- Geodesy.com

CG506 GEODESY 1
TOPIC 6.0
DATUM AND GEODETIC COORDINATE SYSTEM
Sr Harith Fadzilah Abd Khalid
2)
Reference:
1)
Geodesy 2nd Edition, Wolfgang Torge : page 35-59
Introduction to Geodesy, James T. Smith : page 83-99 and 135-137
What is DATUM?
Definition of datum (Oxford dictionaries) :
-
a piece of information
a fixed starting point of a scale or operation
A datum is a reference point, surface, or axis
on an object against which measurements
are made or
A set of parameters
defining a coordinate
system.
What is DATUM in Geodesy?
In surveying and geodesy, a datum is a set
of reference points on the Earth's surface
against which position measurements are
made and (often) an associated model of the
shape of the Earth (reference ellipsoid) to
define a geographic coordinate system.
Geodetic Datum
(Source - Trimble Navigation Ltd.)
A reference datum is a known and constant surface which
is used to describe the location of unknown points on the
earth.
Since reference datums can have different radii and
different center points, a specific point on the earth can
have substantially different coordinates depending on
the datum used to make the measurement.
There are hundreds of locally-developed reference
datums around the world, usually referenced to some
convenient local reference point.
Contemporary datums, based on increasingly accurate
measurements of the shape of the earth, are intended to
cover larger areas. The most common reference Datums
in use is WGS84
Geodetic reference systems
Importance of Datum
A datum specifies the earth-model
(ellipsoid), and the origin associated with a
particular set of coordinates.
Datums provide the link between the
earth and coordinate systems.
Without a datum, coordinates have no
meaning.
There are many datums used worldwide.
DATUMS IN MALAYSIA

Datums used in Malaysia
MRT48/68
- Peninsular
Ellipsoid = Modified Everest (Peninsular)
Origin = Kertau
PMSGN94 (Peninsular Malaysia Geodetic Scientific Network)
- Peninsular
Ellipsoid = WGS84
Origin = Kertau (NSWZ-9D)
BT68
- Sabah and Sarawak
Elliposid = Modified Everest (Borneo)
Origin = Timbalai
 EMSGN97 (East Malaysia Geodetic Scientific Network) - Sabah
and Sarawak
Elliposid = WGS84
Datum = STRE94 GPS Campaign
GDM2000
- Malaysia
Ellipsoid = GRS80
Datum= ITRF2000
REFERENCE ELLIPSOIDS FOR MRT, BT68,
WGS84 AND ITRF
GEODETIC REFERENCE SYSTEMS IN MALAYSIA
GEODETIC REFERENCE SYSTEMS IN MALAYSIA
GEODETIC REFERENCE SYSTEMS IN
MALAYSIA
MyRTKnet
GDM 2000
What is Coordinate System?
In geometry, a coordinate system is
a system which uses one or more numbers, or
coordinates, to uniquely determine the
position of a point.
Why Coordinate System is important?
3 Types of Coordinates System
 Cartesian coordinate
Geographic Coordinate Systems (unprojected)
A reference system using latitude and longitude to
define the location of points on the surface of a
sphere/spheroid/geoid
Projected Coordinate Systems
A map projection is the systematic transformation of
locations on the earth (latitude/longitude) to planar
coordinates
Cartesian Coordinate System
A Cartesian coordinate system
specifies each point uniquely in a plane by a
pair of numerical coordinates, which are
the signed distances from the point to two
fixed perpendicular directed lines, measured
in the same unit of length.
3D Cartesian Coordinate System
A.K.A
EARTH CENTERED, EARTH FIXED X, Y, AND Z

Earth Centered, Earth Fixed Cartesian coordinates are also used to define three
dimensional positions.

Earth centered, earth-fixed, X, Y, and Z, Cartesian coordinates (XYZ) define three
dimensional positions with respect to the center of mass of the reference ellipsoid.

The Z-axis points toward the North Pole.

The X-axis is defined by the intersection of the plane define by the prime meridian
and the equatorial plane.

