11.1.2 Transforming GPS Surveying Results: Coordinate Systems & Datums

GEODETIC DATUMS

The GPS Datum

The commonly used space-based datums are founded on the geocentric (earth-centred) 3-D Cartesian systems defined by a global ensemble of U.S. military tracking stations (specifically those of the Defense Mapping Agency -- DMA, now known as the National Imagery & Mapping Agency -- NIMA) that have been established over the decades since the start of the Space Age. As far as GPS is concerned this datum is:

• maintained by the assigned Cartesian coordinates of the handful of tracking stations making up the Control Segment (section 2.2),
• transferred to the (time-varying) satellite coordinates broadcast to users in the Navigation Message during the orbit determination process, carried out by the system controllers at the Master Control Station, and
• ultimately is realised in a local region by the network coordinates that result from a GPS survey.

The standard "GPS datum" is the so-called World Geodetic System 84 (WGS84), nominally defined as having (DMA, 1991):

• The origin at the earth's centre of mass.
• The Z-axis aligned parallel to the direction of the Conventional Terrestrial Pole (CTP) for polar motion, as defined by the International Earth Rotation Service (formerly the BIH).
• The X-axis being the intersection of the WGS84 Reference Meridian Plane and the plane of the CTP Equator (the Reference Meridian being parallel to the Zero Meridian defined by the IERS).
• The Y-axis completes a right-handed, earth-centred, earth-fixed (ECEF) orthogonal coordinate system, measured in the plane of the CTP Equator, 90° east of the X-axis.

This global geometric datum requires no reference ellipsoid or geoid model to be specified.

Ultimately, how well the GPS survey results relate to WGS84 is dependent on the quality of the Broadcast Ephemerides in the Navigation Message, and the quality of the Datum Station coordinates within the network. The accuracy of the GPS orbit information (related to WGS84 system) is at the few metre to few tens of metre level.

Because GPS surveying techniques only provide relative position, and hence are insensitive to absolute coordinates (that is, those relative to the WGS84 / geocentre origin), the coordinates of the datum station in effect defines the origin of the GPS survey in what is in reality a "near-WGS84" system. That is:

• the origin is defined by the vector of the Datum Station coordinates (if based on a pseudo-range point position it may be tens of metres in error).
• the scale of the system may vary depending upon the accuracy of modelling the phase observations (for example, single frequency results may be biased by the neglected ionospheric effects), hence different GPS survey networks may have different implicit scales.
• the orientation of the coordinate axes implicit in the GPS network results in relation to the WGS84 system although probably comparatively well defined, there may nevertheless be a deviation of a few arcseconds.

Hence, how well the Datum Station in the GPS network is related to WGS84 will influence how well the GPS results are referred to the WGS84 system. The implication therefore is that: (a) there may be a suitable set of published transformation parameters that will precisely relate the GPS results to a local datum, or (b) the transformation parameters relating the GPS survey to a local datum may have to be determined from the survey data itself.

The Conventional Geodetic Datum

In general, conventional geodetic datums are "locally defined". The label "local" may refer to an arbitrary datum of convenience, having relevance only in a very localised area, or it may be the more familiar "national" geodetic datum. There are in general two distinct components:

• HORIZONTAL datum system based on curvilinear (ellipsoidal) coordinates defined in relation to some "reference ellipsoid", and
  
• an independent VERTICAL datum based on a local geoid definition (at one or more tide gauge, or "vertical datum" stations).

The datum is in general non-geocentric, the origin being the centre of the reference ellipsoid associated with the datum. However, the datum origin plays no part in defining the vertical datum. In relation to the horizontal datum:

• The datum is, in the first instance, defined (origin and curvature) by the selection of a best-fitting ellipsoid to the geoid over region of the datum.
• It is realised "on the ground" by a single Datum Station, and the network of control stations established from and linked to this station.
• The Z-axis coincides with the semi-minor axis of the reference ellipsoid, the X-axis passes through the point =0°, =0°, and the Y-axis completes the right-handed triad system.

In the Australian context, the datums are:

The Australian Geodetic Datum (AGD) for horizontal control comprising several thousand geodetic control stations distributed across Australia (Figure below). In particular the AGD is realised by the AGD66 coordinate set in the states of New South Wales, Victoria, Tasmania and the Northern Territory; and the AGD84 coordinate set in the remaining states of Australia (ALLMAN & VEENSTRA, 1984). The origin station is the Johnston Trigonometrical Station, with the assigned coordinates (NMC, 1986):

	= 25°56'54.5515"S
	= 133°12'30.0771"E
h	= 571.2m (ellipsoidal height)

and the associated reference ellipsoid is the Australian National Spheroid, defined by the parameters:

semi-major axis	6378160m
inverse of ellipsoidal flattening	298.25

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Figure 1. Layout of the Australian Geodetic Survey.

The Australian Height Datum (AHD) for vertical control is realised by several thousand level benchmarks across Australia (Figure 2 below). However, the zero height datum surface is not coincident with any unique equipotential surface of the earth's gravity field, but is the surface of mean sea level as defined by 30 tide gauge sites around the coast of Australia (ROELSE et al, 1971).

The Australian datum has been redefined (section 12.1.5). The new datum will be known as the Geocentric Datum of Australia (GDA) (MANNING & HARVEY, 1994). As the name implies, this datum will be "geocentric" and hence very close to the WGS84 datum. However, what is even more remarkable is that the basic framework of the GDA is provided by a super-precise GPS survey linking together selected, evenly-distributed geodetic control stations (at an approximate spacing of 500km) with permanent GPS tracking stations around the world. Such a datum redefinition has already occurred in the U.S. with respect to the North American Datum 1983 (NAD83).

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Figure 2. Lines of the Australian Levelling Survey.

Despite the different bases of the coordinate datums (whether GPS or conventional), all geodetic datums may be related to one another, or with any of the global space datums (including WGS84), by a number of transformation models. Associated with the transformation process are the conversion procedures relating ellipsoidal, topocentric and Cartesian coordinates (and any variance-covariance information), the projection coordinate systems and the issue of height systems.

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© Chris Rizos, SNAP-UNSW, 1999