Program -
Concentrations
Integral Approach
GPS is an
interdisciplinary utility that has become an asset to the national
and international economies. The material of the GPS-GAP has been
carefully selected to provide a solid foundation on its workings,
capabilities and limitations. Equipped with such a foundational
knowledge, students will be able to contribute to the development
of the sheer endless stream of GPS applications, but also
understand ongoing efforts to modernize GPS, and to incorporate
other satellites systems such as GLONASS and Galileo.
With the needs of the users in
mind, the focus of the GPS units is on geospatial positioning.
Therefore, we assume that the satellite ephemeris is available,
either in form of the broadcast ephemeris as extracted from the
navigation message, or in form of the precise ephemeris as
determined by the IGS (International GPS Service). We do not
provide the specific knowledge needed to further improve the
state-of-the-art of satellite orbital determination. Also, these
courses do not address the mapping of the spatial and temporal
variation of the ionosphere and troposphere in any great detail,
even though this is an important area of research activity.
Least
squares adjustments and Kalman filtering
are the primary
estimation techniques relevant to geospatial positioning using
engineering and scientific measurements. The material is presented
with sufficient rigor and completeness to enable the
mathematically mature student to apply estimation with confidence.
The concepts, algorithms, and
interpretations of least squares presented in theses courses are
widely applicable in many areas of engineering and science. The
least-squares courses are viewed as "service courses" for
engineering and physical science and treated as a separate and
independent subject that applies to many types of observations.
The numerical examples studied in these units involve nonlinear
functional models and are taken from the areas of GPS, surveying,
geodesy, photogrammetry, digital image extraction and feature
recognition.
Geodesy deals with the
scientific foundation of positioning. It does not address specific
measurement tools. Three courses offer a streamlined approach to
geodetic theory and geodetic models with sufficient depth to allow
students to operate confidently within a geodetic frame,
consisting of geocentric coordinate reference systems, datums, and
gravity.
We adopt a somewhat narrow view
of geodetic science in these courses. We make use of the
existing geodetic foundation and only present geodetic models
relevant to positioning. As is the case for the U.S.A. and many
other countries, a modern geodetic datum has been established by
national agencies using techniques known from the discipline of
satellite geodesy. This means that the location and orientation of
the ellipsoid is well known, and that corresponding sets of
deflection of the vertical angles and geoid undulations are
readily available. These "connecting elements" plus polar motion
coordinates and models of other time-dependent phenomena such as
tectonic plate motions and ocean loading are then used to reduce
the physical observations to simple 3D geodetic model
observations.
The
adjustment, geodesy, and GPS courses together comprise an
integral knowledge base for a modern expert in geospatial
positioning. GPS relies on geodesy for the geospatial/geodetic
reference frame. Because GPS and geodesy deal with observations,
both rely on estimation.
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