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.     

THE TRANSVAAL-SOUTHERN RHODESIA GEODETIC CONNEXION

Abstract

In the original geodetic series in Southern Rhodesia—completed by Mr Alexander Simms in 1901—the geographical coordinates of all stations were referred to the point SALISBURYas origin. The coordinates of SALISBURY were fixed by interchange of telegraphic signals with the Royal Observatory at the Cape for longitude, combined with astronomical determinations of time, latitude, and azimuth (see Vol. III, “Geodetic Survey of South Africa”).     

GEODETIC WORK IN INDIA—WAR AND POST-WAR

Abstract

Although during World War II field work on geodetic subjects other than those directly connected with the war effort remained practically in abeyance, the war provided unique opportunities for the study and execution of several interesting problems such as the linking of Indian triangulation with Iraq and Iran on the one hand and Siam and Malaya on the other. A detailed account of the Geodetic work of the Survey of India during the period 1939-47 is given in the Survey of India “Technical Report 1947—Part III, Geodetic Work”.     

A NOTE ON THE TRIGONOMETRICAL SURVEY OF SOUTHERN RHODESIA

Abstract

After the completion of Simms's Geodetic Chain in 1901 and the publication of the results in 1905—Volume iii of the Geodetic Survey of South Africa—nothing further of a geodetic nature was done until 1928 when a short chain was run westwards from Simms's chain, at about latitude 17° 10′, to fix the Copper Queen mining area. The Eastern Circuit was commenced shortly after this; it runs from Salisbury eastwards to the Portuguese Boundary, southwards through Umtali to about latitude 20° and then westwards, joining Simms's chain again to the east of Bulawayo. Another chain running north from Simms's work has been commenced near Bulawayo. The several series are exhibited on the outline map attached.     

THE GEODETIC SURVEY OF CANADA

Abstract

Shortly after the inception of the Geodetic Survey of Canada in 1905, reconnaissance for primary triangulation was commenced in the Ottawa-Montreal area. About the same time, precise levelliilg operations were begun from a bench mark already established by the United States Coast and Geodetic Survey near the International border at Rouses Point in Quebec.     

World Geodetic Datum 2000

 Based on the current best estimates of fundamental geodetic parameters {W ₀,GM,J ₂,Ω} the form parameters of a Somigliana-Pizzetti level ellipsoid, namely the semi-major axis a and semi-minor axis b (or equivalently the linear eccentricity ) are computed and proposed as a new World Geodetic Datum 2000. There are six parameters namely the four fundamental geodetic parameters {W ₀,GM,J ₂,Ω} and the two form parameters {a,b} or {a,ɛ}, which determine the ellipsoidal reference gravity field of Somigliana-Pizzetti type constraint to two nonlinear condition equations. Their iterative solution leads to best estimates a=(6 378 136.572±0.053)m, b=(6 356 751.920 ± 0.052)m, ɛ=(521 853.580±0.013)m for the tide-free geoide of reference and a=(6 378 136.602±0.053)m, b=(6 356 751.860±0.052)m, ɛ=(521 854.674 ± 0.015)m for the zero-frequency tide geoid of reference. The best estimates of the form parameters of a Somigliana-Pizzetti level ellipsoid, {a,b}, differ significantly by −0.39 m, −0.454 m, respectively, from the data of the Geodetic Reference System 1980. Received: 1 February 1999 / Accepted: 31 August 1999     

THE UNITED STATES COAST AND GEODETIC SURVEY: ITS WORK AND PRODUCTS

Abstract

As the name of the Coast and Geodetic Survey indicates, it is the agency of the United States Government which is responsible for geodetic control surveys. Originally our geodetic surveys were made for control of surveys of the coast and to provide a proper base for the nautical charts of the coastal waters. By Congressional action in 1871 these activities were expanded to furnish basic control for the interior of the country, including geodetic connections between the Atlantic, Gulf, and Pacific coasts of the United States.     

