ESTABLISHMENT OF NEW FITTED GEOID MODEL IN UNIVERSITI TEKNOLOGI MALAYSIA

The purpose of this study is to produce fitted geoid for Universiti Teknologi Malaysia (UTM), Johor Bahru by using precise levelling and 3D GNSS control network technique. This study focuses on the theory, computation method and analysis of fitted geoid around Universiti Teknologi Malaysia. The computation of accuracy fitted geoid model is based on the GNSS levelling and Precise Levelling. The achieved accuracy of UTM Fitted Geoid Model is at 8mm. In conclusion, this research can contribute to Universiti Teknologi Malaysia by providing good UTM fitted geoid model that can give better accuracy for various purposes of work related to surveying and mapping. * amihassan@utm.my


INTRODUCTION 1.1 Research Backgrounds
For decades, one of the main studies in Science of Geodesy is precise geoid determination (Nordin, 2009).Jabatan Ukur dan Pemetaan Malaysia (DSMM), also known as the Department of Survey and Mapping Malaysia (DSMM) has implemented a project to map the geoid with the main objective to produce high precise geoid in order to determine the geoid height across the country in 2002.The geoid can be broadly defined as an equipotential surface of Earth's gravity field that closely approximates with mean sea level (MSL) neglecting long term effect of sea surface topography (Singh et al., 2007).Geoid determination includes collecting the gravity data over a wide area.In order to collect gravity data, DSMM has conducted an Airborne Gravity and Geoid Mapping Project across East and West Malaysia (Jamil, 2011).
Research institutes and agencies responsible for geodetic positioning have spent millions of dollars to precisely determine the local and regional geoid using GNSS.Also, terrestrial gravity data, satellite altimeter data, global geoid models and digital terrain model were used in the calculation of the geoid model Malaysia.Furthermore, GNSS levelling has managed to simulate the vertical datum bias and further correspondence issued geoid (geoid fitted) with the vertical datum that is based on the mean sea level.This study area will focus on Universiti Teknologi Malaysia, Johor Bahru as shown in Figure 1.
The aim of this study is to produce a localised fitted geoid for Universiti Teknologi Malaysia (UTM), Johor Bahru using the combination of precise levelling and three dimensional GNSS network techniques.The main problem of this study is the insufficient fitting point from the existing fitted geoid model, which is MyGEOID in UTM area.Less density of fitting point will affect the accuracy of the geoid fitting to give better solutions for height measurements.The benefits of this study are the determination of local precise geoid models (UTM fitted geoid) by using more intensive data that will support the less density of fitting points from MyGEOID.This research intended to prove that local fitted geoid (UTM fitted geoid) can have better results compared to the existing fitted geoid model of MyGEOID.
Generally, the achievable accuracy of the fitted geoid from MyGEOID in Peninsular Malaysia is around 5 cm (1σ).This accuracy can be increased by increasing the density of the fitting points observed by GNSS levelling at benchmark.

MyGEOID
MyGEOID is the product that was produced for first Malaysian geoid model (DSMM, 2005).It is able to compute orthrometric height H, referred to as the national geodetic vertical datum (NGVD).It contains the height of geoid N relative to the reference ellipsoid GRS80 surface in the form of a grid.The geoid determination of Malaysia is based on the available gravimetry (airborne, surface and satellite altimetry), which is continued downward to the surface of the topography, after removal of a spherical harmonic reference field expansion (DSMM, 2008).In addition, it consists of two geoid models, which are WMGEOID04 for Peninsular Malaysia and EMGEOID05 for Sabah and Sarawak as illustrated in Figure 2 and 3, respectively.The achievable accuracy with MyGEOID is around 5 cm (1σ) and 10 cm (1σ) for Peninsular Malaysia and Sabah and Sarawak, respectively.However, claimed accuracy of DSMM of MyGEOID is only representative of an entire general region without concerning how it represents a small area (DSMM, 2005).

