TYBSC IT PGIS Unit III Chapter I Spatial Referencing and Positioning

SPATIAL REFERENCING
AND POSITIONING
UNIT III, CHAPTER-I
TYBSC IT SEM VI
PROF. ARTI GAVAS
ANNA LEELA COLLEGE OF COMMERCE AND ECONOMICS,
SHOBHA JAYARAM SHETTY COLLGE FOR BMS, KURLA
TYBSC IT SEM VI
PROF. ARTI GAVAS

SPATIAL REFERENCNG
 A spatial reference is the geo-referencing and
coordinate system assigned to any geographic data,
including raster datasets and raster catalogs. The
spatial reference defines how geographic data is
mathematically transformed onto a flat map with the
least amount of distortion.
 REFERENCE SURFACE FOR MAPPING
 The Earth's surface, and two reference surfaces used to
approximate it: the Geoid, and a reference ellipsoid. The
deviation between the Geoid and a reference ellipsoid is
called geoid separation (N).

REFERENCE SURFACE FOR
MAPPING
The earths surface is not uniform due to elevations or
valleys.
Two models are used: Geoid, and a reference
ellipsoid

The Geoid and the Vertical
Datum
 define datums -
various surfaces
from which "zero"
is measured
 Geoid is a
vertical datum
tied to MSL
(Mean Sea
Level)
 geoid height is
ellipsoid height
from specific
ellipsoid to geoid
 types of geoid
heights:
gravimetric versus
hybrid
 A vertical datum or height datum is a reference surface
for vertical positions, such as the elevations of Earth
features including terrain, bathymetry, water level, and man-
made structures; in any particular case one must be
assigned even if arbitrarily, and commonly adopted criteria
for a vertical datum include the following approaches:
 Tidal, based on sea level when specific conditions occur,
such as NOAA's National Geodetic Survey-produced Tidal
Datums;
 Gravimetric, based on a geoid; or geodetic, based on the
same ellipsoid models of the Earth that are used in
computing a horizontal datum, such as NOAA's planned
gravimetric and Global Navigation Satellite Systems
(GNSS)-based Datum of 2022 set to be released that year
by the National Geodetic Survey.
 Prominent vertical datum in use by professionals include
the National Geodetic Vertical Datum of 1929 and the North
American Vertical Datum of 1988.

The Geoid and the Vertical
Datum

Measuring MSL using Geodetic
Leveling
 In common usage, elevations are often cited
in height above sea level, although what “sea
level” actually means is a more complex issue
than might at first be thought
 The height of the sea surface at any one place
and time is a result of numerous effects,
 including waves,
 wind and currents,
 atmospheric pressure,
 tides,
 topography, and
 differences in the strength of gravity due to the
presence of mountains etc.

The Ellipsoid
 An ellipsoid is a
surface that may be
obtained from a
sphere by deforming
it by means of
directional scaling.
 Standard equation:
 where a, b, c are
positive real numbers.

The Ellipsoid
 Reference ellipsoids are primarily used
as a surface to specify point
coordinates such as latitudes
(north/south), longitudes (east/west)
and elevations (height).
 The most common reference ellipsoid
in cartography and surveying is the
 World Geodetic System (WGS84).
 The Clarke Ellipsoid of 1866 and was
recomputed for the North American
Datum of 1927 (NAD27).
 When comparing NAD27 and NAD84,
latitude and longitude coordinates can
be displaced on the degree of tens of
meters (with the same latitude and
longitude coordinates).

THE LOCAL/GLOBAL HORIZONTAL
DATUM
 A horizontal datum provides a
reference frame for latitude and
longitude coordinates on the
Earth.
 It is a terminology which
constitutes of shape model and
an anchor point.
 Local ellipsoids have been
established to fit the Geoid
(mean sea level) well over an
area of local interest.
 Local ellipsoids have been
established to fit the Geoid
(mean sea level) well over an
area of local interest. (figure
below).

COORDINATE SYSTEMS
 Coordinate systems enable
geographic datasets to use
common locations for
integration.
 A coordinate system is a
reference system used to
represent the locations of
geographic features, imagery,
and observations, such as
Global Positioning System
(GPS) locations, within a
common geographic
framework.
 A geographic coordinate
system (GCS) uses a three-
dimensional spherical surface
to define locations on the
earth.
 A GCS is often incorrectly
called a datum, but a datum
is only one part of a GCS.
 A GCS includes an angular
unit of measure, a prime
meridian, and a datum (based
on a spheroid).

