The accuracy of astronomic azimuth determinations

Astronomic azimuths are used in classical geodesy, through the Laplace equation, to control the orientation of geodetic networks. The method most commonly used by the United States National Geodetic Survey for the determination of astronomic azimuth is often referred to as the “direction method”, and is based on observations of Polaris at any hour angle. We have analyzed repeat determinations, by analysis of variance (ANOVA) techniques, to derive realistic estimates of the expected accuracy of typical astronomic azimuths to be used in the readjustment of the North American Datum. We found that the dominant errors are systematic in nature, with a very important source being observer bias, or “personal equation”. We were unable to decompose the remaining systematic error, which presumably consists primarily of instrument biases, anomalous refraction, and setup errors. We found, from an analysis of determinations that were first corrected for observer bias, an increase in the variance of repeat azimuth determinations as a function of latitude that agrees reasonably well with theoretical expectations.     

Method of simultaneous determination of astronomic latitude,azimuth and longitude by observing only time and horizontal angles between a pair of stars near elongation and a south star near meridian

Summary This paper endeavours to evolve a method of simultaneous determination of astronomic latitude, azimuth and longitude from observations of a star-pair near their times of east and west elongations and a south star near its time of meridian transit. The star-pair of observation being within a short distance of elongation, either east or west, their motion in azimuth then is extremely slow and the small error in time has therefore insignificant effect on their azimuth, and in addition, the south star with its azimuth known from observations of the previous star-pair, being very fast-moving, the method is especially suitable for determining the astronomic latitude, azimuth and longitude by observing only the time and horizontal angees between them, and also a reference mark for ensuring the orientation of the horizontal circle side by side.     

天文方位角测量中的主要系统误差分析及处理

卫星及航天器发射、陀螺标枝等领域均离不开天文方位角,天文方位角的测量准确性直接影响着上述工作的完成质量.本文研究了影响天文方位角测量准确性的几种主要系统误差源,定量分析了各误差对测量结果的影响大小,并给出了处理措施,对提高天文方位角的测量准确性及作业效率、避免系统偏差的产生具有重要意义.     

我国陆地垂线偏差精化计算

我国天文大地网与高精度GPS2000网进行联合平差时,为满足地面观测数据归算到WGS84椭球的需要,采用移去-恢复技术和高阶次地球重力位模型,应用全国重力资料和30″×30″数字地形模型,完成了参加联合平差的48 919个大地点的相应于WGS84椭球垂线偏差的精化计算,并用115个与天文点重合的GPS点的实测垂线偏差对计算结果进行了外部检验,得到全国垂线偏差子午分量的总体精度为±1.45″,卯酉分量的总体精度为±1.50″。     

瞬时极坐标与时号改正的自动解算

天文测量数据处理软件在解算经纬度、方位角和人仪差时,需要预先计算出瞬时极坐标值和测前测后时号改正值。本文使用天文数据处理软件的准备文件数据直接进行极坐标和时号改正的解算,对传统内业解算步骤进行编程,减少内业计算的人工干预和数据处理环节。实验与分析表明,自动解算方法能够显著提高作业效率,减少计算的人为误差。     

新技术在北极星天文方位角测量中的应用

使用GPS接收机的UTC作为北极星天文方位角测量的时间比对的标准时间，利用推估UTl与UTC的差值，将时间归算到UTl的方法，可满足各等级天文方位角测量的要求，现场计算零点恒星时和北极星坐标的精度满足北极星天文方位角测量的要求，实现了现场评估测量精度。     

Computation of geodetic direct and indirect problems by computers accumulating increments from geodetic line elements

By choosing sufficiently small elements of the length of the geodetic line, or of the latitude or longitude difference, the other two can be computed at each element and the results can be accumulated to solve the problem with more than twenty significant number accuracy if desired. Ten to twelve number accuracy was computed in the examples of this paper. The geodetic line elements are kept in correct azimuth by Clairaut’s equation for the geodetic line. The computers can do millions of necessary computations very economically in a few seconds. All other published methods solving the direct or indirect problem can be reliably checked against results obtained by this method. The run of geodetic lines around the back side of the Ellipsoid is outlined.     