Precise levelling
Precise Levelling is a precise form of differential levelling, where differential levelling is defined as the operation of determining differences in elevation of points some distance apart of established benchmarks (BM), which use highly accurate and a more rigorous observing procedure than general engineering levelling (Mui, 2006).From this method, 1D control network can establish a UTM fitted geoid model around UTM area.Process by using precise levelling method run for the measurement of elevation is considered the most accurate method to produce the best quality results in fitted geoid levelling.According to (DSMM, 2009), the reading of precise level is acceptable if the observation misclosure is lower than the allowable misclosure where, (2)

GNSS Levelling 3D Network
Department of Survey and Mapping Malaysia (DSMM) has established GNSS infrastructure in Malaysia as a reference control stations for cadastral and mapping purposes.With the increasing potential of Global Navigation Satellite System (GNSS) satellites and its calculation techniques, determination of height using GNSS has been widely used to replace the geometric levelling.By using GNSS levelling technique, knowing the geoidal height N, the orthometric height H can be calculated from ellipsoidal height h.Deriving orthometric height using this technique with certain level of accuracy could replace conventional spirit levelling and therefore make the levelling procedures cheaper and faster (Abu, 2005).The interpolated geoidal heights are the prerequisite for deriving orthometric or normal heights from GNSS heights without levelling (Ihde, 2009).From GNSS observation, we can establish the 3D control network around UTM.
The aim of this paper is to establish new fitted geoid model in UTM in order to increase the reliability of fitted geoid model from MyGEOID.It is also aimed to determine how good the new fitted geoid model represents small region, especially in UTM, by using precise levelling and 3D control network technique using GNSS observation and Gravimetric geoid data.

DATA AND METHODS
A general overview of the process for this study is shown in  ).The MSL heights were transferred from standard benchmark J4352 in UTM, located at Faculty Alam Bina (FAB), to all 19 benchmarks.Verification of benchmark is carried out to ensure the accuracy of the benchmark.
Establishing benchmark requires good distribution position of benchmark since the benchmark will later be used for GNSS observation.The known value for standard benchmark J4352 FAB in UTM is shown in Table 1.The precise levelling planning network contains 21 levelling routes, 3 levelling loops and 1 network as shown in Figure 5.

GNSS levelling using 3D Control Network
A GNSS network consists of 19 point that have been observed on established benchmark using five TOPCON GR5 dual frequency receivers.There are several important factors that need to be considered in designing 3D control network: •Design good network geometry •Acquire control within project area •Incorporate independent baselines Static GNSS observation (1 hour) method is applied for all observations located at UTM.The GNSS data is processed by using network processing in TBC software.Only independent baselines were processed between 19 stations.The 3D control networks for GNSS levelling are connected with 3 Malaysian Real Time Kinematic Network (MyRTKnet) stations, which are JHJY, KUKP and SPGR.Baselines were processed between P1, P2, P3, KTR, FKA, FKN05, PKU, DESA BAKTI, SMPG 3, SPS, G11, NC, SEK AGAMA, FKE, KTC, P19, KRP, FGHT and FAB.The observed baselines are shown in Figure 6, while holding 3 CORS, which are JHJY, KUKP and SPGR, as fixed in latitude, longitude and ellipsoidal height.Then, adjusted coordinates (latitude, longitude and ellipsoidal height) were generated for each target point.
Figure 6.3D control network for GNSS levelling.

Gravimetric Geoid Retrieval from MyGEOID
Gravimetric geoid is one of the MyGEOID's products that can be retrieved from DSMM.MyGEOID provides data with size 1' by 1' (1.8km x 1.8km) covering Malaysia.In this case, in order to obtain the gravimetric geoid data at the established temporary benchmark, Golden Surfer software is used to extract the data.
There are several interpolation methods to transform point data and each of them can have different results, however, it is important to determine which one give better solution in terms of accuracy (Anonym, 1999).Thus, in Golden Surfer process, Kringing method is used because it fits the data better (Erol and Celik, 2004).

