CHAPTER 1 INTRODUCTION 1. 1 Background of Study Coordinate systems form a common frame of reference for description of positions and on the other hand, coordinates are simply an ordered set of numbers that are used to describe the positions or features in coordinate system. Transformation parameters are required to move from one system to another. Also, new technologies like global positioning system have provide new methods of coordinates determination the map production, update and revision are based on geographical coordinates, map-grid coordinates or coordinates in an arbitrary system.
Some other based on old (local) system. With so many geodetic datums in current use, it is becoming almost common practice to transform coordinates from one datum to another. For an example, a surveyor, using GPS, will obtain the WGS 84 geocentric, geodetic or Cartesian coordinates of the survey point. In order to plot the position on the corresponding local map, these WGS 84 coordinates must be first transformed into the local datum on which the map is based, which in Malaysia would most probably be Malayan Revised Triangulation 1948 (MRT 48) for Peninsular Malaysia and Borneo Triangulation 1968 (BT68) for East Malaysia.
Therefore, coordinates transformation play many important roles in land survey development for coordinates transformation, datum conversion and map projection. Thus, development and manipulation in coordinate transformation system software currently become more exclusive together with the growing technology in Malaysia. 1. 2 Problem Statement As already known, there is few coordinates system in Malaysia and most off situation for a surveyor required doing a coordinate transformation from one datum to another datum.
However, datum conversion and transformation can be accomplished by many methods. Hence, a computer programming becomes a useful tool to solve our problems using manual computation for a coordinate transformation is totally not an easy task and very challenging. Coordinate transformation software can make it easier and faster. Thus, in this project has to develop software based on coordinate transformation using Mathworks Matlab 7. 1 software. 1. Objective of Study The aim of this study is to develop software for generating coordinates from one system to another. There are some objectives of study this study: (i) To study formulas for coordinate transformation in Malaysia from satellite datum vice verse local geodetic datum. (ii) To develop software for generating coordinates transformations using Mathworks Matlab 7. 1 software. 1. 4 Scope of study However, this study is limited as follows: i) Understanding of formula coordinate transformation system such as World Geodetic System 1984 (WGS84), Malayan Revised Triangulation 1948 (MRT48), Borneo Triangulation 1968 (BT68), Rectified Skew Orthomorphic (RSO), Cassini Soldner System, and the geocentric system, Geocentric Datum of Malaysia 2000 (GDM200). (ii) Learning of Mathworks Matlab 7. 1 to develop coordinate transformation software. (iii) Verify the computation transformation, and compare the computation result with Geodetic Datum Transformation System (GDTS) software. 1. Significance of Study The following are potential benefits that can be expected from this study: (i) To introduce coordinate transformation software that cover Malaysia. Furthermore, to introduce software where served one module that transformation parameter can be modified by user. (ii) To find all information about coordinate transformation parameter, calculation algorithm, formulas, definition and concept. 1. 6 Research Methodology This research is studies that need to perform by four stages and finalize it in given time.
The stage is briefly explained by the flow chart of Figure 1. 1. Figure 1. 1 Flow chart of Research Methodology. 1. 7. 1 Stage I Firstly in stage one, an overview for the field of study must be done by finding any relevant information related to the transformation coordinate. It is covered for basic understanding and concept in Malaysia coordinate system. All information gathered from various written and published sources like books, articles, journals, internet and other sources. 1. 7. 2 Stage II
From the collected informations in stage one, in this stage, gathering and continuing find related informations such as transformation algorithm, transformation parameter and also in this stage, it is cover for understanding about theory of coordinate systems, projection theory, and transformation coordinate module vice versa between datum conversion and transformation. 1. 7. 3 Stage III There are a lot of calculation involved for this study, it is not be beneath if perform manual calculation. The computer programming is employed to perform calculation consistently can be done in a short period.
