SUG514 - Hydrographic Surveying - SUG514 - Assignment 4 - WGS84 To Cassini - Soldner Coordinate...

MARA UNIVERSITY OF TECHNOLOGY

BACHELOR OF GEOMATIC AND SURVEYING SCIENCE (AP220) ASSIGNMENT 4HYDROGRAPHIC SURVEYING (SUG514) Coordinates Conversion, Datum Transformation, Map Projection

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1.0 WGS 84 COORDINATE SYSTEM TO UTM COORDINATE SYSTEM CONVERSION

1.1 What is WGS 84 Coordinates System?

It is currently the reference system being used by

the Global Positioning System. It is geocentric and

globally consistent within ±1 m. It comprises a

standard coordinate frame for the Earth, a standard

spheroidal reference surface (the datum or

reference ellipsoid) for raw altitude data, and a

gravitational equipotential surface (the geoid) that

defines the nominal sea level. The coordinate origin

of WGS 84 is meant to be located at the Earth's

center of mass; the error is believed to be less than 2 cm.

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Figure: The WGS 84 Coordinate System Definition

Figure: The WGS 84 Ellipsoidal Parameters (Peter H. Dana 9/1/94)

http://en.wikipedia.org/wiki/Center_of_mass

http://en.wikipedia.org/wiki/Geoid

http://en.wikipedia.org/wiki/Equipotential_surface

http://en.wikipedia.org/wiki/Gravitation

http://en.wikipedia.org/wiki/Altitude

http://en.wikipedia.org/wiki/Reference_ellipsoid

http://en.wikipedia.org/wiki/Spheroid

http://en.wikipedia.org/wiki/Earth

http://en.wikipedia.org/wiki/Cartesian_coordinates

http://en.wikipedia.org/wiki/Global_Positioning_System



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1.2 What is UTM Coordinate System?

The Universal Transverse Mercator (UTM) coordinate system is a grid-based method of specifying

locations on the surface of the Earth that is a practical application of a 2-dimensional Cartesian coordinate

system. It is a horizontal position representation, i.e. it is used to identify locations on the earth

independently of vertical position, but differs from the traditional method of latitude and longitude in

several respects.

The Universal Transverse Mercator (UTM) coordinate systems use a metric-based cartesian grid laid out

on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not

a single map projection. The system instead employs a series of sixty zones, each of which is based on a

specifically defined secant transverse Mercator projection. Currently, the WGS84 ellipsoid is used as the

underlying model of Earth in the UTM coordinate system.

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Figure: The Reference Ellipsoid for Malaysia Parameters

http://en.wikipedia.org/wiki/World_Geodetic_System

http://en.wikipedia.org/wiki/Transverse_Mercator_projection

http://en.wikipedia.org/wiki/Map_projection

http://en.wikipedia.org/wiki/Universal_Transverse_Mercator

http://en.wikipedia.org/wiki/Altitude

http://en.wikipedia.org/wiki/Horizontal_position_representation

http://en.wikipedia.org/wiki/Cartesian_coordinate_system

http://en.wikipedia.org/wiki/Cartesian_coordinate_system

http://en.wikipedia.org/wiki/Coordinate_system



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1.3 Geographical and Cartesian Coordinates

Three-dimensional geographical coordinates can be defined with respect to an ellipsoid as follows:

Latitude: the angle north or south from the equatorial plane

Longitude: the angle east or west from the prime meridian

Height: the distance above the surface of the ellipsoid.

A set of cartesian coordinates is defined with the three axes at the origin at the center of the ellipsoid,

such that:

Z-axis: is aligned with the minor (or polar) axis of the ellipsoid

X-axis: is in the equatorial plane and aligned with the prime meridian

Y-axis: forms a right-handed system

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Figure: Malaysia is located in

UTM 47 and 48 zone



_________________________________________________________________________________________________________In this regard, positions in geographical coordinates of latitude, longitude and height (Φ, λ, h) can be

converted into cartesian coordinates (X, Y, Z) and vice-versa.

