Global Positioning System Reference
In-Depth Information
In the content of numerical tests, beside the global models, the most recent regional geoids
TG03 and TG09 were also validated against the GNSS/levelling heights at the test
benchmarks. The validation results showed that although TG09 model provided
approximately 12% improvement comparing to TG03 in terms of accuracy of geoid heights,
the absolute accuracy of regional geoid models is not yet below 10 cm. This indicates that
the regional geoid models remain insufficient to be applied for GNSS levelling purposes in
large scale map production and applications that require centimetre level accuracy in
heights. Since the lack of a 5-centimetre or higher precision regional geoid in the country;
local geoid models, as an alternative solution for height transformation problems, are
determined and used. This chapter presents examples of local geoid modelling using
geometric approach, at the two case study areas, Istanbul and Sakarya situated in the north
east of Turkey, which have precise GNSS/levelling data. Also from the test results of the
computed local geoids, it is obvious that the topographic character of the local area, the
quality of GNSS and levelling data, the density and distribution of the geoid reference
benchmarks are very critical for the accuracy and reliability of the local geoid model. As
such the design of the geoid reference network and data acquisition needs to be planned in a
specific manner. Applied methodology for modelling the local geoid is another critical
parameter that affects the final accuracy. In the numerical tests, the Istanbul and Sakarya
local geoids were computed using classical polynomial type multi regression equations and
ANFIS method. In Istanbul a fifth order polynomial equation fitted the best the reference
geoid data, where as in Sakarya a fourth order polynomial was decided as an optimal
model. Evaluation of the polynomial models at the test benchmarks revealed ±4.4 cm and
±20.4 cm absolute accuracies in Istanbul, and Sakarya, respectively. When the topographies
and densities of the benchmarks in both local areas are compared, the difference between
the accuracies of the polynomial representations of two local geoids can be understood
(Figure 7 vs. Figure 8). On the other hand the ANFIS approach provided marked
improvements in results with ±3.5 cm and ±18.9 cm accuracies, in Istanbul and Sakarya.
TG03 regional geoid model has ±10.8 cm and ±18.6 cm accuracies in Istanbul and Sakarya.
When comparing the regional model, in Istanbul, a local geoid model provides much better
accuracy but in Sakarya many of the local geoid model solutions did not provide a better
alternative to regional geoid for GNSS levelling purposes. The numerical tests on the local
geoid modelling also provided an opportunity to compare the two surface approximation
techniques. Hence it is concluded that although, ANFIS has a developed computation
algorithm and potential to provide more improved results, it has handicaps from a practical
point of view: the prediction capability of this method varies depending on the adopted
architecture and it is too sensitive to the selection of the reference/test points. Therefore,
while geoid modelling with ANFIS, one must be very carefully to employ the appropriate
architecture and to decide reference and test data. Otherwise too optimistic and unrealistic
statistics can appear with an over fitted surface model.
In the final part of this chapter, local improvement of geoid models is provided as another
alternative solution to GNSS levelling. In the case study, local improvement of the TG03 in
Çankırı using precise GNSS/levelling data, by corrector surface fitting and adjustment of
derived orthometric height differences on the baselines, is presented. The accuracy of TG03
model in the region is ±26.2 cm. Applying least squares adjustment of height differences
derived from GNSS and TG03 on the baselines approach provided 42% improvement in the
model and the RMSE of the orthometric heights derived from the improved version of TG03
is reported as ±15.0 cm.
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