The Matlab 7. 1 been chosen for this study for building the program as prototype first. Then, the prototype programs need to be test by compare with the other coordinate transformation software such as GTDS software. Therefore, any mistake occurs can be identify and fix. 1. 7. 4 Stage IV Lastly, execute the study and analyzing on the output data from new coordinate transformation software with GDTS software, then make the conclusion and recommendation based on the analysis. CHAPTER 2 LITERATURE REVIEW 2. 1Introduction
The science of geodesy has provided us with two different types of coordinate systems. These are geocentric and regional (local) coordinate systems. The origins and axes of these coordinate systems are different. While the geocentric coordinate system has its origin at the centre of the mass of the earth and the regional (local) coordinates system has its centre different from the geocentre. These coordinate systems are associated with the term ‘datum’, which uses coordinates referred to the surface of defined ellipsoid of revolution. (Featherstone and Reit, 1998).
Historically, different ellipsoids have been chosen by different countries of the world in order to simplify surveying and mapping in their region and as such these ellipsoids are not necessarily geocentric. In Malaysia, the region (local) coordinate system is two old or classical triangulation networks, namely the Malayan Revised Triangulation 1968 (MRT68) for Peninsular Malaysia where base on Modified Everest ellipsoid in Kertau and the Borneo Triangulation 1968 (BT68) for Sabah and Sarawak based on Modified Everest ellipsoid in Timbalai.
With the recent advances in space-based positioning technology, many countries have begun to implement and subsequently adopted a global geocentric coordinate reference system. In relation to this, Department of Surveying and Mapping Malaysia (DSMM) itself has embraced in the early 1990s the Global Positioning System (GPS) technology with the eventual objective of adopting a global unified datum for Peninsular Malaysia, Sabah and Sarawak. This later led towards the establishment of a new geodetic framework for the Malaysia.
The new Geocentric Datum for Malaysia (GDM2000) is being built by GPS space geodetic technology based on International Terrestrial Reference Frame (ITRF2000) and Geodetic Reference System 1980 (GRS80) reference ellipsoid. 2. 2Coordinates Reference System in Malaysia The Department of Survey and Mapping Malaysia (DSSM) is a government agency under the Ministry of Land and Co-operative Development which acts as the technical advisor to the Government of Malaysia on all matters pertaining to surveys and mapping in the country.
It is the sole government body which maintains the Malaysian spatial reference frame for various works such as for geodesy, mapping, engineering, cadastral, and scientific, geodynamics and creations of Geographical or Land Information Systems. The coordinate reference systems that have been introduced and used since the late 1800s in Malaysia are listed in Table 2. 1. No. | Coordinate Reference System| | Coordinate System| Geodetic Datum| | Malaysia Revised Triangulation 1968 (MRT68)| KertauEllipsoid: Modified Everest| 2| Borneo Triangulation 1968 (BT68)| TimbalaiEllipsoid: Modified Everest| 3| Peninsular Malaysia Geodetic ScientificNetwork 1994 (PMGSN94)| WGS84Ellipsoid: WGS84Reference Frame: WGS84Epoch: 1987. 0| 4| East Malaysia Geodetic Scientific Network1997 (EMGSN97)| WGS84Ellipsoid: WGS84Reference Frame: WGS84 (G783)Epoch: 1997. 0| 5| Malaysia Active GPS System (MASS)| GDM2000Ellipsoid: GRS80Reference Frame: ITRF2000Epoch: 2000. 0| 6| Malaysia Primary Geodetic Network 2000(MPGN2000)| GDM2000Ellipsoid: GRS80Reference Frame: ITRF2000Epoch: 2000. | | | GDM2000 (2009)Ellipsoid: GRS80Reference Frame: ITRF2000Epoch: 2000. 0| Table 2. 1: Coordinate Reference System in Malaysia. 2. 3Datum Transformation Three – dimensional coordinates could be converted Cartesian to curvilinear or vice versa trough the knowledge of the parameters of adopted reference ellipsoid. The forward transformation from geodetic coordinates (, , h) to Cartesian coordinates (X, Y, Z) is given in Heiskanen and Moritz (1967) as Figure 2. 1. Figure 2. 1: Coordinates conversion. X = ( N + h )coscos Y = ( N + h) coscos
Z = b2a2 N+hsin … (2. 1) Where the prime vertical radius of curvature (N) is: N = a2a2cos + b2sin212 … (2. 2) With: a| : the semi-major axis of the reference ellipsoid;| b| : the first eccentricity of the reference ellipsoid. | | | The non-iterative reverse transformation from Cartesian coordinates (X, Y, Z) to geodetic coordinates (, , h) is given in Bowring (1985) as: = arctanZ+ 2bsin3uP-e2acos3u = arctanYX = P cos + Z sin – a1- e2sin2 … (2. 3) With: u = arctanaZbP P = X2+ Y2 = e21- e2 … (2. 4) Where, u| : the parametric latitude;| b| : the semi-minor axis of the reference ellipsoid;| | : the second eccentricity of the reference ellipsoid. | | | The Bursa-Wolf is a seven parameter model for transforming three dimensional Cartesian coordinates between two datums (see Figure 2. 2). This transformation model is more suitable for satellite datums on global scale (Krakwisky and Thomson, 1974).
