GNSS in Practical Determination of Regional Heights - Global Navigation Satellite Systems: Signal,Theory and Applications - page 139

levelling observations the relative accuracy of Helmert orthometric heights is reported as 0.2
ppm by Çelik et al. (2002). The GNSS coordinates are in ITRF96 datum, while the
orthometric heights are in TUDKA99 datum.

The distribution of the 109 GNSS/levelling benchmarks is homogenous but rather sparse, and
given the rough topography of the region, the coverage of the benchmarks cannot characterize
the topographic changes well. The reference point density is 1 benchmark per 165 km 2 .
Figure 8 shows the reference network benchmarks on the topographic map of the area.

model point
test point

IZNIK LAKE

Longitude ( ° E)

Fig. 8. Geoid reference benchmarks in Sakarya (topographic data from SRTM3 (USGS, 2010)

3.1.2 Methods

Since the computation algorithms, applied for local GNSS/levelling geoid determination in
the study, are not able to detect potential blunders in data sets, the geoid heights derived
from the observations at the benchmarks were statistically tested and the outliers were
cleaned before modelling the data (see Erol (2011) for a case study in screening the reference
data before geoid modelling). After removing the outliers from data sets, in Istanbul data,
uniformly distributed 200 points of 1205 reference benchmarks (approximately 16% of the
entire data) were selected to form the test data, and the remaining 1005 benchmarks were
used in computation of the geoid. Similarly, in Sakarya, 14 of the 109 data points (nearly
13% of all data) having homogenous distribution were selected and used for external tests of
the geoid model. The model and test points are distinguished with different marks on
Figures 7 and 8. The theoretical review of the applied surface interpolation methods and
comparisons of their performances by means of the test results are provided in the next
section.

3.1.2.1 Polynomials

The polynomial equation for representing a local geoid surface based on the discrete
reference benchmarks with known geoid heights in the closed form is: