椭球子午线弧长计算的新方法

根据子午线弧长的计算原理,推导出一个新的子午线弧长计算实用公式。采用新公式计算由赤道到纬度φ的子午线弧长时,在计算效果及计算精度分析方面比传统公式更加直观、准确。     

用误差椭圆分析正直,交向摄影的点位精度

本文应用几何法推导出正直、文向摄影的点位精度公式和计算点位误差椭圆参数公式，由此用于点位精度分析。     

起伏地区航摄像片相对定向元素解算公式的研究

本文内容是研究并推导用解析法测求一对像片相对定向元素的公式,目的在提高相对定向元素解算的精度,使供用于解析法空中三角测量。本文所拟解决的问题是：1．推导相对定向元素的严密公式及实用公式;2．推论如何利用多余的观测以减少观测的误差。在进行实验的过程中曾发觉影响此项观测结果最主要的一种仪器的系统误差（立体坐标仪）,从而判断其源由并建议顾及此种误差的办法。本文分为第一部分理论的推导和第二部分实验工作。在理论部分内,由纵视差与相对定向元素的基本关采公式出发,推出完全考虑到地形起伏影响的严密公式,使可保证由于计算上近似性的影响不致减低相对方位元素解算的精度。此外从严密公式出发再简化为实用公式,可以使用在一般不特别要求高精度的计算中,也就是达到现有各种精确解算公式所能达到的程度,并制定了计算的表格。在研究如何利用多余的观测以减少观测误差方面,系采用了在像片对重叠面内均匀分布的九个标准点的观测方法,推导使用最小二乘法进行计算的公式。计算的公式并不特别复杂,但是这样做法理论上精度的提高是不很显著的,在航向倾角τ和τ′角方面均方误差的减小为0.9而在旁向倾角差方面均方误差的减小为0.8,因此只有在特别要求高精度的解算中才宜于考虑到这     

子午线收敛角与长度比的一种简捷算法

关于子午线收敛角和长度比的计算公式在许多大地测量书籍中都已导出,但精度要求不同,公式推导方法就不同.子午线收敛角和长度比计算是大地测量学中的常规计算,但其公式推导较复杂,初学者难以掌握.本文提出了一种子午线收敛角与长度比的简捷算法,本法公式推导简单,便于理解,编写了相应的计算程序,与传统方法解算结果相同.     

GLONASS卫星坐标的计算方法

本文严密推导出根据卫星广播星历,在地固坐标系中,用轨道积分方法,精确计算ＧＬＯＮＡＳＳ卫星坐标的公式。通过实际计算结果验证了公式的精度。     

测高重力异常中央区奇异积分数值求积公式

为简化逆Stokes法和逆Vening-Meinesz法反演中央区重力异常计算过程,提高计算效率,本文采用数值求积公式,分别利用Simpson公式和Cotes公式对逆Stokes法和逆Vening-Meinesz法中的奇异积分问题进行了新的研究,系统地推导出了中央区重力异常普适数值积分计算公式.在大地水准面高和垂线偏差理论模型下的分析表明,此公式可直接利用格网节点处的大地水准面高和垂线偏差计算重力异常值,形式简单,计算效率高,计算精度与解析法计算结果精度相当,可以满足实际应用.研究结果可为高精度卫星测高反演重力异常提供基础理论依据.     

天文经纬度归心实用算式推证

文中分析天文经纬度归心公式中各变量的特点,推导基于2000国家大地坐标系统简单实用的归心计算公式,进一步给出由已确定变量推求归心元素测量精度的数学关系式。验证实用公式计算的归心改正数满足专用工程天文经纬度的计算精度需求。     

底点纬度直接解算公式

本文推导了适合我国地区的两组底点纬度直接解算公式。应用这些公式和迭代公式进行计算比较，证明精度分别小于0″.01和0″.0001。     

象片对相对定向元素新公式的研究

本文研究并推导用解析法测定象片对相对定向元素的新公式,目的在于提高相对定向元素解算的精度,简化计算的表格,提高生产效率。全文分为理论的推导和实验工作两部分。第一部分,作者由现有的上下视差和相对定向元素的基本关系公式出发,对相对定向元素采用了一个新的系统,经过公式的推导,提出按主点定向时,上下视差与相对定向元素新的基本关系公式,并且制定了计算的表格。第二部分,在实验工作中,应用f=70毫米和f=100毫米的山区象片进行了测算,并与其他公式作了比较,结果说明了下面几个问题：（1）验证了所推导公式的正确性。（2）新公式解算的精度能达到各种精确解算公式所能达到的程度,生产效率可以提高,适宜于山区象片作业。     

