A total of 39 Benchmark observed with GPS have been used in the computation of Peninsular Malaysia fitted geoid model. The computation was done iteratively, and the results in every iteration, closely examined in every iteration.

Figure 11, shows the corrector surface range between 0.95 – 1.60 m, with two stations namely S0220 (minimum Diff.) and E1142 (maximum Diff.) shows the bull-eyes characteristic. Investigation on the suspected stations show that E1142 located on the highland (Cameron Highland) and S0220 is at the tip of Peninsular Malaysia (Sungai Rengit). Both SBM connected using precise leveling survey but not in the form of leveling loop (hanging line). The levelling lines are also not in the main adjustment of the Peninsular Malaysia Precise Levelling Network.


In the second iteration, S0220 and E1142 were excluded from the process, and the results show an improvement with the corrector surface is well distributed (Figure 12). The corrector surface range is between 1.14 – 1.44 meter with the formal standard error is 0.020 m in the least square collocation adjustment.

In Sabah and Sarawak, 60 out of 71 benchmarks with MSL values were used in the fi tted geoid model computation. Sixiterations have been carried out with eleven benchmarks excluded before the final fitted geoid model finalized.

Figure 13 shows the corrector surface that range between 0.55 – 1.75 meter from the fi rst iteration. The plot clearly shows the “bull-eyes” that represent the existent of outliers in one of the input component. In the subsequent LSC adjustment, benchmarks which suspected as outliers removed. The final 6th iteration with 60s benchmarks yield the formal error of 0.029meter with corrector surface range between 1.10 – 1.45 meter.

In order to have more realistic assessment of the WMgeoid04 model, comparison using three independent data sets has been carried out.

Basic Formula:
H_WMGeoid04 = h_gps – N_WMGeoid04
                                    (11)

This value is more realistic when compare to the formal error of 0.020 m from the LSC adjustment. From a total of 115 benchmarks that have been evaluated (Data 1, II and III), only 13 benchmarks (11.3%) were found to be an outliers.

For EMGeoid05, only one set of independent data are available with achievable accuracy of 0.042 meter.

The Malaysian gravimetric geoid is apparent accurate to few cm r.m.s, with larger errors closer to the international borders (Forsberg, 2005). The geoid is fi tted to GPSlevelling information, and any errors in HLevelling and hGps, will directly affect the high quality of the gravimetric geoid; in other cases it will help control longer wavelength errors. The balance between fit of GPS, and errors in geoid and GPS, is delicate, and undoubtedly there will be many regions in the present geoid where GPS users can expect problems due to fi tting of GPS-levelling data with errors.

Based on the statistical analyses, it can be concluded that the accuracy of fitted geoid models of WMGeoid04 and EMGeoid05 is 0.033 and 0.042 meter respectively, and can be used for height determination. To achieved certain level of accuracy in determination of orthometric height (H), accuracy of observed GPS network has to be better than 1 ppm (relatively) and the vertical errors (95% Conf. Region) have to be less than 3 cm

Real Time Kinematic (RTK) survey and MyRTKnet service provided by DSMM with 3 cm level of accuracy can make use of the models for engineering survey, rapid height monitoring and establishing levelling route.

Fitted geoid model WMGeoid04 and EMGeoid05 is the product of GPS on Benchmark observation. In order to improve the results and to achieve 1
cm geoid, the recommendations listed below need further considerations:-
i. New GPS observation on Standard Benchmark (SBM) to densify current GPS Levelling Network, with the distribution between ˜ 10 km nations wide.

ii. The existing Precise Levelling Network based on spirit levelling carried out from 1985 to 1995. The levelling networks need to be carefully analyzed, and possibility of carry out a new adjustment including analysis of subsidence and land uplift.

iii. Resurvey by levelling and GPS of selected, suspected erroneous points with large geoid outliers. iv. If long GPS observation is needed, GPS processing software must be capable of producing the solution with the statistic and to model the troposphere with the adequate parameters.

v. Make a new GPS-fitted version of the gravimetric geoid as new batches of GPS-levelling data become available, and as GPS users report problem regions for heights.

vi. GPS levelling technique need the antenna height measure correctly. The use of stable Bipod with fixed antenna height will minimize the error especially with the shorter baselines.

vii. Levelling route is always following the federal and states road, hence,
the BMs are established along the roadside, which the clearance of 15° is difficult to get. To overcome this situation, the use of stable Bipod with more than 2 meter will certainly solve the problems and also minimize the disturbance of vehicle passing by.

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Ahmad Fauzi Nordin
JUPEM, Malaysia
fauzi@jupem.gov.my

Samad Hj. Abu
Chang Leng Hua & Soeb Nordin
Department of Survey and Mapping Malaysia