The transformation involves three geocentric datum shift parameters (X, Y, Z), three rotation elements (RX, RY, RZ) and scale factor (1 + L). Figure 2. 2: Bursa-Wolf 3D Model Transformation. The model in its matrix-vector from could be written as (Burford 1985): XWGS84YWGS84ZWGS84= XYZ+ 1+LRZ-RY-RZ1+LRXRY-RX1+LXMRTYMRTZMRT … (2. 5) Where, XWGS84, YWGS84, ZWGS84| : are the global datum (WGS84) Cartesian coordinates;| XMRT, YMRT, ZMRT | : are the local datum (MRT) Cartesian coordinates. | In order to convert the geocentric coordinates of XYZ to the geodetic coordinates of ? ? , h, ellipsoid properties for the respective datum as listed in Table 2. 2 below: Num. | Ellipsoid| a (m)| 1/f (m)| Reference Frame| 1| GRS80| 6378137. 000| 298. 2572221| ITRF91-ITRF2000| 2| WGS84| 6378137. 000| 298. 2572236| WGS84| 3| Modified Everest (Peninsular Malaysia)| 6377304. 063| 300. 8017| MRT48| 4| Modified Everest (East Malaysia)| 6377298. 556| 300. 8017| BT48| Table 2. 2: Ellipsoid Properties. 2. 3. 1Multiple Regression Model a) Displacement Computation The computation and modelling of differences in the coordinate between the two systems, i. . GDM2000 and GDM2000 (2009) were carried out using their respective geographical coordinates in the format of (? , ? and h). These differences are then converted to the local geodetic horizon to avoid mathematical errors for some very small values. The conversion from geographical system to local geodetic system used the following factor, i. e. 1”= 30 meter. The differences in the three components are computed separately by using the following formulae: North (N) = (”GDM2000 – ”GDM2000 (Revised 2006)) x 30 East (E) = (”GDM2000 – ”GDM2000 (Revised 2006)) x 30
Height (U) = hGDM2000 – hGDM2000 (Revised 2006) … (2. 6) b) Displacement Modelling The differences in coordinate of every GPS station are similarly computed between the two systems, i. e. GDM2000 and GDM2000 (2009) using their respective coordinates in the format of (E and N). The coordinate differences are then gridded to derive the Regression Coefficient. The gridding method used is the polynomial regression with the power to the second order. The surface definition used the bi-linear saddle regression coefficient with the following formulae:
Z(E,N) = A00 + A01 N + A10 E + A11 EN … (2. 7) Where, Z | : Value of regression coefficient or the value of displacement correction for each component (i. e. East, North and Up)| E| : East coordinate in decimal degree| N| : North coordinate in decimal degree| c) Basic Formula To convert the coordinate in GDM2000 to GDM2000 (2009), the following formulae shall be used: GDM2000 (2009)| =| GDM2000 + correction| ?”GDM2000 (2009)| =| ? ”GDM2000 + (ZN / 30)| ?”GDM2000 (2009)| =| ? ”GDM2000 + (ZE / 30)| hGDM2000 (2009)| =| hGDM2000 + ZU| (2. 8) Where, ”| =| Latitude in second of arc| ”| =| Longitude in second of arc| h| =| Ellipsoidal height in meter| ZN| =| Displacement correction in northing| ZE| =| Displacement correction in easting| ZU| =| Displacement correction in height| Where, Z(E,N) = A00 + A01 N + A10 E + A11 EN and A00, A01, A10 and A11 are the coefficients of the multiple regression model. 2. 4Map Projection 2. 4. 1Rectified Skew Orthomorphic (RSO) The RSO is an oblique Mercator projection developed by Hotine in 1947 (Synder, 1984). Hotine called the projection as “rectified skew orthomorphic” see Figure 2. 3.
