Global Positioning System Reference
In-Depth Information
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Accurate positioning within the ITRF and ICRF frames requires application of
a number of complex mathematical expressions to account for phenomena, such as
polar motion, plate tectonic movements, solid earth tides, and ocean loading dis-
placements, as well as precession and nutations. The respective software for these
corrections is available, generally on the web. Because the names of computer di-
rectories often change, we do not list the full URLs at which the specific software
resides. Instead, it is recommended that the reader simply navigate to key agencies
and research groups and follow the link to the appropriate levels and directories. A
recommended starting point is IERS (2002). Other important sites are of the Interna-
tional GPS Service (IGS), IGS (2002), the U.S. Naval Observatory, USNO (2002),
and the National Geodetic Survey, NGS (2002). Because the software is readily avail-
able at these sites, we only list mathematical expressions to the extent needed for a
conceptual presentation of the topics. However, users striving to achieve complete
clarity in definition and the ultimate in positional accuracy must make sure that the
software components are mutually consistent and be aware of reductions that might
already have been applied to observations.
Most scientists prefer to work with geocentric Cartesian coordinates. In many
cases, however, it is easier to interpret results in terms of ellipsoidal coordinates such
as geodetic latitude, longitude, and height. It then becomes important to specify the
location of the origin of the ellipsoid and its orientation. Ideally, one would like to see
the origin coincide with the center of mass and the axes coincide with the directions of
the ITRF. The location and orientation of the ellipsoid, as well as its size and shape,
are part of the definition of a datum. Below we discuss the details for converting
between Cartesian coordinates and geodetic latitude, longitude, and height.
GPS observations such as pseudoranges and carrier phases depend only indirectly
on gravity. For example, once the orbit of the satellites has been computed and the
ephemeris is available, there is no need to further consider gravity. To make the use
of GPS even easier, the GPS ephemeris is typically provided in a well-defined earth-
centered earth-fixed (ECEF) coordinate system to which the user can directly relate.
In contrast, astronomic latitude, longitude, and azimuth determinations with a theodo-
lite using star observations refer to the instantaneous rotation axis, the instantaneous
terrestrial equator of the earth, and the local astronomic horizon (the plane perpendic-
ular to the local plumb line). For applications where accuracy matters, it is typically
the responsibility of the user to apply the necessary reductions or corrections to ob-
tain positions in an ECEF coordinate system. Even vertical and horizontal angles as
measured by surveyors with a theodolite or total station refer to the plumb line and
the local astronomic horizon. Another type of observation that depends on the plumb
line is leveling. To deal with types of observations that depend on the direction of
gravity (plumb line, horizon), we introduce the geoid.
The goal is to reduce observations that depend on the direction of gravity and to
model observations that refer to the ellipsoid. This is accomplished by applying geoid
undulations and deflection of the vertical correction. These “connecting elements”
are part of the definition of the datum. For a modern datum these elements are
readily available, typically on the web (for an example, see NGS, 2002). The reduced
observations are the model observation of the 3D geodetic model.
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