地面三维激光扫描点云角度分辨率研究

给出了点云角度分辨率近似等于扫描间隔和光斑直径大小的两种取值条件,以及该条件与测角精度的关系、理论最小角度分辨率与测角精度的关系,在此基础上推导出了它们的简化关系式,并利用推导的公式计算分析了29款扫描仪角度分辨率二种取值的条件及其理论最小角度分辨率大小,验证了公式的实用性。     

行星际深空探测中双程测速的高精度计算方法

对于行星际深空探测（距地球1亿km以上）任务,由于受到计算机字长的限制,传统双程测速模型的计算精度无法满足高精度定轨的需要,其最大误差源于多普勒频移周计数终点和始点上行几何距离之间和下行几何距离之间差分值的计算过程。对此建立行星际双程测速模型,高精度地计算了两个差分值,推导模型的计算公式并给出详细步骤,同时给出计算过程中需要的切比雪夫差分多项式递推公式的形式。将该模型在深空探测器精密定轨与重力场解算软件系统（Wuhan University deep-space orbit determination and gravity recovery system,WUDOGS）中进行了实现,并以欧空局火星快车号（Mars express,MEX）探测任务为背景,利用该软件进行仿真测试,从计算精度和定轨结果两个方面验证该模型的优越性。结果表明,该模型将双程测速的计算值在计算机中表达的精度提高2个数量级,同时避免了定轨过程中引入额外的数值误差,可以为后续高精度的行星际深空探测任务的定轨提供参考。     

Methods of harmonic synthesis for global geopotential models and their first-, second- and third-order gradients

Four widely used algorithms for the computation of the Earth’s gravitational potential and its first-, second- and third-order gradients are examined: the traditional increasing degree recursion in associated Legendre functions and its variant based on the Clenshaw summation, plus the methods of Pines and Cunningham–Metris, which are free from the singularities that distinguish the first two methods at the geographic poles. All four methods are reorganized with the lumped coefficients approach, which in the cases of Pines and Cunningham–Metris requires a complete revision of the algorithms. The characteristics of the four methods are studied and described, and numerical tests are performed to assess and compare their precision, accuracy, and efficiency. In general the performance levels of all four codes exhibit large improvements over previously published versions. From the point of view of numerical precision, away from the geographic poles Clenshaw and Legendre offer an overall better quality. Furthermore, Pines and Cunningham–Metris are affected by an intrinsic loss of precision at the equator and suffer from additional deterioration when the gravity gradients components are rotated into the East-North-Up topocentric reference system. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

采用Belikov列推和跨阶次递推方法计算超高阶缔合勒让德函数

超高阶球谐重力场模型的精确构制与快速计算取决于缔合勒让德函数的计算方法。在前人研究的基础上,文中对适合超高阶缔合勒让德函数计算的Belikov列推和跨阶次递推方法进行介绍,为验证精度,通过两种途径对计算结果进行检验,并比较其计算速度。结果表明,采用两种算法得到的每个勒让德函数的绝对精度均优于10-12,在低阶,跨阶次递推方法的计算用时大约是Belikov列推法的2倍,随着阶数的升高,跨阶次递推算法表现出明显的速度优势。     

解析延拓高阶解的推导方法与比较分析

利用迭代求导法、直接求导法推导了解析延拓高阶解公式,并与经典递推方法进行了比较分析。利用迭代求导法得到了重力异常径向导数在球近似下的通用递推公式,该公式表明,解析延拓的经典递推求解方法实际上是忽略小项的近似,在忽略小项后,迭代求导法与递推法的形式是一样的。虽然直接求导法可以提高计算速度,但利用5°×5°实验区的重力数据进行解析延拓实验的结果表明,直接求导法获得的犵2项数值较其他方法偏小0.1～0.4mGal,这种差异的产生主要由于计算误差引起的。     