2D geographic coordinates (f (PHI),l
(LAMBDA))
 The most widely used global
coordinate system consists of lines of
geographic latitude (phi or f) and
longitude (lambda or l).
 Lines of equal latitude are called
parallels. They form circles on the
surface of the ellipsoid.
 Lines of equal longitude are called
meridians and they form ellipses
(meridian ellipses) on the
ellipsoid.
 Both lines form the graticule when
projected onto a map plane.
 Note that the concept of geographic
coordinates can also be applied to a
sphere as the reference surface.

3D geographic coordinates (f, l,
h)
 3D geographic coordinates (f,
l, h) are obtained by introducing
the ellipsoidal height h to the
system.
 The ellipsoidal height (h) of a
point is the vertical distance of
the point in question above the
ellipsoid.
 It is measured in distance units
along the ellipsoidal normal
from the point to the ellipsoid
surface.
 3D geographic coordinates can
be used to define a position on
the surface of the Earth

Geocentric coordinates (X,Y,Z)
 An alternative method of defining a 3D
position on the surface of the Earth is by
means of geocentric coordinates
(x,y,z), also known as 3D Cartesian
coordinates.
 The system has its origin at the mass-
centre of the Earth with the X- and Y-
axes in the plane of the equator.
 The X-axis passes through the meridian
of Greenwich, and the Z-axis coincides
with the Earth's axis of rotation.
 The three axes are mutually orthogonal
and form a right-handed system.
Geocentric coordinates can be used to
define a position on the surface of the
Earth

2D Cartesian coordinates (X,Y)
 The 2D Cartesian coordinate system is a
system of intersecting perpendicular lines,
which contains two principal axes, called the
X- and Y-axis.
 The horizontal axis is usually referred to as
the X-axis and the vertical the Y-axis (note
that the X-axis is also sometimes called
Easting and the Y-axis the Northing).
 The intersection of the X- and Y-axis forms
the origin. The plane is marked at intervals
by equally spaced coordinate lines, called
the map grid.
 Giving two numerical coordinates x and y for
point P, one can now precisely and
objectively specify any location P on the
map.

2D polar coordinates (a,d)
 Another possibility of defining a point
in a plane is by polar coordinates
(a,d).
 This is the distance d from the origin
to the point concerned and the angle
a between a fixed (or zero) direction
and the direction to the point.
 The angle a is called azimuth or
bearing and is measured in a
clockwise direction.
 It is given in angular units while the
distance d is expressed in length
units.

Map Projections
 A map simply was a
miniature representation of
a part of the world.
 Now that we know that the
Earth’s surface is curved in
a specific way, we know
that a map is in fact a
flattened representation of
some part of the planet.
 The field of map projections
concerns itself with the
ways of translating the
curved surface of the Earth
into a flat map.

Map Projections
 A map projection is a mathematically
described technique of how to represent
the Earth’s curved surface on a flat map.
 To represent parts of the surface of the
Earth on a flat paper map or on a
computer screen, the curved horizontal
reference surface must be mapped onto
the 2D mapping plane.
 The reference surface for large-scale
mapping is usually an oblate ellipsoid, and
for small-scale mapping, a sphere.
 Mapping onto a 2D mapping plane
means transforming each point on the
reference surface with geographic
coordinates (f,l) to a set of Cartesian
coordinates (x,y) representing positions
on the map plane

Classifications of Map
Projections
 Map projections can be
described in terms of their:
 class (cylindrical, conical
or azimuthal),
 point of secancy (tangent
or secant),
 aspect (normal, transverse
or oblique), and
 distortion property
(equivalent, equidistant or
conformal).
 A forward mapping equation
transforms the geographic
coordinates (f,l) of a point on the
curved reference surface to a set of
planar Cartesian coordinates (x,y),
representing the position of the same
point on the map plane:
 (x, y) = f (f, l)
 The corresponding inverse mapping
equation transforms mathematically
the planar Cartesian coordinates
(x,y) of a point on the map plane to a
set of geographic coordinates (f,l) on
the curved reference surface:
 (f, l) = f (x, y)

class (cylindrical, conical or
azimuthal)
 The three classes of map
projections are cylindrical,
conical and azimuthal.
 The Earth's reference surface
projected on a map wrapped
around the globe as a cylinder
produces a cylindrical map
projection.
 Projected on a map formed
into a cone gives a conical
map projection.
 When projected directly onto
the mapping plane it produces
an azimuthal (or zenithal or
planar) map projection.