Figure: Geodetic Latitude, Longitude, and HeightEarth Figure: Earth Centered, Earth Fixed X, Y, and Z

1.4 Conversion between Geographical Coordinates and Cartesian Coordinates

The conversion of three-dimensional coordinates from geographical to cartesian or vice versa can be

carried out through the knowledge of the parameters of an adopted reference ellipsoid. The forward

conversion from geodetic coordinates (Φ, λ, h) to cartesian coordinate ( X ,Y, Z ) is as follows:

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The Non – iterative reverse conversion from Cartesian coordinates (X, Y, Z) to geodetic coordinates (Φ,

λ, h) is as follows:

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Figure: Relationship between

Geographical Coordinates and

Cartesian Coordinates



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2.0 WGS 84 TO MRT 68 DATUM TRANSFORMATION

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Figure: Example of Conversion

Between Geographical Coordinate

and ECEF Cartesian Coordinate



_________________________________________________________________________________________________________Datum transformation is a computational process of converting a position given in one coordinate

reference system into the corresponding position in another coordinate reference system. It requires and

uses the parameters of the transformation and the ellipsoids associated with the source and target

coordinate reference systems.

2.1 Bursa – Wolf Datum Transformation Formulae

Bursa-Wolf formulae is a seven-parameter model for transforming three-dimensional cartesian

coordinates between two datums. This transformation model is more suitable for satellite datums on a

global scale (Krakwisky and Thomson, 1974). The transformation involves three geocentric datum shift

parameters (ΔX, ΔY, ΔZ), three rotation elements (RX, RY, RZ ) and a scale factor (1+ΔL ).

The model in its matrix-vector form could be written as ( Burford 1985):

3.0 MRT 68 TO RSO MAP PROJECTION

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Figure: Bursa – Wolf 7 Parameters

Transformation



_________________________________________________________________________________________________________Typically, there are many different methods for projecting longitude and latitude in coordinate reference

system 1 onto a flat map in the same system:

The rectified skew orthomorphic (RSO) is an oblique Mercator projection developed by Hotine in 1947

(Snyder, 1984). This projection is orthomorphic (conformal) and cylindrical. All meridians and parallel are

complex curves. Scale is approximately 21 true along a chosen central line (exactly true along a great

circle in its spherical form). It is thus a suitable projection for an area like Switzerland, Italy, New Zealand,

Madagascar and Malaysia as well. The RSO provides an optimum solution in the sense of minimizing

distortion whilst remaining conformal for Malaysia.

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Figure: Hotine, 1947 (Snyder, 1984), Oblique Mercator (Source: EPSG)

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_________________________________________________________________________________________________________3.1 MRT 68 to RSO (MRSO & BRSO) Map Projection

Figure: MRSO and BRSO Constant Projection Parameters

The Projection formulae are as follows;

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4.0 MRSO TO STATE CASSINI –

COLDNER MAP PROJECTION

A transverse cylinder is projected onto the globe

conceptually, and is tangent along the central

meridian. Cassini is analogous to the

Equirectangular projection in the same way that the

Transverse Mercator is to the Mercator projection. This projection may also be referred to as the Cassini

Soldner, since ArcView actually uses the formulae based on the more accurate ellipsoidal version

developed in the 19th Century.

There are nine state origins used in the coordinate projection in the cadastral system of Peninsular

Malaysia. The Cassini-Soldner map projection has been used for over one hundred years and shall

continue to be used for cadastral surveys in the new geodetic frame.

The mapping equations are as given in Richardus and Adler, 1974 and the formulas to derive projected

Easting and Northing coordinate are as follows:

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Figure: Example of Conversion Between MRT 68 to MRSO and BT 68 to BRSO



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The old Cassini Soldner Coordinate Origin for each state

4.1 MRSO CASSINI – SOLDNER Map Projection

The relationship between MRSO coordinate and the Cassini Solder is defined by a series of polynomial

function which make use of the coordinate of the origin of both projections for each state in Peninsular

Malaysia. The following are the formulae used:

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_________________________________________________________________________________________________________All the values of the coordinates must be in unit chains (use 0.11678249 as the multiplying factor to

convert from metres.)