GIS环境下污水管网设计流量的快速计算

针对ＧＩＳ环境下污水管网设计问题，提出了一种快速计算管段设计流量的方法——递归方法。分析了递归的原理、链式表的建立以及递归算法的具体实现等，并以实例阐述了递归计算的各个步骤     

BLUE, BLUP and the Kalman filter: some new results

In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector means, we relax the model and assume these means to be unknown. The recursive BLUP is derived from first principles, in which a prominent role is played by the model’s misclosures. As a consequence of the mean state-vector relaxing assumption, the recursion does away with the usual need of having to specify the initial state-vector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the state-vector means unknown. In the standard Kalman filter set-up with known state-vector means, such difference between estimation and prediction does not occur. It is shown how the two intertwined recursions can be combined into one general BLUE–BLUP recursion, the outputs of which produce for every epoch, in parallel, the BLUP for the random state-vector and the BLUE for the mean of the state-vector.     

渤海湾多源重力数据的自适应融合处理

在最小二乘逐步配置基础上,提出了以调整观测信号自协方差及互协方差函数为主要形式的多源重力数据自适应融合处理方法,构建了基于配置结果的自适应融合以及基于观测信号的自适应融合两种融合模式。分别利用两种融合模式对渤海湾陆海交界区域的航空重力数据、卫星测高反演重力数据以及陆地重力数据进行了融合处理,其中基于观测信号的自适应融合模式取得了较优的融合效果,通过船测重力数据的外部检核表明,融合数据的总体精度优于3.7毫伽 。     

The integral formulas of the associated Legendre functions

A new kind of integral formulas for ${\bar{P}_{n,m} (x)}$ is derived from the addition theorem about the Legendre Functions when n ? m is an even number. Based on the newly introduced integral formulas, the fully normalized associated Legendre functions can be directly computed without using any recursion methods that currently are often used in the computations. In addition, some arithmetic examples are computed with the increasing degree recursion and the integral methods introduced in the paper respectively, in order to compare the precisions and run-times of these two methods in computing the fully normalized associated Legendre functions. The results indicate that the precisions of the integral methods are almost consistent for variant x in computing ${\bar{P}_{n,m} (x)}$ , i.e., the precisions are independent of the choice of x on the interval [0,1]. In contrast, the precisions of the increasing degree recursion change with different values on the interval [0,1], particularly, when x tends to 1, the errors of computing ${\bar{P}_{n,m} (x)}$ by the increasing degree recursion become unacceptable when the degree becomes larger and larger. On the other hand, the integral methods cost more run-time than the increasing degree recursion. Hence, it is suggested that combinations of the integral method and the increasing degree recursion can be adopted, that is, the integral methods can be used as a replacement for the recursive initials when the recursion method become divergent.     

A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions

 Spherical harmonic expansions form partial sums of fully normalised associated Legendre functions (ALFs). However, when evaluated increasingly close to the poles, the ultra-high degree and order (e.g. 2700) ALFs range over thousands of orders of magnitude. This causes existing recursion techniques for computing values of individual ALFs and their derivatives to fail. A common solution in geodesy is to evaluate these expansions using Clenshaw's method, which does not compute individual ALFs or their derivatives. Straightforward numerical principles govern the stability of this technique. Elementary algebra is employed to illustrate how these principles are implemented in Clenshaw's method. It is also demonstrated how existing recursion algorithms for computing ALFs and their first derivatives are easily modified to incorporate these same numerical principles. These modified recursions yield scaled ALFs and first derivatives, which can then be combined using Horner's scheme to compute partial sums, complete to degree and order 2700, for all latitudes (except at the poles for first derivatives). This exceeds any previously published result. Numerical tests suggest that this new approach is at least as precise and efficient as Clenshaw's method. However, the principal strength of the new techniques lies in their simplicity of formulation and implementation, since this quality should simplify the task of extending the approach to other uses, such as spherical harmonic analysis. Received: 30 June 2000 / Accepted: 12 June 2001     

嵌入式GIS的三维地形显示算法研究

本文论述了基于嵌入式G IS的三维地形显示的一系列理论和算法。首先介绍了三维地形显示的基本算法步骤,接下来针对嵌入式系统的特点,提出了三个改进方面,分别是递归细分、坐标变换和内存调度。在论文的最后,给出了实验结果并进行了总结。