Vertical Datum Bias (VDB) computation at the selected points
VDB can be derived from Equation 1: where,

VDB = vertical datum bias H GNSS = ellipsoidal height from GNSS H MSL = mean sea level height N gravimetric = gravimetric geoid height
In selecting reference points, keeping the homogeneous distribution of reference points set were considered.Ten points are selected.These points will later be used to perform the fitting process.

Fitting Process using Gravimetric Geoid Surface to MSL Surface
In order to determine the UTM Fitted Geoid model for local area, gravimetric surface must be shifted to MSL surface using this Equation: Fitted geoid surface = gravimetric geoid + VDB Latitude, longitude, fitted geoid value of selected reference points is later used in Golden Surfer software to form a fitted geoid model.

Establishment of MSL height using precise levelling
The MSL height from precise level for every benchmark point is shown in Table 2.Meanwhile, the accuracy validation for precise levelling data for loop A, B, C and network are shown in Table 3.  3. Error factor for 3 loops and a network from precise levelling

GNSS levelling using 3D Control Network
To achieve precise coordinate for points on BM's, GNSS observations were made and the products are in geographical coordinates and ellipsoidal heights.This 3D control network is used mainly for horizontal control but also from this GNSS observation, the by-product, which is the ellipsoidal height, is essential for GNSS levelling purpose or in other words, height modernization.
The accurate geographical coordinates for 19 BM were obtained by processing the GNSS data in TBC software whilst observed by Topcon GR5 receivers.3 MyRTKnet Stations have been used as reference point, which is JHJY, KUKP and SPGR.The results indicate the accurate position of BM points that used static mode observation.The coordinates and ellipsoidal heights for each BM are shown in Table 4.

Gravimetric geoid from MyGEOID
Gravimetric geoid, obtained from Airborne Gravity and Geoid Determination carried out by DSMM, is a geoid of undisturbed characteristic.The gravimetric geoid data is one of the MyGEOID products.The value was then interpolated or modelled by using Golden Surfer software.Figure 7 shows the model or geoid contour map generated by Golden Surfer software for Gravimetric Geoid data.Only small difference of geoid undulation can be observed from the map.From Table 6, we can see that the values of gravimetric geoid or N Gravimetric for UTM area are around 6m with only difference at decimal points.The points also were extracted by using Golden Surfer software.We can conclude that height separation of ellipsoid and geoid in this area is around 6m and the values are positive indicating that the level surface of ellipsoid is below the equipotential surface.

Computation of Vertical Datum Bias
The vertical datum bias (VDB) can be represented by the difference or separation between the Mean Sea Level and Geoid (gravimetric) level surface.For the computation of VDB, the general formula is shown in Equation 1.Ten points were chosen for the fitting process and become the fitting point so computations for vertical datum bias only for the selected points as shown in Table 7.The range of the vertical datum bias at UTM, also known as Sea Surface Topography, is approximately 1m.The results indicated that the separation of MSL and Geoid level surface is around 1m difference.It is generally known that geoid is said to coincide with the MSL surface, yet the difference is significant.7. Vertical Datum Bias at selected points

Fitting process
To realize the height modernisation system concept, a fitting process has been conducted.Fitting is the process of shifting the geoid of gravimetric surface to MSL surface by eliminating the SST or VDB culminating in a continuous level surface called fitted geoid.The UTM Fitted Geoid model is the product of height modernisation system and modelled by Golden Surfer software.Prior to fitting, a total of ten selected points (VDB points) are used along with their respective accurate position.After applying the VDB to the gravimetric geoid height, ten fitting points are produced.Fitted geoid surface can be calculated by using Equation 2 as shown below: where, N fitted = fitted geiod height N gravimetric = gravimetric geoid height VDB = vertical datum bias Based on Table 8, the values of Geoid height are between the ranges of approximation of 8 m.These are only for the points of fitting and by putting aside temporarily the other ten points for further use, these points are used to produce the model of UTM fitted Geoid contour map.The differences are only in sub-meter level throughout the area in UTM.
The model of final product of height modernisation is depicted in Figure 8.The main objective of having UTM Fitted Geoid model has been realised.The geoid separation or undulation is ranged between 7.8m to 8.0m from the map.This map is produced from the same prior which is Golden Surfer.

