Geodetic systems or geodetic data are used in geodesy, navigation, surveying by cartographers and satellite navigation systems to translate positions indicated on their products to their real position on earth. An old geodetic pillar (1855) at Ostend, Belgium A Munich archive with lithography plates of maps of Bavaria Geodesy (pronounced [1]), also called geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three...
This article is about determination of position and direction on or above the surface of the earth. ...
Surveyor at work with a leveling instrument. ...
Cartography is the study of map making and cartographers are map makers. ...
It has been suggested that this article or section be merged into Global Navigation Satellite System. ...
This article is about Earth as a planet. ...
The systems are needed because the earth is not a perfect sphere. This article is about Earth as a planet. ...
For other uses, see Sphere (disambiguation). ...
Examples of map data are: The difference in coordinates between data is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, and can be anything from zero to hundreds of metres (or several kilometres for some remote islands). The North Pole, South Pole and Equator may be assumed to be in different positions on different datums, so True North may be very slightly different. Different datums use different estimates for the precise shape and size of the Earth (reference ellipsoids). The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ...
Part of an Ordnance Survey map at 1 inch to the mile scale from 1945 Ordnance Survey (OS) is an executive agency of the United Kingdom government. ...
ED 50 (European Datum 1950) is a geodetic datum which was defined after World War II for the international connection of geodetic networks. ...
For other uses, see North Pole (disambiguation). ...
For other uses, see South Pole (disambiguation). ...
World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses IlhÃ©u das Rolas, in SÃ£o TomÃ© and PrÃncipe. ...
True Pizza is a navigational term referring to the direction of the North Pole relative to the navigators position. ...
In geodesy, a reference ellipsoid is a mathematicallydefined surface that approximates the geoid, the truer figure of the Earth, or other planetary body. ...
The difference between WGS84 and OSGB36 is up to 140 metres (450 feet), which for some navigational purposes is an insignificant error. For most applications, such as surveying and dive site location for SCUBA divers, 140 metres is an unacceptably large error. Surveyor at work with a leveling instrument. ...
A scuba diver in usual sport diving gear SCUBA is an acronym for SelfContained Underwater Breathing Apparatus. ...
The main reason that there are a number of datums is that before the advent of GPS positioning, national map making organizations did not have a common surveying reference point and only produced maps for their locality. Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ...
Datum
In surveying and geodesy, a datum is a reference point or surface against which position measurements are made, and an associated model of the shape of the earth for computing positions. Horizontal datums are used for describing a point on the earth's surface, in latitude and longitude or another coordinate system. Vertical datums are used to measure elevations or underwater depths. Surveyor at work with a leveling instrument. ...
An old geodetic pillar (1855) at Ostend, Belgium A Munich archive with lithography plates of maps of Bavaria Geodesy (pronounced [1]), also called geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three...
This article is about Earth as a planet. ...
This article is about the geographical term. ...
Longitude is the eastwest geographic coordinate measurement most commonly utilized in cartography and global navigation. ...
Horizontal datums The horizontal datum is the model used to measure positions on the earth. A specific point on the earth can have substantially different coordinates, depending on the datum used to make the measurement. There are hundreds of locallydeveloped horizontal datums around the world, usually referenced to some convenient local reference point. Contemporary datums, based on increasingly accurate measurements of the shape of the earth, are intended to cover larger areas. The WGS84 datum, which is almost identical to the NAD83 datum used in North America, is a common standard datum. WGS 84 is the 1984 revision of the World Geodetic System. ...
Vertical datum A vertical datum is used for measuring the elevations of points on the earth's surface. Vertical data are either tidal, based on sea levels, gravimetric, based on a geoid, or geodetic, based on the same ellipsoid models of the earth used for computing horizontal datums. For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...
The GOCE project will measure highaccuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...
In common usage, elevations are often cited in height above sea level; this is a widely used tidal datum. Because ocean tides cause water levels to change constantly, the sea level is generally taken to be some average of the tide heights. Mean lower low water — the average of the lowest points the tide reached on each day during a measuring period of several years — is the datum used for measuring water depths on some nautical charts, for example; this is called the chart datum. Whilst the use of sealevel as a datum is useful for geologically recent topographic features, sea level has not stayed constant throughout geological time, so is less useful when measuring very longterm processes. For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...
This article is about tides in the Earths oceans. ...
Averages redirects here. ...
A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. ...
The chart datum is the level of water that charted depths displayed on nautical charts are measured from. ...