Classifications of Map Projections:
point of secancy (tangent or secant)
 The planar, conical, and cylindrical are
all tangent surfaces; they touch the
horizontal reference surface in one
point (plane) or along a closed line
(cone and cylinder) only.
 Another class of projections is
obtained if the surfaces are chosen to
be secant to (to intersect with) the
horizontal reference surface;
 Then, the reference surface is
intersected along one closed line
(plane) or two closed lines (cone and
cylinder).
 Secant map surfaces are used to
reduce or average scale errors
because the line(s) of intersection are
not distorted on the map

aspect (normal, transverse or
oblique)
 Projections can also be described in terms
of the direction of the projection plane's
orientation (whether cylinder, plane or
cone) with respect to the globe.
 This is called the aspect of a map
projection.
 The three possible apects are normal,
transverse and oblique.
 In a normal projection, the main orientation
of the projection surface is parallel to the
Earth's axis
 A transverse projection has its main
orientation perpendicular to the Earth's
axis.
 Oblique projections are all other, non-
parallel and non-perpendicular, cases. The

Classifications of Map Projections:
distortion property (equivalent, equidistant or
conformal).
 The distortion properties of map are typically
classified according to what is not distorted on the
map:
 In a conformal (orthomorphic) map projection the
angles between lines in the map are identical to
the angles between the original lines on the curved
reference surface. This means that angles (with short
sides) and shapes (of small areas) are shown
correctly on the map.
 In an equal-area (equivalent) map projection the
areas in the map are identical to the areas on the
curved reference surface (taking into account the
map scale), which means that areas are represented
correctly on the map.
 In an equidistant map projection the length of
particular lines in the map are the same as the
length of the original lines on the curved reference
surface (taking into account the map scale).
 A particular map projection can have any one of

Scale distortions on a map
 A map projection without distortions
would correctly represent shapes,
angles, areas, distances and
directions, everywhere on the map.
 Unfortunately, any map projection
is associated with scale
distortions.
 There is simply no way to flatten out
a piece of ellipsoidal or spherical
surface without stretching some parts
of the surface more than others.
 The amount and which kind of
distortions a map will have depends
largely - next to size of the area
being mapped - on the type of the
map projection that has been
selected.

Coordinate transformations
 Map and GIS users are mostly
confronted in their work with
transformations from one two-
dimensional coordinate system to
another.
 This includes the transformation of
polar coordinates delivered by the
surveyor into Cartesian map
coordinates or the transformation
from one 2D Cartesian (x,y) system of
a specific map projection into another
2D Cartesian (x,y) system of a defined
map projection.
 Datum transformations are also
important, usually for mapping
purposes at large and medium scale.

Changing map projection
 Forward and inverse mapping
equations are generally used to
transform data from one map
projection to another.
 The inverse equation of the source
projection is used first to transform
source projection coordinates (x,y) to
geographic coordinates (f,l).
 Next, the forward equation of the
target projection is used to transform
the geographic coordinates (f,l) to
target projection coordinates (x’,y’).
 The first equation takes us from a
projection A into geographic
coordinates.
 The second takes us from geographic
coordinates (f,l) to another map

Datum transformations
 A change of map projection may also include a
change of the horizontal datum (also called
geodetic datum).
 This is the case when the source projection is
based upon a different horizontal datum than
the target projection.
 If the difference in horizontal datums is ignored,
there will be no perfect match between
adjacent maps of neighbouring countries or
between overlaid maps originating from different
projections.
 It may result in up to several hundred metres
difference in the resulting coordinates.
 Therefore, spatial data with different underlying
horizontal datums may need a so-called datum
transformation.
 Datum transformations are transformations
from a 3D coordinate system (i.e. horizontal
datum) into another 3D coordinate system.
Datum shift between two geodetic datums. Apart
from different ellipsoids, the centres or the rotation
axes of the ellipsoids do not coincide.

SATELLITE BASED
POSITIONING
 The global positioning system (GPS) is widely used in automotive navigation and
traffic engineering studies such as traffic time studies.
 Many cell phones are equipped with positioning functions, and hence they are
considered in the same category as the GPS.
 The GPS is a satellite-based navigation system made up of a network of 24 satellites
placed in orbit by the US Department of Defense.
 GPS satellites circle Earth twice a day in a very precise orbit and transmit
signal information to Earth.
 GPS receivers take this information and use triangulation to calculate the
user’s exact location
 Essentially, the GPS receiver compares the time when a signal was transmitted by a
satellite with the time when it was received.
 The time difference tells the GPS receiver how far away the satellite is.
 Now, with distance measurements from a few more satellites, the receiver can
determine the user’s position and display it on the unit’s electronic map.

