Modern GNSS coordinate systems

World Geodetic System 1984 (WGS84)

In this section, we look at the coordinate systems used in GNSS positioning, starting with WGS84. We’ll discuss GNSS coordinate systems in terms of the coordinate system concepts summarised in ''.

The datum used for GPS positioning is called WGS84 (World Geodetic System 1984). It consists of a three-dimensional Cartesian coordinate system and an associated ellipsoid so that WGS84 positions can be described as either XYZ Cartesian coordinates or latitude, longitude and ellipsoid height coordinates. The origin of the datum is the Geocentre (the centre of mass of the Earth) and it is designed for positioning anywhere on Earth.

In line with the definition of a datum given in section '' the WGS84 datum is nothing more than a set of conventions, adopted constants and formulae. No physical infrastructure is included, and the definition does not indicate how you might position yourself in this system. The WGS84 definition includes the following items:

The WGS84 Cartesian axes and ellipsoid are geocentric; that is, their origin is the centre of mass of the whole Earth including oceans and atmosphere.
The scale of the axes is that of the local Earth frame, in the sense of the relativistic theory of gravitation.
Their orientation (that is, the directions of the axes, and hence the orientation of the ellipsoid equator and prime meridian of zero longitude) coincided with the equator and prime meridian of the Bureau Internationale de l’Heure at the moment in time 1984.0 (that is, midnight on New Year’s Eve 1983).
Since 1984.0, the orientation of the axes and ellipsoid has changed such that the average motion of the crustal plates relative to the ellipsoid is zero. This ensures that the Z‑axis of the WGS84 datum coincides with the International Reference Pole, and that the prime meridian of the ellipsoid (that is, the plane containing the Z and X Cartesian axes) coincides with the International Reference Meridian.
The shape and size of the WGS84 biaxial ellipsoid is defined by the semi-major axis length a = 6378137.000 metres, and the reciprocal of flattening 1/f = 298.257223563. This ellipsoid is very, very close in shape and size to the GRS80 ellipsoid.
Conventional values are also adopted for the standard angular velocity of the Earth, and for the Earth gravitational constant. The first is needed for time measurement, and the second to define the scale of the system in a relativistic sense. We will not consider these parameters further here.

There are a couple of points to note about this definition. Firstly, the ellipsoid is designed to best‑fit the Geoid of the Earth as a whole. This means it generally doesn’t fit the Geoid in a particular country as well as the non-geocentric ellipsoid used for mapping that country. In Britain, GRS80 lies about 50 metres below the Geoid and slopes from east to west relative to the Geoid, so the Geoid-ellipsoid separation is 10 metres greater in the west than in the east. Our local mapping ellipsoid (the Airy 1830 ellipsoid) is a much better fit.

Secondly, note that the axes of the WGS84 Cartesian system, and hence all lines of latitude and longitude in the WGS84 datum, are not stationary with respect to any particular country. Due to tectonic plate motion, different parts of the world move relative to each other with velocities of the order of ten centimetres per year. The International Reference Meridian and Pole, and hence the WGS84 datum, are stationary with respect to the average of all these motions. But this means they are in motion relative to any particular region or country. In Britain, all WGS84 latitudes and longitudes are changing at a constant rate of about 2.5 centimetres per year in a north-easterly direction. Over the course of a decade or so, this effect becomes noticeable in large-scale mapping. Some parts of the world (for example Hawaii and Australia) are moving at up to one metre per decade relative to WGS84.

The full definition of WGS84 is available on the Internet – see '' for more details.

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World Geodetic System 1984 (WGS84)

In this section, we look at the coordinate systems used in GNSS positioning, starting with WGS84. We’ll discuss GNSS coordinate systems in terms of the coordinate system concepts summarised in ''.

The WGS84 Cartesian axes and ellipsoid are geocentric; that is, their origin is the centre of mass of the whole Earth including oceans and atmosphere.

The scale of the axes is that of the local Earth frame, in the sense of the relativistic theory of gravitation.

Their orientation (that is, the directions of the axes, and hence the orientation of the ellipsoid equator and prime meridian of zero longitude) coincided with the equator and prime meridian of the Bureau Internationale de l’Heure at the moment in time 1984.0 (that is, midnight on New Year’s Eve 1983).

Since 1984.0, the orientation of the axes and ellipsoid has changed such that the average motion of the crustal plates relative to the ellipsoid is zero. This ensures that the Z‑axis of the WGS84 datum coincides with the International Reference Pole, and that the prime meridian of the ellipsoid (that is, the plane containing the Z and X Cartesian axes) coincides with the International Reference Meridian.

The shape and size of the WGS84 biaxial ellipsoid is defined by the semi-major axis length a = 6378137.000 metres, and the reciprocal of flattening 1/f = 298.257223563. This ellipsoid is very, very close in shape and size to the GRS80 ellipsoid.

Conventional values are also adopted for the standard angular velocity of the Earth, and for the Earth gravitational constant. The first is needed for time measurement, and the second to define the scale of the system in a relativistic sense. We will not consider these parameters further here.

The full definition of WGS84 is available on the Internet – see '' for more details.