A geodetic vertical datum takes some specific zero point, and computes elevations based on the geodetic model being used, without further reference to sea levels. Usually, the starting reference point is a tide gauge, so at that point the geodetic and tidal datums might match, but due to sea level variations, the two scales may not match elsewhere. One example of a geoid datum is NAVD88, used in North America, which is referenced to a point in Quebec, Canada. The GOCE project will measure highaccuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ...
This article is about the Canadian province. ...
Geodetic coordinates In geodetic coordinates the Earth's surface is approximated by an ellipsoid and locations near the surface are described in terms of latitude (φ), longitude (λ) and height (h). The ellipsoid is completely parameterised by the semimajor axis a and the flattening f.
Geodetic versus geocentric latitude The same position on a spheroid has a different angle for latitude depending on whether the angle is measured from the normal (angle α) or around the center (angle β). Note that the "flatness" of the spheroid in the image is greater than that of the Earth; therefore, the corresponding difference between the "geocentric" and "geodetic" latitudes is also greater. It is important to note that geodetic latitude (φ) is different than geocentric latitude (φ'). Geodetic latitude is determined by the angle between the normal of the spheroid and the plane of the equator, whereas geocentric latitude is determined around the centre (see figure). Unless otherwise specified latitude is geodetic latitude. A surface normal, or just normal to a flat surface is a threedimensional vector which is perpendicular to that surface. ...
Geodetic defining parameters Parameter  Symbol  Semimajor axis  a  Reciprocal of flattening  1/f  Geodetic derived geometric constants From a and f it is possible to derive the semiminor axis b, first eccentricity e and second eccentricity e′ of the ellipsoid Parameter  Value  semiminor axis  b = a(1f)  First eccentricity squared  e^{2} = 1b^{2}/a^{2} = 2ff^{2}  Second eccentricity  e′^{2} = a^{2}/b^{2}  1 = f(2f)/(1f)^{2}  Parameters for some geodetic systems A more comprehensive list of geodetic systems can be found here
Australian Geodetic Datum 1966 [AGD66] and Australian Geodetic Datum 1984 (AGD84) AGD66 and AGD84 both use the parameters defined by Australian National Spheroid (see below)
Australian National Spheroid (ANS) ANS Defining Parameters Parameter  Notation  Value  semimajor axis  a  6378160.000 m  Reciprocal of Flattening  1/f  298.25  Geocentric Datum of Australia 1994 (GDA94) and Geocentric Datum of Australia 2000 (GDA2000) Both GDA94 and GDA2000 use the parameters defined by GRS80 (see below)
Geodetic Reference System 1980 (GRS80) GRS80 Defining Parameters Parameter  Notation  Value  semimajor axis  a  6378137 m  Reciprocal of flattening  1/f  298.257222101  see GDA Technical Manual document for more details.
World Geodetic System 1984 (WGS84) The global positioning system (GPS) uses the world geodetic system 1984 (WGS84) to determine the location of a point near the surface of the Earth. WGS84 Defining Parameters Parameter  Notation  Value  semimajor axis  a  6378137.0 m  Reciprocal of flattening  1/f  298.257223563  WGS84 derived geometric constants Constant  Notation  Value  Semiminor axis  b  6356752.3142 m  First Eccentricity Squared  e^{2}  6.69437999014x10^{3}  Second Eccentricity Squared  e′^{2}  6.73949674228x10^{3}  see The official World Geodetic System 1984 document for more details.
Other Earth based coordinate systems Earth Centred Earth Fixed (ECEF) coordinates The Earthcentred Earthfixed (ECEF) or conventional terrestrial coordinate system rotates with the Earth and has its origin at the centre of the Earth. The X axis passes through the equator at the prime meridian. The Z axis passes through the north pole. The Y axis can be determined by the right hand rule to be passing through the equator at 90^{o} longitude. ECEF stands for EarthCentered, EarthFixed, and is a Cartesian coordinate system used for GPS, and is sometimes known as a conventional terrestrial system[1]. It represents positions as an X, Y, and Z coordinate. ...
Local east, north, up (ENU) coordinates In many targeting and tracking applications the local East, North, Up (ENU) Cartesian coordinate system is far more intuitive and practical than ECEF or Geodetic coordinates. The local ENU coordinates are formed from a plance tangent to the Earth's surface finxed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane. By convention the east axis is labeled x, the north y and the up z.
Local north, east, down (NED) coordinates In an aeroplane most objects of interest are below you, it is therefore sensible to define down as a positive number, the NED coordinates allow you to do this as an alternative the ENU local tangent plane. By convention the north axis is labeled x', the east y' and the down z'. To avoid confusion between x and x', etc in this web page we will restrict the local coordinate frame to ENU.
