Abstract:
Global Navigation Satellite Systems (GNSS) have been used widely in 3‐dimensional
positioning globally, regionally and locally. Global Positioning System (GPS) is one of
the most extensively used GNSS in Earth sciences. GPS which employs World
Geodetic System adopted in 1984 (WGS84) as the reference system has extensively
been used for height determination and has brought a revolution on how relative
and absolute heights on earth’s surface are determined. GPS measures ellipsoidal
heights above a reference ellipsoid (WGS84). Although these heights can be useful
in deformation surveys, machine monitoring and guidance, they are not applicable
in engineering projects (e.g. sewer lines, pipelines and road construction among
others) where heights referenced to an equipotential surface (geoid) are required.
The separation between the geoid and a reference ellipsoid (geoid undulation) is
necessary in converting ellipsoidal height into orthometric height. In this study we
determine geoid undulation from Earth Gravitational Model of 2008 (EGM2008)
using freely available Alltrans EGM2008 calculator software version 3.002 at 18
GPS/levelling points. The determined geoid undulations are used to determine
estimated orthometric heights from ellipsoidal heights. We then model the
differences between spirit‐levelled orthometric and estimated orthometric heights
by a four parameter model (first order polynomial) at 11 GPS/levelling points using
least squares technique for improvement on the estimated orthometric heights. 7
GPS/levelling points are used for testing the performance of the four parameter
model over Nairobi County and its environs. The standard deviations of the
differences between observed and estimated orthometric heights (obtained from
EGM2008 and GPS) at all GPS/levelling points (18) and 7 test points are ±0.52 and
±0.35 m respectively. When the four parameter model is applied, the standard
deviations of the differences between spirit‐levelled and improved estimated
orthometric heights at the 7 test points reduces to ±0.10 m, representing an
improvement of 71%. The accuracy of ±0.10 m obtained at the test points may be
sufficient for some engineering projects that do not require very high orthometric
height accuracy.
