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Use of Similarity Transformations to Improve GPS Heighting
5.2 Adjustment Results for National Compartments
Figure 2, shows the national distribution of 140 GPS points, it is clearly seen from Figure 2 that the hinterland is largely uncovered by any kind of geodetic information, be it gravity, GPS or levelling. When test are carried out for the whole 140 GPS points distributed nationally through out Peninsular Malaysia, it is evident as is shown in Table 4, that the fit of the CG2 to the national data set is not too good. The mean of 0 indicates that all the schemes are capable of removing any bias however the large standard deviations indicate there are still discrepancies between the three components, h, H and N. These discrepancies may be due to systematic biases, or simple errors in the data and the results from Tables 2 and 3 would tend to suggest they are geographically correlated, in these Tables only 25 data points for Johor were used as opposed to the data set containing 140 data points for the whole of the Peninsular Malaysia. Table 4: Statistical summary using CG2 to derive the coefficients for the similarity transformation and polynomial fitting at 140 GPS points
 Figure 2: Distribution of 140 GPS points for Peninsular Malaysia In order to determine if this is so, tests are conducted were the whole data set is broken down into individual compartments based on States, as is shown in Figure 3.  Figure 3: Distribution of 140 GPS points for Peninsular Malaysia, based on their respective State This is similar to what was conducted in France, (eg. Zhiheng and Duquenne, 1996) where the geoid was divided up into smaller pieces and then adjusted to the GPS levelling with constraint conditions applied, in this case there will be no constraint conditions applied. This is due largely to the fact that the necessary information is not available, therefore it is considered a semi-rigorous attempt to model the spatial differences there may be between the three components of the observation equations. Tables 5 through to Table 10 , show the results for all States included, and only with the eight parameter transformation, CS8 as this has already proven to be a well developed scheme, see Tables 2 and 3. |