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Use of Similarity Transformations to Improve GPS Heighting<
M.N. J.P. Vella
Centre for Geodetic and Geodynamic Studies (CGGS) Faculty of Geoinformation Science and Engineering University of Technology Malaysia Johor, Malaysia 1 Introduction Orthometric heights traditionally are determined through optical methods involving the transfer of height difference from a datum point to the unknown point, where the orthometric height is required. This can sometimes be a very arduous task and now with the advent and proliferation of the use of the Global Positioning System (GPS), this task realistically seems more possible now than ever before. With the use of GPS and a regional gravimetric geoid model it is possible to transfer heights simply, as the following relationship demonstrates in an absolute sense: 
This relationship shows how the orthometric height HA is related to the geometrical ellipsoidal height obtained from GPS measurements hA and the physical geoid/ellipsoid separation NA. The relationship however, is not always appropriate due to the physical way in which GPS surveys are conducted; in general it is more suited to use the following relative case of Eq. (1). 
Eq. (2) shows the relationship with respect to relative differences for the orthometric heights HA and HB, the ellipsoid heights hA and hB and the physical geoid/ellipsoid separations NA and NB. This relationship allows differential GPS measurements to be used, which are known to be more precise and in conjunction to this geoid models are now becoming more precise and are constantly pushing the 1cm level of accuracy. Having such accurate information in the form of the geoid and ellipsoid heights enables Geomatics Engineers and other research Scientist to apply this information in their respective fields thus realistically providing the opportunity for GPS to be used in GPS levelling and other applications. Studies carried out on the geoid and GPS/Levelling, in different countries show that GPS and the geoid are now more than ever important tools, such studies are (Kotsakis and Sideris.,, 1999), (Mainville et al., 1997), (Zhong., 1997) and (Martensson, 2002). In Malaysia computing the geoid has been of prime interest in the past and geoid models have been computed for either the whole of Peninsular Malaysia or a part thereof, see (Kadir et al., 1999) and (Vella et al., in press). Peninsular Malaysia is a country traversed north and south by very rugged mountain ranges that have largely prevented access to the hinterland for conventional terrestrial gravity surveys. All previous attempts at computing the geoid in Peninsular Malaysia have suffered from lack of data and non-homogeneity of the data distribution. However the Department of Surveying and Mapping Malaysia (DSMM) have embarked upon a very ambitious project to collect new gravity data and update the existing database through the use and implementation of airborne gravity surveys. This provides the impetus for the current study in that the new data will provide new geoid models, which in turn will benefit from studies showing which is the most appropriate technique to apply for corrector surfaces (CS) in Peninsular Malaysia. Corrector surfaces need to be applied as the relationship in Eq. (1) is rarely satisfied, reasons for this are as described in (Kotsakis and Sideris., 1999). These might be, (1) random noise in the ellipsoidal heights, orthometric heights or geoid/ellipsoid separations, (2) datum inconsistencies and other systematic distortions, (3) various geodynamic effects and (4) theoretical approximations in the computation of either the orthometric height (H) or the geoid/ellipsoid separation (N) are not good enough. Peninsular Malaysia lies well away from any major subduction zones, the possible reasons for (3) could well be land subsidence at tide gauges used for the vertical datum and or mean sea level rise. This however is not investigated here and is beyond the scope of this work.
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