A CONTRIBUTION TO POSTMODERN GEODESY:
PERSPECTIVES AND FORMS IN
DESCRIBING SPACE FOR GEODESY
Mairie Doufexopoulu
NTUA Athens Greece
1. Engineering Geodesy
A rigorous connection between space and measurements
should be established.
How space is described and how much “information” about
its supposed description from a set of data provides a
particular perspective.
This space is physical and continuous (=definition of space
in Physics ) BUT by humans is sensed in Cartesian form
and this reduces its final description and interpretation in
3D forms.
The “geometry” of this space is adapted to the direction
along the local plum-line as height.
Geometry is mixed with Physics in discrete forms
The same space has the perspective of a model
space and that of measurement or data space.
Thus each set of measurements provides a particular
viewpoint about model space. Different NEARBY
viewpoints are optimized to receive a UNIQUE
representation
Finally we have :



Model space
Data space
Representation space ( various forms )
Out of these 3 different perspectives a geometry of
model space is rigorously defined by Earth’s
standards. The two other perspectives interchange
perspectives according to combinations depending on
the type of measurements (modes and impacts ) –
variable impacts and variable criteria to optimize
The “disagreements” between model space and
measurement space are assumed to have a statistical
distribution (=a collective impact of not known
impacts).
Statistical moments describe the stochastic distribution
by mean value, the variance ( standard deviation),
covariance and ( sometimes only ) the amplitude
spectrum.
2. Why Geodesy is thought as hightechnology implementation
Obstacles of estimating 3D coordinates:
Gravity measuring “information” is rare and restricted on
the terrestrial gravity
Paper maps illustrate 3D coordinates separately for surface
and for heights
Geodesy interpretation has controversies:
x=AX +s+u
Space of measurements is limited onto the Earth’s
topography
Different methods in Geodesy to deal with a more
complex Mathematical space
For model space: separation of surface coordinates from
the height
For measuring space: interpretation of each measurement
through the appropriate form of the model’s space
coordinate geometry and a statistical model to account for
“discrepancies” between model space and measuring
space. The non linear character of this concrete task has
been approached through the over-determined shapes by
the measurements; use kind of conditional optimization of
discrepancies
New technologies in Geodesy to deal with a more
complex Physical space
Using the transmission time of energy pulses to measure
distances & the extent of measuring space with the profit
of the satellites
Considering more impacts on the global representation
of measurements from the gravity field (geometry or
statistics), and more impacts coming from measuring
modes, inclusion of atmospheric, tropospheric effects
The model space keeps a main perspective of simple
Riemann geometry and gravity field models.
The measured space “can tell” now more about the
physical space than its model form
How this “new” feature can be used?
To improve in a way the geodetic models. In practice
this aim leads to increase / extend the statistical
modeling of “discrepancies”.
To use “new” types of geodetic measurements as
“means” that contain information about physical (
environmental ) factors ( varying with respect to space /
time domain )
3. The space in the period
of Space Geodesy
Characterisation of Space Geodesy
Observation space is extended into the whole 3D space
with respect to the Earth’s Model.
Model space and observation space are common. The
perspective and the form of their description IS NOT.
Model space is described by synchronous X, Y, Z optimal
coordinates of a geocentric Cartesian frame. BUT this
space includes more physical parameters in the
perspective of measurements.
The needs of Earth disciplines bring a transformation of
the Cartesian X, Y, Z form into an Earth’s datum as φ,λ,
h (or H ) description.
Treatment of „discrepancies” coming from the
extension of observation space into model space
As an extra impact, which should be eliminated by applying
analytic, statistical methods ( e. g filtering ). In statistical
approach the “discrepancies” may be viewed as variables
composed by partly known deterministic and stochastic
variations. In analytical approach (a quite familiar process in
Geodesy) they simply represent a differential variation of a
much simpler model space. .
As physical data ( “information” ) carrying physical
“information” of non stochastic character. This “information”
can be used without processing to indicate or evaluate
determinism ( causes ).
Why using the term post modern Geodesy?
Post modernism is known as an ideology term by the middle of
19th century about arts, policy and thinking streams. About the
space it came through Geography by the 60s and during 80s it
penetrated to technical sciences; meaning is to allow different
perspectives in considering the complex models
Measurement space in Space Geodesy as a complex
continuous space-time entity, which is much more complex
than any applied reference frame for Geodetic positioning.
Geodesy has reached to an end of its technology evolution for
its basic goals. The time to use measurements in the frame of
Geodesy for other objectives has arrived and now this space
needs increased standards about the Earth’s models. This will
be the Earth’s system
Post modern Geodesy (in particular to the use of
measurements) shows the tendency to extend the Earth’s
models to the Earth’s system models.
The very first example of such a
perspective of model’s complexity
has been given long ago by the
relativistic theory - as extension of
Newtonian Physics.
POST MODERN GEODESY
DEALS WITH THE PHYSICS OF SPACE-TIME
CONTINUUM FOR THE PARTICULAR OBJECTIVE
TO DESCRIBE BY CARTESIAN COORDINATE
GEOMETRY
Thanks!