The Y-axis completes a right handed orthogonal system by a plane 90° east of the
X-axis and its intersection with the equator.
EARTH CENTERED, EARTH FIXED X, Y,
AND Z
Local x,y,z- and global X,Y,Z - system
Local x,y,z- and global X,Y,Z - system
Geodetic Coordinate System
LATITUDE, LONGITUDE, AND HEIGHT

The most commonly used coordinate system today - the latitude, longitude, and
height system.

The Prime Meridian and the Equator are the reference planes used to define
latitude and longitude
Geodetic Coordinate System



The geodetic latitude (there are many other defined latitudes) of a point
is the angle from the equatorial plane to the vertical direction of a line
normal to the reference ellipsoid.
The geodetic longitude of a point is the angle between a reference plane
and a plane passing through the point, both planes being perpendicular
to the equatorial plane.
The geodetic height at a point is the distance from the reference ellipsoid
to the point in a direction normal to the ellipsoid.
Relationship between Geodetic Coordinate
System and Cartesian Coordinate System
LOCAL GEODETIC SYSTEM (TOPOCENTRIC)
 Classically 3-dimensional
coordinates of points are given
in terms of latitudes, longitudes
and heights
 The latitudes and longitudes
are defined by projecting points
from the earth’s surface to a socalled reference ellipsoid
 The position, orientation,
size and shape of this ellipsoid
is what constitutes a classical
geodetic datum
GEOCENTRIC SYSTEM

Definition, have their center at
the center of mass of the earth
and the direction of their axes
are defined arbitrarily (usually
used averaged astronomical
phenomena)

Systems are easy to define.

Advantages are that they can
provide seamless positioning
across the world and they relate
directly to the modern spacebased positioning systems that
are nowadays being used for
various purposes including
surveying and mapping
DATUM CONVERSIONS
Datum conversions are accomplished by various
methods.
 Complete datum conversion is based on seven
parameter transformations that include three
translation parameters, three rotation parameters and
a scale parameter.
 Simple three parameter conversion between latitude,
longitude, and height in different datums can be
accomplished by conversion through Earth-Centered,
Earth Fixed XYZ Cartesian coordinates in one
reference datum and three origin offsets that
approximate differences in rotation, translation and
scale.

DATUM CONVERSIONS
RELATIONSHIP BETWEEN CARTESIAN AND
GEODETIC COORDINATE SYSTEM
TO CONVERT GEODETIC TO CARTESIAN
Datum Transformation & Map Projection
Flowchart For Peninsular Malaysia
MRT 48 PMSGN 94 GDM 2000
RSO
N,E
MGPM2000
Map Projection
,,h
,,h
,,h
(Map Grid of P.Malaysia 2000)
N,E
Map Projection
(Polynomial Fitting)
Coordinate
Conversion
Coordinate
Conversion
Coordinate
Conversion
N,E
X,Y,Z
X,Y,Z
X,Y,Z
N,E
CASSINI
6 Parameter
Transformatio
n
7 Parameter
Transformatio
n
7 Parameter
Transformatio
n
CASSINI 2000
MyRTKnet
GDM 2000
TO CONVERT GEODETIC TO CARTESIAN
TO CONVERT CARTESIAN TO GEODETIC

The longitude can be computed as:
λp = arctan(Yp/Xp)
Iteratively,
ELLIPSOIDAL HEIGHT
OR USING A CLOSED FORMULA BY
BOWRING(1976):
MRT TO WGS84 (DMA)
X (WGS84) = X (MRT) - 11m
 Y (WGS84) = Y (MRT)
+ 851m
 Z (WGS84) = Z (MRT)
+
5m

MALAYAN REVISED TRIANGULATION (MRT)






