Reference Systems
Reference Systems
Paolo Zatelli - Alfonso Vitti
Dept. Civil and Environmental Engineering
University of Trento
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Reference Systems
Outline
1
Reference Systems and Coordinate Systems
2
Terrestrial reference systems and coordinate systems
3
Geoid and ellipsoid
4
Ellipsoid - shape and orientation
5
Global and local systems
6
Reference systems in Italy
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Reference Systems | Reference Systems and Coordinate Systems
Position
Position is relative.
A point position is always relative to other reference points.
It is useful to express a point position by means of
“labels” attached to each single point
↓
coordinates
To determine the point’s coordinates, which express the point relative
position, a reference system has to be defined.
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Reference Systems | Reference Systems and Coordinate Systems
Examples
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Reference Systems | Reference Systems and Coordinate Systems
Reference systems and coordinate systems
It is often an implicit choice.
For example, on a plane, by fixing the Cartesian coordinates of 2
points (4 degrees of freedom), one has fixed also:
the origin point (2 constrains)
the reference direction (1 constrain)
the reference unit (1 constrain)
In general, for a reference system it is possible to use different
coordinate systems to express points coordinates.
In practice, a reference system (RS) is realized by choosing a specific
coordinate system (CS) and by fixing a set of points coordinates in that
specific CS.
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Reference Systems | Terrestrial reference systems and coordinate systems
Terrestrial reference systems and coordinate systems
A terrestrial reference system and the associated coordinates should
be related to:
the Earth’s shape
the Earth’s gravitational field
which are themselves related, too.
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Reference Systems | Terrestrial reference systems and coordinate systems
Natural coordinates
A “natural” choice is the triplet (HW , Φ, Λ), where:
HW is a linear function of the Earth’s gravitational field potential W
HW =
W − W0
γ0
Φ and Λ are the angles denoting the direction of the force of gravity
The values of Φ and Λ depend on the definition of a reference direction.
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Reference Systems | Terrestrial reference systems and coordinate systems
Natural coordinates
(HW , Φ, Λ)
1
have a strong physical meaning
2
have a weak geometrical meaning
1
advantage
HW tells what is up and what is down; Φ and Λ can be obtained by
astronomical measurements (marine navigation)
2
disadvantage
it is not possible to compute the distance between two points
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Reference Systems | Terrestrial reference systems and coordinate systems
Orthometric height
HW is replaced by the orthometric height H, the distance from an
equi-potential surface of the Earth’s gravitational field with W = W0
(the Geoid). H is measured along the line of force of the gravity field.
The use of H balances the geometrical and the physical meaning of
such coordinate.
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Reference Systems | Geoid and ellipsoid
Geoid
It is a reference surface where W = W0
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Reference Systems | Geoid and ellipsoid
Geodetic coordinates
To get coordinates with a full geometrical meaning, an ellipsoid is used
as reference surface. The ellipsoid’s shape approximates the Geoid’s
shape (locally or globally).
An ellipsoid has an analytical form and its surface is much more simple
(smooth and regular) than the Geoid
↓
geometrically meaningful coordinates
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Reference Systems | Geoid and ellipsoid
Geodetic coordinates
The triplet (φ, λ, h) has a weak physical meaning (the ellipsoid is an
approximation of the Geoid).
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Reference Systems | Geoid and ellipsoid
Geodetic coordinates - Latitude and Longitude
latitude φ angle between the ellipsoid’s normal in P and the
equatorial plane
−90◦ ≤ φ ≤ +90◦ or 90◦ S ≤ φ ≤ 90◦ N
φ = cost. → parallel
longitude λ angle between the meridian plane in P and the meridian
plane of a reference point,
−180◦ ≤ λ ≤ +180◦ or 180◦ W ≤ λ ≤ 180◦ E
λ = cost. → meridian
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Reference Systems | Geoid and ellipsoid
Geodetic coordinates and orthometric height
Most of the times, e.g., in Cartography, an hybrid choice is made by
using the triplet (φ, λ, H), where:
(φ, λ) have a strong geometrical meaning
H is a compromise between the physical and the geometrical
meanings
GPS gives (φ, λ, h), whereas in classical surveys (optical instruments)
and in Cartography we use (φ, λ, H). It is necessary to know the so
called Geoid undulation to transform from H to h and vice-versa.
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Reference Systems | Geoid and ellipsoid
Orthometric and ellipsoid heights - Geoid undulation
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Reference Systems | Geoid and ellipsoid
Geoid undulation
From red (85.4 m) to magenta (-107.0 m)
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - shape and orientation
An ellipsoidal reference surface is completely defined by fixing:
1
the shape by choosing:
the semi-axes a and b, or
the semi-major axis a and flattener f =
q
a−b
a ,
the semi-major axis a and eccentricity e =
2
q
or
a2 −b2
a2
the orientation (the position relative the the Earth surface)
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - shape
The semi-major axis a lies on the equatorial plane, the semi-minor axis
b is aligned to the Earth’s rotation axis:
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - shape
Late 1800 and early 1900 geodetic measures were used to determine
an optimal ellipsoid:
Name
Everest
Bessell
Airy
Clarke
Clarke
Helmert
International Hayford
Krasovsky
GRS80
WGS84
Year
1830
1841
1849
1866
1880
1907
1924
1940
1980
1984
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a[m]
6377276
6377397
6377563
6378206
6378249
6378200
6378245
6378245
6378137
6378137
b[m]
6356079
6356079
6356257
6356584
6356515
6256818
6356912
6356863
6356752
6356752
Used in
India Sri Lanka
Cent.Eu. Cile Indon.