5.0 COORDINATE CONVERSION SOFTWARE 1

WGS 84 Coordinate: 3d 3’ 56.49” Northing and 101d 30’ 17.92” Easting

Location: Top of the SAAS Tower, UiTM Shah Alam

Software: Franson CoordTrans Version 2.3 (WGS 84 to MRT 68) and GDTS Version 4.01 (MRT 68 to

MRSO, MRSO to State Cassini – Soldner)

5.1 WGS 84 TO MRT 48 – Franson CoordTrans Version 2.3

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1. Select the “Longitude / Latitude” for WGS 84.2. Select the Datum “WGS84”3. Choose the option for “DMS” and Insert the coordinate in the Degree, Minutes, Seconds, East for Longitude

and Degree Minutes, Seconds, North for Latitude. And Altitude if available. (E.g. 3d 3’ 56.49” Northing and 101d 30’ 17.92” Easting)

4. Since the both were geocentric coordinates, select the “Longitude / Latitude” for MRT48.5. Select the Datum “Kertau” which is origin of MRT48 that referred to the Modified Everest ellipsoid.6. Click the “Next” button to convert7. And the result of conversion would appear. (3d 3’ 57.147” Northing, 101d 30’ 23.069” Easting)8. The black point shows the position of location before conversion and the red point shows the position of

location after the conversion.9. User also can view the position in Google Maps for a clearer view



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5.2 MRT 68 TO MRSO – GDTS Version 4.01

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1. Select the “Peninsular Malaysia” for MRSO conversion in the Main Modules.2. Select the “Map Projection” since the MRSO is the map projection for the MRT48.3. Select the number 5. MRT48 to MRSO(Old). “Old” here means the old MRSO since there

was a new geocentric MRSO referred to the GDM2000.4. Insert the Station Name for the position. (E.g. Station 1)5. Insert the Latitude in degree, minutes, seconds (E.g. 3d 3’ 57.147”)6. Insert the Longitude in degree, minutes, seconds (E.g. 101d 30’ 23.069”)7. Click “Transform” to convert or “Reset” to reset the Latitude and Longitude column back to

zero.8. The result would appear. (339327.910 Northing, 390025.506 Easting)9. Choose either to “Save” or print out the result.



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5.3 MRSO TO STATE CASSINI-SOLDNER – GDTS Version 4.01

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1. Select the number 7. MRSO(Old) to Cassini – Soldner (Old). “Old” here means the old Cassini before the new geocentric Cassini that referred to the GDM2000.

2. Select the State Selection for the number 12. Selangor and Kuala Lumpur.3. Insert the Station Name for the position. (E.g. Station 1)4. Insert the Northing (E.g. 339327.910)5. Insert the Easting (E.g. 390025.506)6. Click “Transform” to convert or “Reset” to reset the Latitude and Longitude column back to zero.7. The result would appear. ( -11981.973 Northing, -21962.414 Easting)8. Choose either to “Save” or print out the result.



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6.0 COORDINATE CONVERSION SOFTWARE 2

WGS 84 Coordinate: 3d 3’ 56.49” Northing and 101d 30’ 17.92” Easting

Location: Top of the SAAS Tower, UiTM Shah Alam

Software: GPCAS Version 1.02 (WGS 84 to State Cassini – Soldner)

6.1 WGS 84 TO STATE CASSINI – SOLDNER

_________________________________________________________________________________________________________Page 20 of 221. Select the “GPS (WGS84) System to Cassini System” for the conversion.



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2. Select the Output unit for Metres.3. Select the State for Selangor.4. Insert the Latitude in the degree, minutes, seconds (E.g. 3d 3’ 56.49”)5. Insert the Longitude in the degree, minutes, seconds (E.g. 101d 30’ 17.92”)6. Insert the ellipsoidal height if available or leave it blank if not available.7. Click the button “Compute” to make the conversion.8. And the result would appear (-11982.179 Northing, -21962.294 Easting)

1. Select the “GPS (WGS84) System to Cassini System” for the conversion.



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COMPARISON BETWEEN THE SOFTWARE

WGS 84 – MRT 68 – MRSO – STATE CASSINI – SOLDNER = -11981.973 N -21962.414 E

WGS 84 – STATE CASSINI SOLDNER = -11982.179 N -21962.294 E

Differences = 0.206 M 0.120 M

7.0 REFERENCES

1. Pekeliling Ketua Pengarah Ukur Dan Pemetaan Bilangan 3 2009 - Garis Panduan Mengenai

Penukaran Koordinat, Transformasi Datum dan Unjuran Peta Untuk Tujuan Ukur Dan Pemetaan.

2. A Technical Manual on the Geocentric Datum of Malaysia (GDM2000), Department of Survey and

Mapping Malaysia, August 2003.

3. "Geodetic Datum Presentation", Prof. Madya Dr. Khairul Anuar bin Abdullah, UTM

[email protected]

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