

图形化方式的测量平差程序开发与研究

采用Autolisp[1]及VC++[2]语言编程,按照测量平差[3]的传统模式,在计算机屏幕上绘制控制网草图,用类似于在草图上标注已知数据和观测数据的形式输入数据,然后进行平差计算。程序的使用直观方便,操作简单,容易掌握。本程序能对各种类型的控制网进行严密平差及方差分量估计,并输出平差后的各种信息。