Editing World Geodetic System (section)

==History==
Efforts to supplement the various national [[surveying]] systems began in the 19th century with [[Friedrich Robert Helmert|F.R. Helmert's]] book {{lang|de|Mathematische und Physikalische Theorien der Physikalischen Geodäsie}} (''Mathematical and Physical Theories of Physical Geodesy''). [[Austria]] and [[Germany]] founded the {{lang|de|Zentralbüro für die Internationale Erdmessung}} (Central Bureau of International [[Geodesy]]), and a series of global [[ellipsoid]]s of the Earth were derived (e.g., Helmert 1906, [[John Fillmore Hayford|Hayford]] 1910 and 1924).

A unified geodetic system for the whole world became essential in the 1950s for several reasons:
* International [[space science]] and the beginning of [[astronautics]].
* The lack of inter-continental geodetic information.
* The inability of the large [[geodetic system]]s, such as European Datum ([[ED50]]), [[North American Datum]] (NAD), and [[Tokyo Datum]] (TD), to provide a worldwide geo-data basis
* Need for global maps for [[navigation]], aviation, and [[geography]].
* Western [[Cold War]] preparedness necessitated a standardised, [[NATO]]-wide geospatial reference system, in accordance with the NATO [[STANAG|Standardisation Agreement]]

==={{anchor|WGS60}} WGS&nbsp;60===
In the late 1950s, the [[United States Department of Defense]], together with [[scientist]]s of other institutions and countries, began to develop the needed world system to which geodetic data could be referred and compatibility established between the coordinates of widely separated sites of interest. Efforts of the U.S. Army, Navy and Air Force were combined leading to the DoD World Geodetic System 1960 (WGS&nbsp;60). The term ''datum'' as used here refers to a smooth surface somewhat arbitrarily defined as zero elevation, consistent with a set of surveyor's measures of distances between various stations, and differences in elevation, all reduced to a grid of [[latitude]]s, [[longitude]]s, and [[elevation]]s. Heritage surveying methods found elevation differences from a local horizontal determined by the [[spirit level]], [[plumb-bob|plumb line]], or an equivalent device that depends on the local gravity field (see [[physical geodesy]]). As a result, the elevations in the data are referenced to the [[geoid]], a surface that is not readily found using [[satellite geodesy]]. The latter observational method is more suitable for global mapping.  Therefore, a motivation, and a substantial problem in the WGS and similar work is to patch together data that were not only made separately, for different regions, but to re-reference the elevations to an ellipsoid model rather than to the [[geoid]].
[[Image:GRAVIMETRIC DATUM ORIENTATION.SVG|thumb|upright=1.75|Gravimetric datum orientation.
{{legend-line|solid cyan|Ellipsoid of [[Geodetic astronomy|astro-geodetically]] oriented datum}}
{{legend-line|solid lime|[[Geoid]]}}
{{legend-line|solid red|[[Gravimetry|Gravimetrically]]-oriented ellipsoid}}]]

In accomplishing WGS&nbsp;60, a combination of available surface [[gravity]] data, [[astro-geodetic]] data and results from HIRAN<ref>{{cite web|url=http://www.history.noaa.gov/stories_tales/ak7.html |title=NOAA History - Stories and Tales of the Coast & Geodetic Survey - Personal Tales/Earth Measurer/Aslakson Bio |website=History.noaa.gov |access-date=24 May 2017}}</ref> and Canadian [[SHORAN]] surveys were used to define a best-fitting [[ellipsoid]] and an earth-centered orientation for each initially selected datum. (Every datum is relatively oriented with respect to different portions of the geoid by the astro-geodetic methods already described.)  The sole contribution of [[satellite]] data to the development of WGS&nbsp;60 was a value for the [[ellipsoid]] flattening which was obtained from the nodal motion of a satellite.

Prior to WGS&nbsp;60, the U.S. Army and [[U.S. Air Force]] had each developed a world system by using different approaches to the gravimetric datum orientation method.  To determine their gravimetric orientation parameters, the Air Force used the mean of the differences between the gravimetric and astro-geodetic [[vertical deflection|deflections]] and geoid heights (undulations) at specifically selected stations in the areas of the major datums. The Army performed an adjustment to minimize the difference between astro-geodetic and [[gravimetric]] [[geoid]]s. By matching the relative astro-geodetic geoids of the selected datums with an earth-centered gravimetric geoid, the selected datums were reduced to an earth-centered orientation. Since the Army and Air Force systems agreed remarkably well for the NAD, ED and TD areas, they were consolidated and became WGS&nbsp;60.