Analysing the accuracy of UTM Fitted Geoid
To analyse the external accuracy of the UTM fitted geoid, a set of external data or the other ten points that are not fitted are used for assessment.To realise this assessment, the seven points of non-fitted are extracted and interpolated from the UTM geoid model.The value of N fitted is represented by Table 9.

Mean Sea Level (MSL) comparison between MyGEOID and precise levelling
Based on the calculation of RMSE between the H GNSS and H MSL in Table 11, the error is about 8mm, which is smaller than the RMSE value from the comparison of Mean Sea Level from MyGEOID and precise levelling, which is about 8cm as shown in Table 12.This result has proved that the level computation from localised UTM fitted geoid is much better compared with the MyGEOID.

CONCLUSION
The establishment of UTM fitted geoid has been achieved successfully with RMSE value for external accuracy of 8mm.
The results and analysis prove that height modernisation of GNSS levelling and Fitted Geoid is a very efficient means of height system.This is alternative for conventional tedious levelling even though the accuracy of GNSS levelling itself is relatively lower than the precise level.GNSS levelling can be applied to engineering survey works and other projects that take only centimetre level of accuracy into account.

Figure 4 .
The process is mainly divided into four main steps: (1) research area identification; (2) data acquisition; (3) data processing; (4) data verification.The list of software used in this study are STAR*NET for precise levelling processing and adjustment, Trimble Business Centre (TBC) for GNSS data processing and Golden Surfer Software for data interpolation, fitting and plotting.

Figure
Figure 4. General overview of the process 2.1 Establishment of the Mean Sea Level (MSL) Height Using Precise Levelling 19 benchmarks were established covering UTM area (2km x 2km).The MSL heights were transferred from standard benchmark J4352 in UTM, located at Faculty Alam Bina (FAB), to all 19 benchmarks.Verification of benchmark is carried out to ensure the accuracy of the benchmark.Establishing benchmark requires good distribution position of benchmark since the benchmark will later be used for GNSS observation.The known value for standard benchmark J4352 FAB in UTM is shown in Table1.

Figure 8 .
Figure 8. Contour map of UTM Fitted Geoid

Table 1 .
Benchmark known value

Table 2 .
MSL heights from precise level for every benchmark pointFrom Table2, the value of H MSL from each point are obtained by using the precise levelling method starting from the standard benchmark of J4352.Thus, three survey loops are proposed in order to cover the area.
Table 5 tabulates the standard deviations of latitude, longitude and ellipsoidal height using one sigma.

Table 8 .
Value of N fitted and positions at selected fitting points

Table 10 .
After applying the aforementioned formula, a set of geometric geoid height, or N geometric, is derived as shown in Table10.The main function of N geometric is to evaluate and verify the external accuracy of the fitted geoid in UTM.In other words, N geometric is for verifying geoid.The positions and value of N geometric for external accuracy points.fFigure9.Contour map of Geometrics geoid model.These values of N geometric from Table10are later compared to the N fitted at the same points from Table9.The differences are called external accuracy, which depict the accuracy of the UTM Geoid Model.Equation 4 as shown below is applied to get the difference:From Table11, the difference of N fitted and N geometric can be said to be less than around 1 cm accuracy difference.This difference should later be presented in Root Mean Square Error (RMSE) value.The biggest difference comes from FKN05, which give the value of 12 mm, and the smallest difference is KTC, which is only 0.4 mm.The RMSE actually depicts the overall accuracy of the project.According to Table11, the accuracy of the UTM fitted geoid is at 8mm.

Table 11 .
RMSE value from the comparison of Mean Sea Level from UTM N fitted (H GNSS ) with Mean Sea Level from precise levelling (H MSL )

Table 12 .
RMSE value from the comparison of Mean Sea Level from MyGEOID N fitted (H GPS ) with Mean Sea Level from precise levelling (H MSL )