This projection is Orthomorphic (conformal) and cylindrical. All meridians and parallel are complex curves. Scae is approximately true along 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 provide an optimum solution in the sense of minimizing distortion whilst remaining conformal for Malaysia. Table 2. 3 tabulates the new geocentric RSO parameters for Peninsular Malaysia and East Malaysia. (DSMM, 2008). Figure 2. 3: Oblique Mercator. Hotine, 1947 & Synder, 1984), | Peninsular RSO| East Malaysia BRSO| Ellipsod parameter| Ellipsoid| GRS 80| GRS 80| Major axis, a| 6378137. 000 meters| 6378137. 000 meters| Flattening, 1/f| 298. 2572221| 298. 2572221| Defined Parameters| Latitude of origin, o| 4 00’ 00” N| 4 00’ 00” N| Longitude of origin, | 102 15’ 00” E| 115 00’ 00” E| Rectified to Skew Grid, o| -Sin-1 (0. 6)| -Sin-1 (0. 8)| Azimuth of central Line, c| 323 01’ 32. 86728”| 53 18’ 56. 91582”| Scale Factor, k| 0. 99984| 0. 99984| False Origin (Easting)| 804,671 meters E| Nil| False Origin (Northing)| Nil| Nil| Table 2. : The New Geocentric RSO Projection Parameters. 2. 4. 2Cassini – Soldner Projection Cassini – Soldner projection system is classified as cylindrical, tangent, transverse, equidistant and semi geometric (Richardus and Adler, 1974). The cylindrical is tangent along the meridian centrally situated, so that the narrow belt is bisected by it as symmetrically as possible. The North-South grid lines of the projection system are the Projections of small circles, parallel to the central meridian. The distances along the X-axis in the projection are always greater than the corresponding arc distances on the datum surface.
Meanwhile the Y-coordinate of the projection represent true to scale the arc distance from the central meridian. Table 2. 4 tabulates re-definition of states origin in GDM2000. State| Station Location| Coordinates of State Origins| | | GDM2000| Cassini – Soldner| | | Latitude(N)| Longitude(E)| Northing(m)| Easting(m)| Johor| Gunung Belumut| 2 02’ 33. 20196”| 103 33’ 39. 83730”| 0. 000| 0. 000| N. Sembilan & Melaka| Gun Hill| 2 42’ 43. 63383”| 101 56’ 22. 92969”| 0. 000| 0. 000| Pahang| Gunung Sinyum| 3 42’ 38. 69263”| 102 26’ 04. 60772”| 0. 000| 0. 00| Selangor| Bukit Asa| 3 40’ 48. 37778”| 101 30’ 24. 48581”| 0. 000| 0. 000| Terengganu| Gunung Gajah Trom| 4 56’ 44. 97184”| 102 53’ 37. 00496”| 0. 000| 0. 000| P. Pinang & S. Perai| Fort Cornwallis| 5 25’ 15. 20433”| 100 20’ 40. 76024”| 0. 000| 0. 000| Kedah & Perlis| Gunung Perak| 5 57’ 52. 82155”| 100 38’ 10. 93860”| 0. 000| 0. 000| Perak| Gunung Hijau Larut| 4 51’ 32. 64488”| 100 48’ 55. 47038”| 0. 000| 0. 000| Kelantan| Bukit Panau (Baru)| 5 53’ 37. 07975”| 102 10’ 32. 24529”| 0. 000| 0. 000| Table 2. 4: Re-Definition of States Origin in GDM2000. 2. Other Software Review 2. 5. 1Geodetic Datum Transformation System (GDTS) Version 4. The Geodetic Datum Transformation System (GDTS) software lets you transform and converts the station’s coordinates from and to various reference datum. It was developed by Info-Geomatik Sdn Bhd. GDTS Version 4. 0 is more effective and more user friendly than previous versions. GDTS Version 4 also supplied with a number of transformation options. For most users, the projections, zones, and datum transformations that are supplied with these systems will be all they need. All the features listed below: . Conversion between geographical (Latitude, Longitude and Ellipsoidal Height) to 3-Dimensional Cartesian (X, Y and Z) and vice versa using user-defined and pre-defined ellipsoid. 2. Bearing and Distance computation between two stations with the input given in 2-Dimensional coordinates (Northing and Easting). 3. Universal Transverse Mercator (UTM) projection covering all UTM zone world wide as well as user-defined parameter. 4. 3, 4 and 7 parameters derivation using the Bursa-Wolf and Molodenski-Badekas models. 5. Three-Dimensional transformation with user-defined input parameters. 6.
