Global Positioning System Reference
In-Depth Information
3. Local GNSS/levelling geoids
Among the computation methods of geoid models (see e.g. Schwarz et al., 1987;
Featherstone, 1998; Featherstone, 2001; Hirt and Seeber, 2007; Erol et al., 2008; Erol et al.,
2009), geometric approach that GNSS and orthometric heights (h and H, respectively) can be
used to estimate the position of the geoid at discrete points (so called geoid reference
benchmarks) through a simple relation between the heights (N ≈ h-H) provides a practical
solution to the geoid problem in relatively small areas (typically a few kilometers)
(Featherstone et al., 1998; Ayan et al., 2001, 2005; Erol and Çelik, 2006). This method
addresses the geoid determination problem as “describing an interpolation surface
depending on the reference benchmarks” (Featherstone et al., 1998; Erol et al., 2005; Erol &
Çelik, 2006; Erol et al., 2008). The approximate equality in the equation arises due to the
disregard for the deflection of the vertical that means the departure of the plumbline from
the ellipsoidal normal (Heiskanen and Moritz, 1967). However the magnitude of error
steming from this oversight is fairly minimal and therefore acceptable for the height
transformation purposes (Featherstone, 1998).
The data quality, density and distribution of the reference benchmarks have important role
on the accuracy of local GNSS/levelling geoid model (Fotopoulos et al., 2001; Fotopoulos,
2005; Erol & Çelik, 2006; Erol, 2008, 2011). There are certain criteria on the geoid reference
benchmark qualities and locations, as described in the regulations and reference topics
(LSMSDPR, 2005; Deniz&Çelik, 2007) that will be mentioned in the text that follows. On the
other hand using an appropriate surface approximation method in geoid modelling with
geometrical approach is also critical for the accuracy of the model. The modelling methods
are various but those most commonly employed among are; polynomial equations (of
various orders) (Ayan et al, 2001; Erol, 2008; Erol, 2011), least squares collocation (Erol and
Çelik, 2004), geostatistical kriging (Erol and Çelik, 2006), finite elements (Çepni and Deniz,
2005), multiquadric or weighted linear interpolation (Yanalak and Baykal, 2001). In addition
to these classical methods, soft computing algorithms such as artificial neural networks
(either by itself, see e.g. Kavzaoğlu and Saka (2005) or as part of these classical statistical
techniques, e.g. Stopar et al. (2006)), adaptive network-based fuzzy inference systems
(ANFIS) (Yılmaz and Arslan, 2008) and wavelet neural networks (Erol, 2007) were also
evaluated by researchers in the most recent investigations on local geoid modelling.
3.1 Case studies: Istanbul and Sakarya local geoids
In this section, we discuss and explain the handicaps and advantages of geometric approach
and local geoid models from the view point of transformation of GNSS ellipsoidal heights.
This includes two case studies: Istanbul and Sakarya local geoids, using polynomial
equations and ANFIS methods.
3.1.1 Data
One of the case study areas, Istanbul, is located in the North West of Turkey (between 40°30'
N - 41°30' N latitudes, 27°30' E - 30°00' E longitudes, see Figure 7). The region has a
relatively plain topography and elevations vary between 0 and 600 m. The GNSS/levelling
network (Istanbul GPS Triangulation Network 2005, IGNA2005) was established between
2005 and 2006 as a part of IGNA2005 project (Ayan et al., 2006), and the measurement
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