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# 4: Modern GPS coordinate systems

4.1 World Geodetic System 1984 (WGS84)

In this section we look at the coordinate systems used in GPS positioning, starting with WGS84. We'll discuss GPS coordinate systems in terms of the coordinate system concepts summarised in table 1.

The datum used for GPS positioning is called WGS84 (World Geodetic System 1984). It consists of 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 3.2, 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 and the reciprocal of flattening. This ellipsoid is the same shape and size as 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 that it generally doesn't fit the Geoid in a particular country as well as the non-geocentric ellipsoid used for mapping that country. In Great Britain GRS80 lies about fifty metres below the Geoid and slopes from east to west relative to the Geoid, so the Geoid-ellipsoid separation is ten 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 Great 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 section 8 for the address.

4.2 Realising WGS84 with a TRF

So much for the theoretical definition of WGS84 - how can we use it? At first sight a coordinate system centred on the centre of mass of the Earth, oceans and atmosphere might seem very difficult to realise. Actually, this definition is very convenient for satellite positioning, because the centre of mass of the Earth (often called the geocentre) is one of the foci of the elliptical orbits of all Earth satellites, assuming the mass of the satellite itself is negligible. Therefore, observing a satellite can tell us, more or less, where the centre of the Earth is.

There are no fewer than three TRFs realising WGS84 which are very important to us in Great Britain. They are: the United States military broadcast realisation; the International Terrestrial Reference Frame (ITRF) precise scientific realisation; and the European Terrestrial Reference Frame (ETRF) Europe-fixed realisation. We will look at each in turn. We will see that each of these actually realises a slightly different datum, although all of them are loosely referred to as 'WGS84 realisations'.

The primary means of navigating in the WGS84 coordinate system is via the WGS84 positions of the 24 GPS satellites, which are continuously broadcast by the satellites themselves. This satellite constellation is a TRF - that is, it is a general-purpose access tool making the WGS84 coordinate system available to users.

The WGS84 satellite positions are determined by the US Department of Defense using a network of tracking stations, the positions of which have been precisely computed. The tracking stations observe the satellites and, hence, determine the WGS84 coordinates of the satellites. The quality of the resulting satellite coordinates depends on the quality of the known tracking station coordinates. These were initially not very good (probably ten metre accuracy) but have been refined several times. The most recent coordinate set, including thirteen tracking stations distributed over the globe, was introduced in January 2002. The tracking station coordinates are now accurate to better than five centimetres, and are in very close agreement with the International Reference Meridian and International Reference Pole.

The network of GPS tracking stations can be considered the original WGS84 TRF. The satellite constellation, which is a derived TRF, can be seen as a tool to transfer this realisation over the horizon to wherever positioning is needed in the world. The current coordinates of the tracking station antennae at epoch 1997.0 are available on the Internet (see section 8 for addresses). These coordinates implicitly state the physical origin, orientation and scale of the system: they have been computed such that these elements are as close as possible to the theoretical requirements listed in section 4.1. Of course, no TRF is perfect; this one is probably good to five centimetres or so.

Prior to May 2000, the full accuracy of the US tracking station TRF was not made available to non-military users. In the transfer of this TRF to satellite positions, positional accuracies were deliberately worsened by a feature known as selective availability (SA). This meant that a civilian user with a single GPS receiver could not determine WGS84 position to an accuracy better than about 100 metres. In May 2000, this intentional degradation of the GPS signals was officially switched off.

With a pair of GPS receivers we can accurately measure their relative positions (that is, the three-dimensional vector between the two receivers can be accurately determined). We must put one of these receivers on a known point and leave it there. This is known as relative GPS positioning or differential GPS. Fortunately, there are methods of accurately determining the real WGS84 position of the known point and, hence, recovering correct WGS84 positions, using the civil GPS TRFs which are the subject of the following sections.

The International Terrestrial Reference Frame (ITRF)

The ITRF is an alternative realisation of WGS84 that is produced by the International Earth Rotation and Reference System Service (IERS) based in Paris, France. It includes many more stations than the broadcast WGS84 TRF - more than 500 stations at 290 sites all over the world. Four different space positioning methods contribute to the ITRF: Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), GPS and Doppler Ranging Integrated on Satellite (DORIS). Each has strengths and weaknesses - their combination produces a strong multi-purpose TRF. ITRF was created by the civil GPS community, quite independently of the US military organisations who operate the broadcast TRF.

Each version of the ITRF is given a year code to identify it - the current version is ITRF2005. ITRF2005 is simply a list of coordinates (X Y and Z in metres) and velocities (dX, dY and dZ in metres per year) of each station in the TRF, together with the estimated level of error in those values. The coordinates relate to the time 2005.0 - to obtain the coordinates of a station at any other time, the station velocity is applied appropriately. This is to cope with the effects of tectonic plate motion. ITRF2005 is available as a SINEX format text file from the IERS Internet web site - see section 8 for the addresses.

The datum realised by the ITRF is actually called ITRS (International Terrestrial Reference System) rather than WGS84. There used to be a difference between the two, but they have been progressively brought together and are now so similar that they can be assumed identical for almost all purposes. Because the ITRF is of higher quality than the military WGS84 TRF, the WGS84 datum now effectively takes its definition from ITRS. Therefore, although in principle the broadcast TRF is the principal realisation of WGS84, in practice ITRF has become the more important Terrestrial Reference Frame because it has proven to be the most accurate global TRF ever constructed. The defining conventions of ITRS are identical to those of WGS84 given in section 4.1.