CANADIAN SHORAN EFFORT, 1949–1953

Abstract

The application, in Oanada, of shoran electronic length measurement to surveying and mapping may be regarded as having been initiated in 1947, when experimental work by Federal Government bureaus was conducted in the vicinity of Ottawa over several long lines between stations of the first-order triangulation. During the succeeding two winters this work was continued, and the results indicated shoran as suitable for establishing position, in Canada's vast northland, quickly and with greater accuracy than by means of astronomic methods. It was realized that trilateration might fail in securing the necessary accuracy because of the many factors involved. Since no information was available, or even existed, from the experience of other survey organizations as to the error in position which might be generated in a comparatively long arc, the first work planned was for a 1100-mile axial-length arc between geodetic bases. This arc, situated in Manitoba and Saskatchewan, was measured in 1949 and 1950. The result indicated that shoran, with careful supervision of all details, could produce results of accuracy superior to astronomic positioning, which is the only reasonable and speedy alternative method of control for mapping at the present stage of development of the northern areas.     

解析法测定天文方位角计算软件

介绍北极星时角法测定天文方位角的基本方法，进而说明解析法测定天文方位角的基本原理，阐述计算软件的功能、菜单设计特点和操作方法，以实例说明软件的实用性。     

贝赛尔大地主题解算分析

贝赛尔大地主题解算是少数适合长距离大地主题计算的方法之一。文章通过对贝赛尔大地主题解算进行计算分析,发现贝赛尔大地主题反算中的大地线长计算精度受起点方位角的影响很大,误差可达8m。为了消去这一巨大误差,本文提出在大地主题反算时互换大地线起点和终点的方法,计算结果表明该方法可以有效消除方位角对大地线长误差的影响。     

PRACTICAL APPLICATION OF THE LAPLACE LONGITUDE-AZIMUTH RELATION TO CONTROL OF GEODETIC ANOMALIES

Abstract

1. In geodetic work a ‘Laplace Point’ connotes a place where both longitude and azimuth have been observed astronomically. Geodetic surveys emanate from an “origin” O, whose coordinates are derived from astronomical observations: and positions of any other points embraced by the survey can be calculated on the basis of an assumed figure of reference which in practice is a spheroid formed by the revolution of an ellipse about its minor axis. The coordinates (latitude = ?, longitude = λ and azimuth = A) so computed are designated “geodetic”.     

Radio source instability in VLBI analysis

The source position time-series for many of the frequently observed radio sources in the NASA geodetic very long baseline interferometry (VLBI) program show systematic linear and non-linear variations of as much as 0.5 mas (milli-arc-seconds) to 1.0 mas, due mainly to source structure changes. In standard terrestrial reference frame (TRF) geodetic solutions, it is a common practice to only estimate a global source position for each source over the entire history of VLBI observing sessions. If apparent source position variations are not modeled, they produce corresponding systematic variations in estimated Earth orientation parameters (EOPs) at the level of 0.02–0.04 mas in nutation and 0.01–0.02 mas in polar motion. We examine the stability of position time-series of the 107 radio sources in the current NASA geodetic source catalog since these sources have relatively dense observing histories from which it is possible to detect systematic variations. We consider different strategies for handling source instabilities where we (1) estimate the positions of unstable sources for each session they are observed, or (2) estimate spline parameters or rate parameters for sources chosen to fit the specific variation seen in the position-time series. We found that some strategies improve VLBI EOP accuracy by reducing the biases and weighted root mean square differences between measurements from independent VLBI networks operating simultaneously. We discuss the problem of identifying frequently observed unstable sources and how to identify new sources to replace these unstable sources in the NASA VLBI geodetic source catalog.     

Space orientation and geodetic azimuths of long lines from observations of the ANNA Satellite

The space orientation and geodetic azimuths of lines ranging from 300 km to 1400 km have been determined from simultaneous optical observations of the ANNA Flashing Satellite. The results of this test prove that the azimuth and the space direction between two stations can be achieved to an accuracy of 0.5″ and 0.8″ second respectively with only a limited amount of data. The reason for the high accuracy is attributed to two factors: [1] the metric quality of the PC-1000's stellar cameras, and [2] the “perfect” simultaneity in the observations provided by the ANNA flashing light. Much of this work was accomplished by the writer while employed by the Geodesy and Gravity Branch of Cambridge Research Laboratories.     