SATELLITE BASED
POSITIONING
 Space Segment: GPS satellites (a minimum
of 24 in constellation) send signals to earth
with satellite position information, including
time the signal is received.
 Control Segment: There are ground stations
on the earth that are receiving the information
from the GPS satellites, and sending data to
the GPS satellite to correct position and relay
information.
 User Segment: User holding a GPS unit
using the data from the satellite to locate
position on Earth.
 Trilateration: This is the process of using
three points of reference to determine
location.
 3D trilateration: This is the process of
determining location based on three satellites.
(A) The three segments of GPS. (B) The receiver lies at the
intersection of the spheres centered at the four satellites.

ABSOLUTE/RELATIVE
POSITIONING
 Absolute location helps to
determine the location of a place
with respect to certain
coordinates that themselves
have a fixed reference.
 The relative position of a place is
determined in reference to
certain landmarks or known
locations.
 The absolute location of a
place is determined with the help
of longitude and latitude lines.
 It indicates the position of a place
on the surface of the earth.

PSEUDO-RANGE POSITIONING
 The pseudorange (from pseudo-
and range) is the pseudo distance
between a satellite and a navigation
satellite receiver.
 To determine its position, a satellite
navigation receiver will determine the
ranges to (at least) four satellites as well
as their positions at time of transmitting.
 Knowing the satellites' orbital
parameters, these positions can be
calculated for any point in time.
 The pseudoranges of each satellite are
obtained by multiplying the speed of
light by the time the signal has taken
from the satellite to the receiver.
 As there are accuracy errors in the time
measured, the term pseudo-ranges is
used rather than ranges for such
distances.

PSEUDO-RANGE POSITIONING
 The reason we speak of pseudo-ranges
rather than ranges, is precisely this
"contamination" with unknown receiver
clock offset.
 GPS positioning is sometimes referred to
as trilateration, but would be more
accurately referred to as pseudo-
trilateration.
 Following the laws of error propagation,
neither the receiver position nor the clock
offset are computed exactly, but
rather estimated through a least
squares adjustment procedure known
from geodesy.
 To describe this imprecision, so-
called GDOP quantities have been defined:
geometric dilution of precision (x,y,z,t).

TIME, CLOCKS AND WORLD
TIME
 Global Timezone Map displays
current time and daylight in any
place around the world right now.
 WorldTime Clock & Map is an
indispensable utility for everyone who
deals with people abroad or
anybody who is keen on knowing
what time is it further than locally.
 Coordinated Universal Time (UTC) and
Greenwich Mean Time (GMT)
 Coordinated Universal Time (UTC) is the basis for
modern civil time.
 Since January 1, 1972, it has been defined to
follow International Atomic Time (TAI) with an
exact offset of an integer number of seconds,
changing only when a leap second is added to
keep clocks synchronized with the rotation of the
Earth.

TIME, CLOCKS AND WORLD
TIME
 Greenwich Mean Time (GMT) is an older standard, adopted starting with
British railroads in 1847.
 Using telescopes instead of atomic clocks, GMT was calibrated to the
mean solar time at the Royal Observatory, Greenwich in the UK.
 Universal Time (UT) is the modern term for the international telescope-
based system, adopted to replace "Greenwich Mean Time" in 1928 by the
International Astronomical Union.
 Observations at the Greenwich Observatory itself ceased in 1954, though
the location is still used as the basis for the coordinate system.
 Because the rotational period of Earth is not perfectly constant, the
duration of a second would vary if calibrated to a telescope-based standard
like GMT or UT - in which a second was defined as a fraction of a day or
year.

ERRORS IN ABSOLUTE
POSITINING
 Errors related to space segment
 Incorrect clock reading
 Incorrect orbit position
 Related to the medium (can change the speed of propagation of a GPS signal.)
 Troposphere
 Ionosphere
 Related to the receiver’s environment
 Multipath signal
 Related to the relative geometry of satellites and receiver
 Geometric Dilution of Precision(GDOP)

POSITIONING TECHNOLOGY:
GPS
 The Global Positioning System (GPS), originally NAVSTAR GPS, is a
satellite-based radio navigation system owned by the United States
government and operated by the United States Air Force.
 It is a global navigation satellite system (GNSS) that provides geo
location and time information to a GPS receiver anywhere on or near
the Earth where there is an unobstructed line of sight to four or more GPS
satellites.
 Obstacles such as mountains and buildings block the relatively weak GPS
signals.
 The GPS does not require the user to transmit any data, and it operates
independently of any telephonic or internet reception, though these
technologies can enhance the usefulness of the GPS positioning
information.
 The GPS provides critical positioning capabilities to military, civil, and
commercial users around the world. The United States government