The ITRF is important to us for two reasons. Firstly, we can use ITRF stations equipped with permanent GPS receivers as reference points of known coordinates to precisely coordinate our own GPS stations, using GPS data downloaded from the Internet. This procedure is known as 'fiducial GPS analysis'. Secondly we can obtain precise satellite positions (known, rather bizarrely, as ephemerides) in the ITRF2005 TRF that are more accurate than the ephemerides transmitted by the GPS satellites. Both these vital geodetic services are provided free by the International GNSS Service on the Internet.

The International GNSS Service (IGS)

The IGS is essential for anybody requiring high accuracy GNSS positions. The IGS operates a global TRF of more than 374 GPS stations (4th May 2010) and from these produces the following free products, distributed via the Internet:

• IGS tracking station dual-frequency GPS data.

• Precise GPS satellite orbits (ephemerides).

• GPS satellite clock parameters.

• Earth orientation parameters.

• IGS tracking station coordinates and velocities; listed in the ITRF.

• Zenith path delay estimates.

Of these, the first two are commonly used for general-purpose high-accuracy positioning, and the third is becoming increasingly important. The satellite ephemerides, clock parameters and Earth rotation parameters are available 2 days after the time of observation, and also in advance of the observation in a less accurate predicted version.

The IGS products give us access to a high-accuracy realisation based on ITRF (currently, ITRF2005). Used in conjunction with the ITRF2005 coordinates of nearby IGS tracking stations and the dual-frequency GPS data from those stations, a user can position a single geodetic-quality GPS receiver to within a few millimetres . Hence, the IGS products are a vital part of the civil GPS community's access to the ITRF.

Because the subject of this booklet is coordinate systems, not GPS positioning methods, no more will be said about IGS here. Please see the further information list in section 8 for more information on precise GPS positioning and the IGS web page address.

European Terrestrial Reference System 1989 (ETRS89)

With each of the three GPS TRFs we have encountered so far (US DoD tracking stations, broadcast GPS orbits, and IERS/IGS TRF), a new version of the WGS84 datum has been introduced. Geodetic datums are like this - in theory the datum is exactly specified by the adopted conventions (listed in section 4.1) but, in practice each TRF intended to realise that specification actually implements a slightly different datum. Often there are deliberate reasons for this, as in the case of the deliberate random element (Selective Availability) that was at one time introduced to the WGS84 datum in the broadcast satellite orbits.

Another type of deliberate variation to the WGS84 datum definition is found in realisations which are intended to serve a particular geographic region for mapping purposes. As we saw in section 4.1, the WGS84 position of any particular point on the Earth's surface is changing continuously due to various effects, the most important of which is tectonic motion. So WGS84 itself is unsuitable for mapping - the ground keeps sliding across the surface of any WGS84 mapping grid!

However, it is still useful to have a mapping coordinate system which is compatible with GPS. This is done by selecting a particular moment in time (in geodesy a moment in time is called an epoch, which is an unusual usage of that word) and stating the WGS84 coordinates of points in the region of interest at that epoch, regardless of the time of observation. Remember that the Cartesian axes and ellipsoid of WGS84 move steadily such that the motion is minimal with respect to the average of tectonic plate motions worldwide. Fixing the datum epoch has the effect of creating a new datum definition (that is, that a new set of Cartesian axes and ellipsoid location and orientation) which initially coincides exactly with WGS84, but from then on remains stationary with respect to the particular piece of the Earth's crust where the fixed points are, while moving steadily away from the WGS84 axes and ellipsoid.

This adoption of a particular WGS84 epoch to remove the effect of tectonic motion has been done in various places in the world - in fact, everywhere WGS84 has been adopted for mapping. Examples of WGS84-like datums, which are gradually diverging from WGS84, are North American Datum 1983, New Zealand Geodetic Datum 2000 and the Geocentric Datum of Australia. There is also a European example, ETRS89, which, as the name suggests, is a datum which coincided with WGS84 at the moment in time 1989.0 and has been slowly diverging ever since, moving with the Eurasian land mass. ETRS89 has not yet been used for a Europe-wide consistent mapping project, but it would be appropriate for this purpose.

There is a TRF associated with ETRS89 called ETRF89. This is based on ITRF89, an old version of the series of realisations of WGS84 which has now reached ITRF2005. Since 1989 this TRF has been densified by GPS in many parts of Europe to give good local access to the datum.

Although not identical with WGS84, these locally-fixed GPS datums are very easily and accurately related back to WGS84. This is because tectonic plate motion is very steady, predictable and precisely known. The ETRS89 coordinate of any point can easily be converted to a WGS84 coordinate via a simple transformation, which is given in section 6.5.

The importance of ETRS89 and ETRF89 to us in Great Britain is that this is the datum and TRF used for all Ordnance Survey GPS positioning. It is a convenient system because we can forget about the tectonic effects apparent in WGS84 (which do not concern us in British mapping), while still being able easily to convert these coordinates to WGS84 when required. OS Net uses ETRS89 as its datum, and is a densification of the ETRF89 TRF. More about this in the next section.

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