There are two existing local geodetic reference systems in
Malaysia
Malayan Revised Triangulation (MRT) for Peninsular Malaysia .
Borneo Triangulation System 1968 (BT68) for Sabah and
Sarawak.
The MRT is the coordinate system used for mapping in
Peninsular Malaysia.
The datum is based on the old Repsold Triangulation and
computed using data collected mainly in the period 1948 to 1966
using the Modified Everest ellipsoid.
It consists of about 1,200 stations plus a number of more recent
standard traverses and has an inter-station accuracy of around 13
to 15 ppm.
BORNEO TRIANGULATION SYSTEM 1968 (BT68)
The first datum for Sabah and Sarawak was the
Primary Triangulation of Borneo 1948 (BT48)
established by the Directorate of Overseas Survey
(DOS)
 Referred as the Timbalai Datum .
 Accuracy of about 5ppm
 This network consists of the Borneo West Coast
Triangulation of Brunei and Sabah (1930-1942)
 Borneo East Coast Triangulation of Sarawak,
extension of the West Coast Triangulation of Sabah
(1955-1960)
 Doppler points surveyed between 1961 to 1968

MAP PROJECTION SYSTEMS -TWO LOCAL
DATUMS
Rectified Skew Orthomorphic (RSO) –
National mapping
WGS84 → MRT/BT68 → RSO
Cassini Soldner (Cassini)
 cadastral purposes
 WGS84 → MRT → RSO → Cassini
 The

UNJURAN PEMETAAN – CASSINI-SOLDNER
Origin berlainan bagi
setiap negeri
GEODETIC REFERENCE SYSTEMS IN
MALAYSIA
MASS STATIONS







What is MASS stations ?
Malaysia Active GPS System
High density national GPS network
Approximately 30km spacing of GPS points over the
Peninsular
A geocentric reference frame
International Terrestrial Reference System (ITRS) that
managed the International Terrestrial Reference Frame
(ITRF) derived using GPS observations.
At present seventeen (17) MASS stations operated
continuously since 1998, ten (10) of the stations are
situated in Peninsular Malaysia and the rest (7 stations)
are in Sabah and Sarawak.
DISTRIBUTION OF 15 MASS STATIONS IN
MALAYSIA
DISTRIBUTION OF ELEVEN (11) IGS
STATIONS
REFERENCE ELLIPSOIDS FOR MRT, BT68,
WGS84 AND ITRF
THE NEW GEOCENTRIC RSO PROJECTION
PARAMETERS FOR PENINSULAR AND EAST
MALAYSIA
DATUM DI MALAYSIA

Datum-datum yang digunakan di Malaysia
MRT48/68
- Semenanjung
Elipsoid = Modified Everest (Semenanjung)
Origin = Kertau
PMSGN94
- Semenanjung
Elipsoid = WGS84
Origin = Kertau (NSWZ-9D)
BT68
- Sabah dan Sarawak
Eliposid = Modified Everest (Borneo)
Origin = Timbalai
EMSGN97
- Sabah dan Sarawak
Eliposid = WGS84
Datum = STRE94 GPS Campaign
GDM2000
- Malaysia
Elipsoid = GRS80
Datum= ITRF2000
7 PARAMETERS TRANSFORMATION/BURSAWOLF FORMULA
7 PARAMETERS TRANSFORMATION/BURSAWOLF FORMULA





(XS, YS, ZS) are the coordinates of the point in the source
geocentric coordinate system
(XT, YT, ZT) are the coordinates of the point in the target
geocentric coordinate system
(dX, dY, dZ): Translation vector
(RX, RY, RZ): Rotations to be applied to the point's vector
M = (1 + dS*10-6) :The scale correction
EXAMPLE:
COORDINATE CONVERSION &
TRANSFORMATION
The Problem
Point A was observed using GPS and their coordinates in WGS84 are found to
be:
Point Latitude
Longitude
Ellip. Ht (m)
A 1o 22’ 35.52238” N 103o 36’ 29.45569”E
90.906
The coordinate of the control point (to be given in latitude, longitude and
height) are required to be in the Cartesian coordinate X, Y and Z.
Ellipsoid Name :
WGS84
a
:
6378137.8 m
f
:
1/298.257223563
Next, the coordinates are required to be transformed into a datum called
MRT. The relationship between MRT and WGS 84 is given by:
X (WGS84) = X (MRT) - 11m
Y (WGS84) = Y (MRT) + 851m
Z (WGS84) = Z (MRT) +
5m
Finally determine the coordinates of point A and B in latitude, longitude and
ellipsoidal height based on the MRT reference datum.