Projections and coordinate systems
Projections and coordinate systems
Projections and coordinate systems
Projections and coordinate systems
• We think of the earth as a
sphere
• It is actually a spheroid,
slightly larger in radius at
the equator than at the
poles
Projections and coordinate systems
Rotate an ellypse around an axis
Projections and coordinate systems
Projections and coordinate systems
Reference ellipsoid
Because of their relative simplicity, reference ellipsoids
are used as a preferred surface on which geodetic
network computations are performed and point
coordinates such as latitude, longitude, and elevation
are defined.
Historically, different reference ellipsoids have been
defined and adopted by different countries.
They are still in use due to technical legacies and
juridical issues
Projections and coordinate systems
Some reference ellipsoids
Name
Equatorial axis (m)
a
Polar axis (m)
b
Inverse flattening
(a-b) / a
Airy 1830
6 377 563.4
6 356 256.9
299.324 975 3
Clarke 1866
6 378 206.4
6 356 583.8
294.978 698 2
Bessel 1841
6 377 397.155
6 356 078.965
299.152 843 4
International 1924
6 378 388
6 356 911.9
297
Krasovsky 1940
6 378 245
6 356 863
298.299 738 1
GRS 1980
6 378 137
6 356 752.3141
298.257 222 101
WGS 1984
6 378 137
6 356 752.3142
298.257 223 563
Projections and coordinate systems
...a little problem: gravity
Projections and coordinate systems
The Geoid
Projections and coordinate systems
Where is the geoid?
Projections and coordinate systems
Levelling network
Tide gauge
Projections and coordinate systems
What is a Datum
Projections and coordinate systems
Example of geodetic datums
•
•
•
•
Adindan (Ethiopia, Senegal)
Moznet (Mozambique)
Arc 1960 (Kenya, Tanzania)
ED50 (Iraq)
• WGS84 is now becoming the International
Standard (GPS)
Projections and coordinate systems
GPS
• Initiated by U.S. Department of Defense
• Military planners wanted a technology where a position could be
obtained without the use of radio transmissions
• Officially named Navigation System with Timing and Ranging
(NAVSTAR)
• First satellite launched in 1974
• The GPS Operational Constellation consists of 24 satellites (21
plus 3 operational spares) that orbit the Earth in very precise orbits
twice a day.
• GPS satellites emit continuous navigation signals.
Projections and coordinate systems
GPS
• Each GPS satellite transmits data that indicates its
location and the current time.
• All GPS satellites synchronize operations so that these
repeating signals are transmitted at the same instant.
• Physically the signal is just a complicated digital code, or
in other words, a complicated sequence of “on” and “off”
pulses.
• The same pseudo-random sequence is generated by the
satellite and the receiver.
• The receiver compares the two
sequences to derive the time
difference.
• The distance from the satellite is
the product of this difference by
the speed of light.
Projections and coordinate systems
GPS
Projections and coordinate systems
GPS
Precision
• Satellites use atomic clocks, receivers
use quartz clocks -> less expensive
• Trees, buildings, mountains can prevent
or reduce a clear line of sight
• Signal refraction in the atmosphere
• Signal interference, e.g. reflection from
other surfaces
• Satellite distribution in the sky
(Geometric Diluition of Precision, GDOP)
Projections and coordinate systems
GPS
Geometric Diluition of Precision
Good
Poor
Projections and coordinate systems
GPS
Precision
• GPS satellites transmit in
two frequencies:
– L1
• C/A code (coarse acquisition code)
• P code (precise code) encrypted
• Navigation data
– L2
• P code (precise code) encrypted
• Standard Positioning System (SPS)
– Only L1 and only C/A code
• Precise Positioning System (PPS)
– Both L1 and L2 (to minimize atmospheric refraction)
– P code (anti-spoofing)
Projections and coordinate systems
GPS
Differential GPS
• One or more ground based station in a known location record
or broadcast the difference between the pseudoranges
received from satellites and the actual internally computed
pseudoranges.
• The difference can be applied by a rover station (individual,
car, airplane etc.) to correct its own pseudoranges
– Post-processing
• A dedicated station
– Real time
•
•
•
•
A dedicated station
A network of stations
Signal broadcasted by local radio network
Signal broadcasted by satellite network
(e.g. WAAS, EGNOS)
Projections and coordinate systems
GPS
Projections and coordinate systems
Other systems
• GLONASS – Russia's global navigation system.
Fully operational worldwide
• Galileo – a global system being developed by
the European Union and other partner countries,
planned to be operational by 2014 (and fully
deployed by 2019)
• COMPASS – People's Republic of China's
global system, planned to be operational by
2020
Projections and coordinate systems
The earth is a spheroid, a map is flat
Projections and coordinate systems
Example of projections
Cylindrical
Conical
Azimuthal
Projections and coordinate systems
Areas or angles?
Mollweide (equivalent)
Mercator (conformal)
Projections and coordinate systems
Areas or angles?
At large scales, most of
the commonly used
projections are
conformal.
Projections and coordinate systems
UTM
Projections and coordinate systems
UTM
Projections and coordinate systems
Projections and coordinate systems
EPSG Geodetic Parameter Dataset
• European Petroleum Survey Group, now absorbed by the
International Association of Oil & Gas Producers (OGP)
• a collection of definitions of coordinate reference systems
and coordinate transformations which may be global,
regional, national or local
• EPSG Geodetic Parameter Registry
online at: http://www.epsg-registry.org/
• example: EPSG:3857
– 3857 is the Spatial Reference System Identifier (SRID)
– WGS 84 / Pseudo-Mercator, used by Google maps
Projections and coordinate systems
• SRIDs are typically associated with a “well known text”
(WKT), i.e. a string definition of the coordinate system
• “well known text” is a kind of data definition language
• Example: EPSG:4326 (correspond to WGS84)
GEOGCS["WGS 84",
DATUM["WGS_1984",
SPHEROID["WGS 84",6378137,298.257223563,
AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
AUTHORITY["EPSG","4326"]]
Projections and coordinate systems
• There are some websites where you can find
complete lists of spatial reference systems and
transformations, along with their description
and definition in different formats
• My favorite ones are
http://spatialreference.org/
http://epsg.io
Projections and coordinate systems
Coordinate conversion
A
A
C
B
B