GPS: Space segment
 The space segment (SS) is composed of 24 to 32 satellites, or Space Vehicles
(SV), in medium Earth orbit, and also includes the payload adapters to the
boosters required to launch them into orbit.
 The GPS design originally called for 24 SVs, eight each in three approximately
circular orbits, but this was modified to six orbital planes with four satellites each.
The six orbit planes have approximately 55° inclination (tilt relative to the
Earth's equator) and are separated by 60° right ascension of the ascending node
(angle along the equator from a reference point to the orbit's intersection).
 The orbital period is one-half a sidereal day, i.e., 11 hours and 58 minutes so
that the satellites pass over the same locations or almost the same locations every
day.
 The orbits are arranged so that at least six satellites are always within line of
sight from everywhere on the Earth's surface (see animation at right).
 The result of this objective is that the four satellites are not evenly spaced (90°)
apart within each orbit. In general terms, the angular difference between
satellites in each orbit is 30°, 105°, 120°, and 105° apart, which sum to 360°.
 Orbiting at an altitude of approximately 20,200 km (12,600 mi); orbital radius of
approximately 26,600 km (16,500 mi), each SV makes two complete orbits each

GLONASS
 GLONASS (Global Navigation Satellite System, Russia)
 GLONASS was developed by the Soviet Union as an
experimental military communications system during the
1970s. When the Cold War ended, the Soviet Union
recognized that GLONASS had commercial applications,
through the system’s ability to transmit weather broadcasts,
communications, navigation and reconnaissance data.
 The first GLONASS satellite was launched in 1982 and
the system was declared fully operational in 1993. After a
period where GLONASS performance declined, Russia
committed to bringing the system up to the required minimum
of 18 active satellites. Currently, GLONASS has a full
deployment of 24 satellites in the constellation.
 GLONASS System Design
 The GLONASS constellation provides visibility to a variable
number of satellites, depending on your location. A minimum
of four satellites in view allows a GLONASS receiver to
compute its position in three dimensions and to
synchronize with system time.

Galileo
 Galileo is the global navigation satellite system (GNSS) that went live in
2016, created by the European Union (EU) through the European GNSS
Agency (GSA), headquartered in Prague in the Czech Republic, with two
ground operations centres, Oberpfaffenhofen near Munich in Germany and
Fucino in Italy.
 The €10 billion project is named after the Italian astronomer Galileo Galilei.
 One of the aims of Galileo is to provide an independent high-precision
positioning system so European nations do not have to rely on the U.S.
GPS, or the Russian GLONASS systems, which could be disabled or
degraded by their operators at any time.
 The use of basic (lower-precision) Galileo services is free and open to everyone. The higher-precision
capabilities are available for paying commercial users.
 Galileo is intended to provide horizontal and vertical position measurements within 1-metre precision, and better
positioning services at higher latitudes than other positioning systems.
 Galileo is also to provide a new global search and rescue (SAR) function as part of the MEOSAR system.
 The first Galileo test satellite, the GIOVE-A, was launched 28 December 2005, while the first satellite to be part of the
operational system was launched on 21 October 2011.

GAGAN & IRNSS: A step towards initial
Satellite based Navigation Services in India
 The Indian Space Research
Organization (ISRO) and Airports
Authority of India (AAI) have
implemented the GPS Aided Geo
Augmented Navigation-GAGAN project
as a Satellite Based Augmentation
System (SBAS) for the Indian
Airspace.
 The objective of GAGAN to establish,
deploy and certify satellite based
augmentation system for safety-of-life
civil aviation applications in India
has been successfully completed.The system is inter-operable with other international SBAS systems like US-WAAS, European EGNOS,
and Japanese MSAS etc. GAGAN GEO footprint extends from Africa to Australia and has expansion
capability for seamless navigation services across the region.
GAGAN provides the additional accuracy, availability, and integrity necessary for all phases of flight, from
enroute through approach for all qualified airports within the GAGAN service volume.
GAGAN Payload is already operational through GSAT-8 and GSAT-10 satellites. The third GAGAN
payload will be carried onboard GSAT-15 satellite which is scheduled for launch this year(2019).

THANK YOU!
TYBSC IT SEM VI
PROF. ARTI GAVAS

TYBSC IT PGIS Unit III Chapter I Spatial Referencing and Positioning

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TYBSC IT PGIS Unit III Chapter I Spatial Referencing and Positioning