==={{anchor|WGS66}}WGS&nbsp;66===
Improvements to the global system included the Astrogeoid of [[Irene Fischer]] and the astronautic Mercury datum. In January 1966, a World Geodetic System Committee composed of representatives from the United States Army, Navy and Air Force was charged with developing an improved WGS, needed to satisfy [[map]]ping, charting and geodetic requirements. Additional surface [[gravity]] observations, results from the extension of [[triangulation]] and [[trilateration]] networks, and large amounts of [[Doppler radar|Doppler]] and [[optical]] satellite data had become available since the development of WGS 60. Using the additional data and improved techniques, WGS 66 was produced which served DoD needs for about five years after its implementation in 1967. The defining parameters of the WGS 66 Ellipsoid were the flattening ({{frac|1|298.25}} determined from satellite data) and the semimajor axis ({{val|6378145|u=meters}} determined from a combination of Doppler satellite and astro-geodetic data). A worldwide 5° × 5° mean free air [[gravity anomaly]] field provided the basic data for producing the WGS 66 gravimetric geoid. Also, a geoid referenced to the WGS 66 Ellipsoid was derived from available astrogeodetic data to provide a detailed representation of limited land areas.

==={{anchor|WGS72}} WGS&nbsp;72===
After an extensive effort over a period of approximately three years, the Department of Defense World Geodetic System 1972 was completed. Selected satellite, surface gravity and astrogeodetic data available through 1972 from both DoD and non-DoD sources were used in a Unified WGS Solution (a large scale [[least squares]] adjustment). The results of the adjustment consisted of corrections to initial station coordinates and coefficients of the gravitational field.<ref name=":0">{{Cite book |url=https://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/toc.htm |title=Geodesy for the Layman |publisher=United States Air Force |year=1984 |language=en |chapter=THE WORLD GEODETIC SYSTEM |chapter-url=https://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003E.HTM#ZZ11}}</ref>

The largest collection of data ever used for WGS purposes was assembled, processed and applied in the development of WGS 72. Both optical and electronic satellite data were used. The electronic satellite data consisted, in part, of Doppler data provided by the U.S. Navy and cooperating non-DoD satellite tracking stations established in support of the Navy's Navigational Satellite System (NNSS). Doppler data was also available from the numerous sites established by GEOCEIVERS during 1971 and 1972. Doppler data was the primary data source for WGS 72 (see image). Additional electronic satellite data was provided by the SECOR (Sequential Collation of Range) Equatorial Network completed by the U.S. Army in 1970. Optical satellite data from the Worldwide Geometric Satellite Triangulation Program was provided by the BC-4 camera system (see image). Data from the [[Smithsonian Astrophysical Observatory]] was also used which included camera ([[Schmidt camera#Baker–Nunn|Baker–Nunn]]) and some laser ranging.<ref name=":0" />

[[Image:DOPPLER SATELLITE GROUND STATIONS PROVIDING DATA FOR WGS 72 DEVELOPMENT.GIF|thumb|upright=1.5|Doppler satellite ground stations providing data for WGS 72 development]]

[[Image:WORLDWIDE GEOMETRIC SATELLITE TRIANGULATION NETWORK, BC-4 CAMERAS.GIF|thumb|upright=1.5|Worldwide geometric satellite triangulation network, BC-4 cameras]]

The surface gravity field used in the Unified WGS Solution consisted of a set of 410 10° × 10° equal area mean free air gravity anomalies determined solely from terrestrial data. This gravity field includes mean anomaly values compiled directly from observed gravity data wherever the latter was available in sufficient quantity. The value for areas of sparse or no observational data were developed from geophysically compatible gravity approximations using gravity-geophysical correlation techniques. Approximately 45 percent of the 410 mean free air gravity anomaly values were determined directly from observed gravity data.<ref name=":0" />

The astrogeodetic data in its basic form consists of deflection of the vertical components referred to the various national geodetic datums. These deflection values were integrated into astrogeodetic geoid charts referred to these national datums. The geoid heights contributed to the Unified WGS Solution by providing additional and more detailed data for land areas. Conventional ground survey data was included in the solution to enforce a consistent adjustment of the coordinates of neighboring observation sites of the BC-4, SECOR, Doppler and Baker–Nunn systems. Also, eight [[geodimeter]] long line precise traverses were included for the purpose of controlling the scale of the solution.<ref name=":0" />

The Unified WGS Solution, as stated above, was a solution for geodetic positions and associated parameters of the gravitational field based on an optimum combination of available data. The WGS 72 ellipsoid parameters, datum shifts and other associated constants were derived separately. For the unified solution, a normal equation matrix was formed based on each of the mentioned data sets. Then, the individual normal equation matrices were combined and the resultant matrix solved to obtain the positions and the parameters.<ref name=":0" />

