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Wissenschaften
GEOID ESTIMATION THROUGH GPS OBSERVATIONS
R. Barzaghi, A. Borghi
DIIAR Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano
D. Dominici
Dipartimento di Architettura ed Urbanistica, Università di L’Aquila, Monteluco di Roio, 67100 L’Aquila
S. Gandolfi
DISTART, Facoltà di Ingegneria, Università di Bologna, Viale Risorgimento 2, 40136 Bologna
Commission VI, Working Group 3
KEY WORDS: GPS, geoid, interpolation
ABSTRACT
GPS observations are more and more used for different purposes. Monitoring deformations caused by
landslide, earthquakes and volcanism has nowadays become possible on a large scale using GPS
techniques. Furthermore, GPS is used in connection with photogrammetry, both for field survey and the
determination of the camera position at shutter release time. Kinematic positioning with GPS is also applied
to terrestrial navigation, in the perspective of its fully automatic control. On a more geodetic side, GPS is a
powerfull tool for checking the precision of a gravimetric geoid estimate. By combinig GPS derived height
and spirit leveling, geoid undulations can be obtained and compared with geoid estimates coming from e.g.
Stokes formula. Besides, this method can be used to derive directly the geoid without knowing gravity, by
directly interpolating a set of observed undulations. In this paper, this way of getting the geoid is revised and
critically analyzed, to possibly define a procedure to get reliable estimates. Numerical tests on simulated data
are presented and discussed and different interpolation methods are compared.
using S-Plus.
'ariate Statistik.
Methods. Me
1. INTRODUCTION
1.1 GPS derived undulations
The basic equation which allows geoid estimation
through GPS observations is the well known formula
(Heiskanen and Moritz, 1967)
N = h - H (1)
orthometric height
where h is the ellipsoidal height from GPS, H is the
orthometric height from spirit leveling and N is the
geoid undulation. This equation holds in an
approximate way but its accuracy is in any case
sufficient for practical purposes.
Hence, by performing GPS observations on spirit
leveling benchmarks, pointwise geoid undulation
values can be obtained.
This values can be then interpolated to get a local
estimate of the geoid to be used in connection with
GPS measuremets to derive orthometric heights. By
simlpy rewriting equation (1) in the following way
H = h - N (2)
the so called GPS leveling method can be applied to
get H. Although the precision of H obtained in this
way is by no means less than the one obtained by
spirit leveling, GPS levelling is much faster than
spirit leveling. So, for standard medium precision
height surveys, this new techinque is preferred.
The weak point of this procedure applied to get H, is
basically related to the precision of the geoid
estimate that one can get by interpolating the point
estimate of N. There are still many open problems in
doing such an operation and many misleading ways
of performing it. The worst way of estimating a geoid