Alignment of geodetic and satellite coordinate systems to the average terrestrial system

The parallelism of geodetic and satellite systems to the average terrestrial system is examined, under the assumption that a geodetic system is a fixed framework invariant with respect to geodetic network adjustment. In this case a geodetic system is rotated with respect to the average terrestrial system only about the ellipsoid normal of the initial point. The method is demonstrated using coordinates and covariance matrices for BC-4 and SECOR satellite tracking stations computed by Mueller and his co-workers. It is shown that the NAD geodetic system is scaled significantly larger than the satellite systems; the SECOR satellite systems have significant Z-rotations with respect to the average terrestrial system; and the ETH geodetic system may have a significant rotation with respect to the average terrestrial system.     

A note on frame transformations with applications to geodetic datums

Rigorous equations in compact symbolic matrix notation are introduced to transform coordinates and velocities between ITRF frames and modern GPS-based geocentric geodetic datums. The theory is general but, after neglecting higher than second-order terms, it is shown that the equations revert to the formulation currently applied in most major continental datums. We discuss several examples: the North American Datum of 1983 (NAD83), the European Terrestrial Reference System of 1989 (ETRS89), the Geodetic Datum of Australia of 1994 (GDA94), and the South American Geocentric Reference System (SIRGAS). Electronic Publication     

美国三维坐标基准现代化新进展

随着空间大地测量技术的发展和对高精度参考系统的迫切需求,美国国家大地测量局（NGS）计划对美国国家空间参考系（NSRS）进行现代化。本文主要介绍了提出并采用板块固定参考框架的理由,并根据NGS的NSRS现代化蓝图阐述了三维坐标基准现代化的基本策略及特点。新的三维坐标基准相比现有的NAD83,主要改进为：①采用了“板块固定”策略,板块参考框架由3个增加至4个;②参考框架实现将主要依靠主动控制点（连续运行基准站）,被动控制点仅充当补充和辅助角色;③将提供框架内速度场模型。目前各板块框架板块旋转的欧拉极点和框架内速度场模型还需进一步确定。     

Preliminary results of the establishment of a marine geodetic point in the Pacific Ocean

In November 1968, a marine geodetic control point was established in the Pacific Ocean at a water depth of6,200 feet. The control point (reference point) consists of three underwater acoustic transponders, two of which are powered with lead-acid batteries and the third with an underwater radioisotope power source “URIPS” with a10- to20- year life expectancy. Four independent measuring techniques (LORAC airborne line-crossing, satellite, ship inertial, and acoustic techniques) were used to measure and determine the coordinates of the control point. Preliminary analysis of the acoustic and airborne data indicates that high accuracies can be achieved in the establishment of geodetic reference points at sea. Geodetic adjustment by the method of variation of coordinates yielded a standard point error of±50 to±66 feet in determining the unknown ship station. The original location of the ship station as determined by shipboard navigation equipment was off by about1,600 feet. Paper previously published in the Proceedings of the Second Marine Geodesy Symposium of the Marine Technology Society.     

Cartesian to geodetic coordinates conversion on a triaxial ellipsoid

A new method of transforming Cartesian to geodetic (or planetographic) coordinates on a triaxial ellipsoid is presented. The method is based on simple reasoning coming from essentials of vector calculus. The reasoning results in solving a nonlinear system of equations for coordinates of the point being the projection of a point located outside or inside a triaxial ellipsoid along the normal to the ellipsoid. The presented method has been compared to a vector method of Feltens (J Geod 83:129–137, 2009) who claims that no other methods are available in the literature. Generally, our method turns out to be more accurate, faster and applicable to celestial bodies characterized by different geometric parameters. The presented method also fits to the classical problem of converting Cartesian to geodetic coordinates on the ellipsoid of revolution.     

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”.     