United Kingdom
N. America Philippines
France Africa
part of Africa
UTM Italy (Rome1940)
Russia Eu. Or.
N.America Global
Global (GPS)
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - orientation
The orientation can be:
global
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local
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - global orientation
the ellipsoid barycenter coincides with the Earth’s center of mass
the axis z is aligned to the Earth’s rotation axis
the axis x lies on a specific plane (Greenwich meridian) containing
the axis z
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Reference Systems | Ellipsoid - shape and orientation
Ellipsoid - local orientation
For a given reference point, in general close to the barycenter of the
local region:

Φ=φ 
Λ=λ
Geoid origin

H=h
the ellipsoid semi-minor axis is parallel to the Earth’s rotation axis
These conditions are often imposed by fixing the coordinates of a set
of points.
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Reference Systems | Global and local systems
Global and local systems
Satellite based positioning systems need global reference systems.
In the past, the definition of global reference systems was hard and of
scarce interest and need.
Surveys did not have a global scope.
For this reason, there are more than 150 local reference systems.
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Reference Systems | Global and local systems
Continental reference systems
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Reference Systems | Reference systems in Italy
Reference systems in Italy
The first national reference system was defined and realized in late
1800:
Bessel ellipsoid orientated in three different points (Genova,
Monte Mario, and Castanea delle Furie), with three different
reference systems
cartographic proiection: modified Flamsteed
block adjusted triangulation network (1908-1919)
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Reference Systems | Reference systems in Italy
Cadastral reference system
Not in use anymore
Bessel ellipsoid
orientation: Genova, Istituto Idrografico della Marina
φ = 44◦ 250 08.23500
λ = 0◦
azimuth to Monte del Telegrafo α = 117◦ 310 08.9100
IGM and cadastral triangulation networks
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Reference Systems | Reference systems in Italy
Italian reference system - Rome1940
It is the official system in use in Italy
International ellipsoid (Hayford)
oriented in Roma Monte Mario (astronomical definition 1940)
φ = 41◦ 550 25.5100
λ = 0◦ (12◦ 270 00.8800 da Greenwich)
azimuth to Monte Soratte α = 6◦ 350 00.8800
h = H = 0 Genova tide gauge
block adjusted triangulation network (1908-1919) using an interim
reference system with successive system transformation
(distortions)
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Reference Systems | Reference systems in Italy
Continental ref. system European Datum 1950 (ED50)
It is a system created to homogenize the European small and medium
scale cartography:
International ellipsoid (Hayford)
European mean orientation (1950)
longitude origin: Greenwich
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Reference Systems | Reference systems in Italy
Global reference systems
There are two types of system currently in use:
celestial reference systems, defined by positions of extragalactic
radio sources and satellites’ orbits
terrestrial reference systems, defined by fixing the coordinates of
reference points on the Earth’s surface
The Earth is not a rigid body → the position of objects and points on
the Earth’s surface are not fixed → coordinates need to be updated
and the reference systems refer to a specific date.
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Reference Systems | Reference systems in Italy
IERS Terrestrial Reference System (ITRS)
Defined by the International Earth Rotation and Reference System
Service
the origin point coincides with the Earth’s center of mass
the axis Z passes through the Conventional International Origin
(CIO)
the axis X is direct toward the Greenwich meridian
the axis Y completes the triad of axes
The IERS periodically publishes the ITRFYY (International Terrestrial
Reference Frame and YY indicates the year) which is a realization at a
given date of the ITRS. The ITRFYY compromises a set of coordinates
and velocities of a set of reference points obtained by processing
measures coming from different geodetic observing techniques (VLBI,
DORIS, LLR, SLR, GPS).
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Reference Systems | Reference systems in Italy
ITRS derived reference system
Europe: EUREF ETRS89–ITRF89 and subsequent ETRFYY
Italy: IGM IGM95 Italian realization of ETRS89
Italy: IGM RDN–ETRF2000
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Reference Systems | Reference systems in Italy
Global reference system WGS84
It is a Cartesian system with an associated reference ellipsoid.
It is the reference system in which the transmitted GPS orbits are given
and hence it is the system used by any GPS device.
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Reference Systems | Appendice | Bibliografia
Bibliografia
Benciolini B., 2004, Report on refrence systems, personal
communication.
Surace L., 1998, La georeferenziazione delle informazioni territoriali,
Bollettino di geodesia e scienze affini, anno LVII, n. 2, pp. 181-234.
For the images http://kartoweb.itc.nl/geometrics/Reference
surfaces/body.htm
For information on “exotic” reference systems: Photogrammetric
Engineering and Remote Sensing (PE&RS) Journal,
http://http://www.asprs.org/PE-RS-Journal/
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Reference Systems | Appendice | Licenza
c
These slides are 2009
Paolo Zatelli, available as
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