Computation and transformation of 2-Dimensional conformal transformation In conclusion, based on the review performed on the transformed coordinate and guide the analysis it is clear that this program was met the specifications of coordinate transformation that closely resembles the value given by the Department of Survey and Mapping Malaysia (JUPEM). The analysis also proved that the program is fulfilling the needs of users of the various aspects involved. CHAPTER 3 METHODOLOGY 3. 1Introduction Nowadays, a computer programming becomes a useful tool to solve our problem especially involving a massive calculation in surveying field.
It is not be beneath perform manual because it consumes time and error due to human mistaken. The computer programming can overcome these limitations. For this study, the main objective is to generate coordinate transformation values by using computer programming to complete this research. Therefore, I am using Mathworks Matlab 7. 1 as the computer programming for this study. Mathworks Matlab is an integrated technical computing environment that combines numeric computation, advanced graphic and visualization, and a high level programming language.
Besides the computer programming, the related mathematic models were an important element in programming and its acts as algorithm for written programming. 3. 2Flow Work of Study 3. 3The Basic Concept Coordinate transformation is related to the use of different coordinate systems. As is well known that the results of observations of GPS satellites are in the WGS84 coordinate system, while users typically use a local coordinate system. Thus, the relationship between the two systems can be done by a certain formula.
The process of transformation of coordinates from one coordinate system to another coordinate system with the involvement of different datum will involve three things, namely: i. Origin shift ii. Axial shift iii. Scale Typically, seven parameters used in the process of transforming three displacement parameters, three parameters of the axis of rotation and a scale parameter. 3. 3. 1Origin Shift Transfer of origin of a coordinate system to another coordinate system involves three types of displacement in the axial displacement of the x axis, y axis displacement and axial displacement z.
Suppose the position of point P (x, y, z) coordinate system was at the origin O was transferred to the new origin, O’. Therefore, this change will result in ? X, ? Y, and ? Z. Finally, the new position of point P (X, Y, Z) is obtained by: X= x + ? X Y= y+ ? Y Z= z+ ? Z … (3. 1) 3. 3. 2Axial Shift Axes in the old system will rotate on their axis. Three elements are crucial in this round omega, phi and kappa. Omega element refers to the x-axis, phi element refers to the y-axis and kappa element refers to the z-axis. 3. 3. 3Scale
Scale changes that occur in a system can be divided into two parts, namely a change in reference to the overall system and scale of change refers to the old coordinates. By taking a pair of straight lines connecting these points PQ (point P and point Q) while the second coordinate system, the line is described as pq. If the straight line PQ is not equal to the line pq then the scale factor has an important role to change it into the new system. 3. 4Mathematical Model Three – dimensional coordinates could be converted Cartesian to curvilinear or vice versa trough the knowledge of the parameters of adopted reference ellipsoid.