Conversion From geodetic coordinates to local ENU coordinates To convert from geodetic coordinates to local ENU up coordinates is a two stage process  Convert geodetic coordinates to ECEF coordinates
 Convert ECEF coordinates to local ENU coordinates
From geodetic to ECEF coordinates Geodetic coordinates (latitude φ, longitude λ, height h) can be converted into ECEF coordinates using the following formulae:
Where a and e^{2} are the semimajor axis and the square of the first numerical eccentricity of the ellipsoid respectively
From ECEF to ENU Coordinates To transform from ECEF coordinates to the local coordinates we need a local reference point, typically this might be the location of the radar. If a radar is located at {X_{r},Y_{r},Z_{r}} and an aircraft at {X_{p},Y_{p},Z_{p}} then the vector pointing from the radar to the aircraft in the ENU frame is
Note: φ is the geodetic latitude. A prior version of this page showed use of the geocentric latitude (φ'). The geocentric latitude is not the appropriate up direction for the local tangent plane. If the original geodetic latitude is available it should be used, otherwise, the relationship between geodetic and geocentric latitude has an altitude dependency, and is captured by:
Note that is also called the Normal, and is the length of the line segment, colinear with the altitude vector and normal to the ellipsoid, which runs from the geodetic ellipsoid at the specified latitude/longitude to the intersection with the line connecting the north and south poles. Obtaining geodetic latitude from geocentric coordinates from this relationship requires an iterative solution approach, otherwise the geodetic coordinates may be computed via the approach in the section below labeled "From ECEF to geodetic coordinates." Reference http://psas.pdx.edu/CoordinateSystem/Latitude_to_LocalTangent.pdf for another example of computing ENU coordinates. The geocentric and geodetic longitude have the same value
Note: Unambiguous determination of φ and λ requires knowledge of which quadrant the coordinates lie in.
From local ENU coordinates to geodetic coordinates As before it is done in two stages  Convert local ENU coordinates to ECEF coordinates
 Convert ECEF coordinates to GPS coordinates
From ENU to ECEF This is just the inversion of the ECEF to ENU transformation so
From ECEF to geodetic coordinates The conversion of ECEF coordinates to geodetic coordinates (such WGS84) is a much harder problem. A number of techniques are available but the most accurate according to Zhu (Ref 6), is the following 15 step procedure summarised by Kaplan. It is assumed that geodetic parameters {a,b,e,e'} are known
Note: Unambiguous determination of λ requires knowledge of the quadrant
From GPS measurements to ENU measurements: sample code This code was written in MATLAB
Step 1: Convert GPS to ECEF function [X,Y,Z] = llh2xyzTest(lat,long, h) % Convert lat, long, height in WGS84 to ECEF X,Y,Z %lat and long given in decimal degrees. lat = lat/180*pi; %converting to radians long = long/180*pi; %converting to radians a = 6378137.0; % earth semimajor axis in meters f = 1/298.257223563; % reciprocal flattening e2 = 2*f f^2; % eccentricity squared chi = sqrt(1e2*(sin(lat)).^2); X = (a./chi +h).*cos(lat).*cos(long); Y = (a./chi +h).*cos(lat).*sin(long); Z = (a*(1e2)./chi + h).*sin(lat); Step 2: Convert ECEF to ENU function [e,n,u] = xyz2enuTest(Xr, Yr, Zr, X, Y, Z) % convert ECEF coordinates to local east, north, up phiP = atan2(Zr,sqrt(Xr^2 + Yr^2)); lambda = atan2(Yr,Xr); e = sin(lambda).*(XXr) + cos(lambda).*(YYr); n = sin(phiP).*cos(lambda).*(XXr)  sin(phiP).*sin(lambda).*(YYr) + cos(phiP).*(ZZr); u = cos(phiP).*cos(lambda).*(XXr) + cos(phiP).*sin(lambda).*(YYr) + sin(phiP).*(ZZr); From ENU measurements to GPS measurements: sample code This code was written in MATLAB Not to be confused with Matlab Upazila in Chandpur District, Bangladesh. ...