ADJUSTMENT OF THE SECONDARY TRIANGULATION OF SOUTH AFRICA

Abstract

The Secondary Triangulation of South Africa consists of a uniform network of triangles of from 5- to 10-mile sides, enmeshed in the Geodetic and Primary Triangulations. As a rule the Primary Triangulation is rigorously adjusted by least squares, and the Secondary made to conform to it by an approximately rigorous method which was introduced into the Trigonometrical Survey in 1920 by the late Dr van der Sterr.     

工程测量中平面坐标转换及其应用

为了更好地利用已有大地测量成果、GPS测量成果,必须进行不同坐标系统之间的坐标转换。不同地域、不同历史时期、不同参考椭球建立的大地测量坐标不同,特别是地方坐标和国家坐标经常进行转换,因此研究平面坐标转换及参数的确定的数学模型有重要的理论意义和实用价值。     

Defining the basic entities in a geodetic data base

The term “entity” covers, when used in the field of electronic data processing, the meaning of words like “thing”, “being”, “event”, or “concept”. Each entity is characterized by a set of properties. An information element is a triple consisting of an entity, a property and the value of a property. Geodetic information is sets of information elements with entities being related to geodesy. This information may be stored in the form ofdata and is called ageodetic data base provided (1) it contains or may contain all data necessary for the operations of a particular geodetic organization, (2) the data is stored in a form suited for many different applications and (3) that unnecessary duplications of data have been avoided. The first step to be taken when establishing a geodetic data base is described, namely the definition of the basic entities of the data base (such as trigonometric stations, astronomical stations, gravity stations, geodetic reference-system parameters, etc...). Presented at the “International Symposium on Optimization of Design and Computation of Control Networks”, Sopron, Hungary, July 1977.     

Software tools for accessing the GPS Seamless Archive

The Scripps Orbit and Permanent Array Center (SOPAC) has completed development for the UNAVCO community of first-generation GPS Seamless Archive (GSAC) software. The GSAC is a virtual archive composed of an assembly of agencies and investigators exchanging information about their respective GPS-related data holdings in a well defined, cohesive manner. The superset of this published information is collected and ingested into centralized databases administered currently by two data brokers (Retailers), who make the data available to the public in a seamless manner. There are three user interfaces available: the interactive GSAC Wizard, a command-line Unix-style executable called gsac-client, and a front door HTTP service called the GSAC Retailer Service Interface. Each user interface provides access to the data collections of 6 different GPS archives (GSAC Wholesalers) in North America. Together these archives have published more than 2 million GPS data files pertaining to over 10,000 different geodetic monuments. These datasets are composed in large part of data collected by US scientists and their collaborators over the period 1986 to the present in Western North America and other tectonically active regions around the globe, as well as the holdings of two IGS global data centers. In this article, we describe how the three GSAC user interfaces provide the community a powerful set of tools for seamlessly mining information and collecting data files from a distributed network of GPS archives.The GPS Toolbox is a column dedicated to highlighting algorithms and source code utilized by GPS Engineers and scientists. If you have an interesting program or software package you would like to share with our readers, please pass it along; e-mail it to us at gps-toolbox@ngs.noaa.gov. To comment on any of the source code discussed here, or to download source code, visit our website at . This column is edited by Stephen Hilla, National Geodetic Survey, NOAA, Silver Spring, Maryland, and Mike Craymer, Geodetic Survey Division, Natural Resources Canada, Ottawa, Ontario, Canada.     

GEODETIC SIGNALS IN SOUTHERN RHODESIA

Abstract

So much has been written in the Empire Survey Review and other publications on the somewhat controversial subject of “Luminous or Opaque Signals in Geodetic and Primary Triangulation” that it may be of interest to give an outline of the types of signals used on such work in Southern Rhodesia, with particular reference to the completion of the Eastern Geodetic Circuit in 1935 and the type of signal that it has been decided to adopt for future work.     

Determination of Indian absolute geodetic datum by least-square solution technique

The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were also considered before actual finalization of the results of the present determination.