The forward transformation from geodetic coordinates (, , h) to Cartesian coordinates (X, Y, Z) is given in Heiskanen and Moritz (1967) as Figure 3. 1. Figure 3. 1: Coordinates conversion. X = ( N + h )coscos Y = ( N + h) coscos Z = b2a2 N+hsin … (3. 2) Where the prime vertical radius of curvature (N) is: N = a2a2cos + b2sin212 … (3. 3) With: a| : the semi-major axis of the reference ellipsoid;| b| : the first eccentricity of the reference ellipsoid. | | The non-iterative reverse transformation from Cartesian coordinates (X, Y, Z) to geodetic coordinates (, , h) is given in Bowring (1985) as: = arctanZ+ 2bsin3uP-e2acos3u = arctanYX h = P cos + Z sin – a1- e2sin2 … (3. 4) With: u = arctanaZbP P = X2+ Y2 = e21- e2 … (3. 5) Where, u| : the parametric latitude;| b| : the semi-minor axis of the reference ellipsoid;| : the second eccentricity of the reference ellipsoid. | | | The Bursa-Wolf is a seven parameter model for transforming three dimensional Cartesian coordinates between two datums (see Figure 3. 2). This transformation model is more suitable for satellite datums on global scale (Krakwisky and Thomson, 1974). The transformation involves three geocentric datum shift parameters (X, Y, Z), three rotation elements (RX, RY, RZ) and scale factor (1 + L). Figure 3. 2: Bursa-Wolf 3D Model Transformation. The model in its matrix-vector from could be written as (Burford 1985):
XWGS84YWGS84ZWGS84= XYZ+ 1+LRZ-RY-RZ1+LRXRY-RX1+LXMRTYMRTZMRT … (3. 6) Where, XWGS84, YWGS84, ZWGS84| : are the global datum (WGS84) Cartesian coordinates;| XMRT, YMRT, ZMRT | : are the local datum (MRT) Cartesian coordinates. | In order to convert the geocentric coordinates of XYZ to the geodetic coordinates of ? , ? , h, ellipsoid properties for the respective datum as listed in Table 3. 1 below: Num. | Ellipsoid| a (m)| 1/f (m)| Reference Frame| 1| GRS80| 6378137. 000| 298. 2572221| ITRF91-ITRF2000| 2| WGS84| 6378137. 000| 298. 2572236| WGS84| | Modified Everest (Peninsular Malaysia)| 6377304. 063| 300. 8017| MRT48| 4| Modified Everest (East Malaysia)| 6377298. 556| 300. 8017| BT48| Table 3. 1: Ellipsoid Properties. 3. 5 Software Developing and Verification Because this study involved a complicated and also a lot calculation, it is not beneath if perform manual calculation. So, the computer programming is employed to perform calculation consistently in a short period of time. The Mathworks Matlab 7. 1 been chosen for this study. After the software is developed, the process of verification is needed for written software.
This is to eliminate any mistaken occurs when developing the software. This verification can be done by providing a sample of data and perform another coordinate transformation software like GDTS to compare the results. 3. 6Data Processing, Result and Analyzing, Conclusion and Recommendation After the software is developed and go trough verification process, execute the study and analyzing on the output data from new coordinate transformation software with GDTS software, then make the conclusion and recommendation based on the analysis. CHAPTER 4 EXPECTED RESULT
A software will be develop by using Mathworks Matlab 7. 1 to generate digital output of values for coordinate transformation from various coordinate transformation and map projection. The result of this study will be compare with the other result form the other software like GDTS. The results are expected to be same or approaching to the result generated by GDTS. REFERENCES 1. Bowring, B. R (1985), The Accuracy of Geodetic Latitude and Height Equations, Survey Review 28(218): 202-206. 2. Burford, B. J (1985), A Further Examination of Datum Transformation Parameters in Australia, The
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