Step 1: Convert ENU to ECEF function [X, Y, Z] = enu2xyz(refLat, refLong, refH, e, n, u) % Convert east, north, up coordinates (labelled e, n, u) to ECEF % coordinates. The reference point (phi, lambda, h) must be given. All distances are in metres [Xr,Yr,Zr] = llh2XYZ(refLat,refLong, refH); % location of reference point phiP = atan2(Zr,sqrt(Xr^2+Yr^2)); % Geocentric latitude X = sin(refLong)*e  cos(refLong)*sin(phiP)*n + cos(refLong)*cos(phiP)*u + Xr; Y = cos(refLong)*e  sin(refLong)*sin(phiP)*n + cos(phiP)*sin(refLong)*u + Yr; Z = cos(phiP)*n + sin(phiP)*u + Zr; Step 2: Convert ECEF to GPS function [phi, lambda, h] = xyz2llh(X,Y,Z) a = 6378137.0; % earth semimajor axis in meters f = 1/298.257223563; % reciprocal flattening b = a*(1f);% semiminor axis e2 = 2*ff^2;% first eccentricity squared ep2 = f*(2f)/((1f)^2); % second eccentricity squared r2 = X.^2+Y.^2; r = sqrt(r2); E2 = a^2  b^2; F = 54*b^2*Z.^2; G = r2 + (1e2)*Z.^2  e2*E2; c = (e2*e2*F.*r2)./(G.*G.*G); s = ( 1 + c + sqrt(c.*c + 2*c) ).^(1/3); P = F./(3*(s+1./s+1).^2.*G.*G); Q = sqrt(1+2*e2*e2*P); ro = (e2*P.*r)./(1+Q) + sqrt((a*a/2)*(1+1./Q)  ((1e2)*P.*Z.^2)./(Q.*(1+Q))  P.*r2/2); tmp = (r  e2*ro).^2; U = sqrt( tmp + Z.^2 ); V = sqrt( tmp + (1e2)*Z.^2 ); zo = (b^2*Z)./(a*V); h = U.*( 1  b^2./(a*V)); phi = atan( (Z + ep2*zo)./r ); lambda = atan2(Y,X); Note: atan2(Y,X) uses quadrant information to return a value of lambda between − π and π.
Sample Implementation Code clear all close all clc %% reference point refLat = 39*pi/180; refLong = 132*pi/180; refH = 0; %% Points of interest lat = [39.5*pi/180; 39.5*pi/180;39.5*pi/180]; long = [132*pi/180;131.5*pi/180;131.5*pi/180]; h = [0;0;1000]; disp('lat long height') for i = 1:length(lat) disp([num2str(lat(i)*180/pi),' ', num2str(long(i)*180/pi), ' ',num2str(h(i))]) end % lat = [39.5*pi/180]; % long = [132*pi/180]; % h = [0]; %% convering llh to enu [Xr,Yr,Zr] = llh2xyz(refLat,refLong,refH); [X,Y,Z] = llh2xyz(lat,long,h); disp('X Y Z') for i = 1:length(X) disp([num2str(X(i)),' ', num2str(Y(i)), ' ',num2str(Z(i))]) end [e,n,u] = xyz2enu(Xr, Yr, Zr, X, Y, Z); disp('e n u') for i = 1:length(e) disp([num2str(e(i)),' ', num2str(n(i)), ' ',num2str(u(i))]) end %% Converting enu to llh [X, Y, Z] = enu2xyz(refLat, refLong, refH, e, n, u); disp('X Y Z') for i = 1:length(X) disp([num2str(X(i)),' ', num2str(Y(i)), ' ',num2str(Z(i))]) end [phi, lambda, h] = xyz2llh(X,Y,Z); disp('phi lambda h') for i = 1:length(X) disp([num2str(phi(i)*180/pi),' ', num2str(lambda(i)*180/pi), ' ',num2str(h(i))]) end Reference material  List of geodetic parameters for many systems
 Kaplan, Understanding GPS: principles and applications, 1 ed. Norwood, MA 02062, USA: Artech House, Inc, 1996.
 GPS Notes
 Introduction to GPS Applications
 P. Misra and P. Enge, Global Positioning System Signals, Measurements, and Performance. Lincoln, Massachusetts: GangaJamuna Press, 2001.
 J. Zhu, "Conversion of Earthcentered Earthfixed coordinates to geodetic coordinates," Aerospace and Electronic Systems, IEEE Transactions on, vol. 30, pp. 957961, 1994.
 P. Misra and P. Enge, Global Positioning System Signals, Measurements, and Performance. Lincoln, Massachusetts: GangaJamuna Press, 2001.
 Peter H. Dana: Geodetic Datum Overview  Large amount of technical information and discussion.
 UK Ordnance Survey
 US National Geodetic Survey
 Borkowski, Kazimiers (1987), "Transformation of Geocentric to Geodetic Coordinates Without Approximations", Astrophysics and Space Science 139: 14, <http://www.astro.uni.torun.pl/~kb/Papers/ASS/GeodASS.htm>
See also The World Geodetic System defines a reference frame for the earth, for use in geodesy and navigation. ...
In the British Isles, an Ordnance Datum or OD is a vertical datum used by an ordnance survey as the basis for deriving altitudes on maps. ...