The value for the semimajor axis ({{mvar|a}}) of the WGS 72 Ellipsoid is {{val|6378135|u=meters}}. The adoption of an {{mvar|a}}-value 10 meters smaller than that for the WGS 66 Ellipsoid was based on several calculations and indicators including a combination of satellite and surface gravity data for position and gravitational field determinations. Sets of satellite derived station coordinates and gravimetric deflection of the vertical and geoid height data were used to determine local-to-geocentric datum shifts, datum rotation parameters, a datum scale parameter and a value for the semimajor axis of the WGS Ellipsoid. Eight solutions were made with the various sets of input data, both from an investigative point of view and also because of the limited number of unknowns which could be solved for in any individual solution due to computer limitations. Selected Doppler satellite tracking and astro-geodetic datum orientation stations were included in the various solutions. Based on these results and other related studies accomplished by the committee, an {{mvar|a}}-value of {{val|6378135|u=meters}} and a flattening of 1/298.26 were adopted.<ref name=":0" />

In the development of local-to WGS 72 datum shifts, results from different geodetic disciplines were investigated, analyzed and compared. Those shifts adopted were based primarily on a large number of Doppler TRANET and GEOCEIVER station coordinates which were available worldwide. These coordinates had been determined using the Doppler point positioning method.<ref name=":0" />

==={{anchor|WGS84}}WGS&nbsp;84===
[[File:WGS84_mean_Earth_radius.svg|thumb|upright=1.15|Equatorial ({{mvar|a}}), polar ({{mvar|b}}) and mean Earth radii as defined in the 1984 World Geodetic System revision (not to scale)]]
In the early 1980s, the need for a new world geodetic system was generally recognized by the geodetic community as well as within the US Department of Defense. WGS 72 no longer provided sufficient data, information, geographic coverage, or product accuracy for all then-current and anticipated applications. The means for producing a new WGS were available in the form of improved data, increased data coverage, new data types and improved techniques. Observations from Doppler, satellite laser ranging and [[very-long-baseline interferometry]] (VLBI) constituted significant new information. An outstanding new source of data had become available from satellite radar altimetry. Also available was an advanced [[least squares]] method called [[Collocation method|collocation]] that allowed for a consistent combination solution from different types of measurements all relative to the Earth's gravity field, measurements such as the geoid, gravity anomalies, deflections, and dynamic Doppler.

The new world geodetic system was called WGS&nbsp;84. It is the reference system used by the [[Global Positioning System]]. It is geocentric and globally consistent within {{val|1|ul=m}}. Current geodetic realizations of the geocentric reference system family [[International Terrestrial Reference System]] (ITRS) maintained by the [[IERS]] are geocentric, and internally consistent, at the few-cm level, while still being metre-level consistent with WGS&nbsp;84.

The WGS&nbsp;84 [[reference ellipsoid]] was based on [[GRS 80]], but it contains a very slight variation in the inverse flattening, as it was derived independently and the result was rounded to a different number of significant digits.<ref>{{Cite book | last = Hooijberg | first = Maarten | date = 18 December 2007 | title = Geometrical Geodesy: Using Information and Computer Technology | location = Germany | publisher = Springer Berlin Heidelberg | page = 20 | isbn = 9783540682257}}</ref> This resulted in a tiny difference of {{val|0.105|u=mm}} in the semi-minor axis.<ref>{{Cite web |title=USER DOCUMENTATION Programs: INVERSE, FORWARD, INVERS3D, FORWRD3D Versions 2.0 |url=https://geodesy.noaa.gov/PC_PROD/Inv_Fwd/readme.htm |access-date=23 May 2022 |website=geodesy.noaa.gov}}</ref>
The following table compares the primary ellipsoid parameters.

{| class="wikitable"
|-
! Ellipsoid reference
! [[Semi-major axis]] {{mvar|a}}
! [[Semi-minor axis]] {{mvar|b}}
! Inverse [[flattening]] {{frac|1|{{mvar|f}}}}
|-
! GRS 80
| {{val|6378137.0|u=m}}
| ≈ {{val|6356752.314140|u=m}}
| {{val|298.257222100882711}}...
|-
! WGS 84<ref>{{cite web | url = https://epsg.org/ellipsoid_7030/WGS-84.html | title = WGS&nbsp;84: Ellipsoid Details | website = EPSG Geodetic Parameter Dataset | access-date=21 December 2022}}</ref>
| {{val|6378137.0|u=m}}
| ≈ {{val|6356752.314245|u=m}}
| {{val|298.257223563}}
|}