Contemporary crustal motion and deformation of South America plate

This paper presents the contemporary motion and active deformation of South America plate and relative motion of Nazca-South America plate using space geodetic data. The South America plate is moving at average 14.5 mm/a with an azimuth of 15.2° and shrinking in the west-east at 10.9 mm/a. The geodetic deformations of sites with respect to the South America plate are in quite good agreement with the estimated deformations from NNR-NUVEL1A, but the deformation of the western South America regions is very large.     

GPS基线向量网方差和协方差分量的MINQUE估计

本文应用最小范数二次无偏估计(MINQUE)理论,研究了GPS基线向量网在椭球面上进行三维平差时的方差和协方差分量的估计问题。从理论上提出了方差—协方差模型的选取原则。并从实践中总结出了同时估计基线之长度、方位、高差的固定方差分量和比例方差分量的交替估计方法。通过大量的实例计算和分析,证明这-方法是有效的。     

THE ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS FOR GPS BASELINE NETWORK BY MINQUE METHOD

This paper studies the estimation of variance and covariance compo-nents for GPS baseline network by MINQUE method.The fundamental rule forselecting variance-covariance model has been presented,and the alternative algo-rithm which simultaneouly estimates fixed variance components and scalled vari-ance components of the distance,azimuth and geodetic height difference for a GPSbaseline vector has been developed.     

General non-iterative solution of the inverse and direct geodetic problems

Summary Improved practical and theoretical formulas are presented for the calculation of geodetic distances, azimuths, and positions on a spheroid. The formulas are designed for use with either electronic computers or desk calculators. For the latter, the formulas lend themselves to the construction of useful interpolation tables. The report includes convenient computation forms and auxiliary equations which assure a high degree of accuracy for any geodetic line, no matter how short or long (up to half or fully around the earth) and regardless of its orientation or location. Numerical examples illustrate the complete calculation procedure.     

Conversion of geodetic coordinates from National Geodetic Reference Systems into Standard Earth System

The method of converting geodetic coordinates from a national geodetic reference system into the standard Earth on having known the geodetic coordinates of at least one station in common with the considered systems, is described in detail; the orientation of the Standard Earth at the initial station of the national geodetic reference system, is also determined side by side. For illustration, use has been made of the known coordinates of the Baker-Nunn station at Naini Tal, in India, being in common with the Indian Everest Spheroid and the Smithsonian Institution Standard Earth C₇ system (Veis, 1967). The method advocated is likely to be more precise than the existing ones as it does not assume the parallelism of axes of reference between the Standard Earth and the national geodetic reference systems which may not necessarily hold good in actual practice.     

Atmospheric Angular Momentum Time-Series: Characterization of their Internal Noise and Creation of a Combined Series

The atmosphere induces variations in Earth rotation. These effects are classically computed using the “angular momentum approach”. In this method, the variations in Earth rotation are estimated from the variations in the atmospheric angular momentum (AAM). Several AAM time-series are available from different meteorological centers. However, the estimation of atmospheric effects on Earth rotation differs when using one atmospheric model or the other. The purpose of this work is to build an objective criterion that justifies the use of one series in particular. Because the atmosphere is not the only cause of Earth rotation variations, this criterion cannot rely only on a comparison of AAM series with geodetic data. Instead, we determine the quality of each series by making an estimation of their noise level, using a generalized formulation of the “three-cornered hat method”. We show the existence of a link between the noise of the AAM series and their correlation with geodetic data: a noisy series is usually less correlated with Earth orientation data. As the quality of the series varies in time, we construct a combined AAM series, using time-dependent weights chosen so that the noise level of the combined series is minimal. To determine the influence of a minimal noise level on the correlation with geodetic data, we compute the correlation between the combined series and Earth orientation data. We note that the combined series is always amongst the best correlated series, which confirms the link established before. The quality criterion, while totally independent of Earth orientation observations, appears to be physically convincing when atmospheric and geodetic data are compared     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.