Report of IAG Special Commission 1
for the period 1995 - 1999
Erik W. Grafarend
Department of Geodesy and GeoInformatics
Stuttgart University
Geschwister-Scholl-Str. 24D
D-70174 Stuttgart


The period of work within the years 1995 - 1999 was a very fruitful one. More than five hundred papers relating to the topics of SC#1 were published and documented in
SC#1-Bulletins 1995.1, 1996.1, 1997.1, 1998.1 and 1999.1 (200 pages).

SC#1 operates in five subcommissions.

Subcommission 1 ("Statistics ) is chaired by A. Dermanis, Aristoteles University Thessaloniki/Greece. The Subcommission Report highlights the IAG International Summer School "Data Analysis and the Statistical Foundations of Geomatics (Ghania/Crete/Greece, 25-30 May 1998) as well as recent geodetic and non-geodetic work related to Subcommission 1. In addition B. Schaffrin and P. Xu (Kyoto University) presented an extension to this report completing the reviewing process of related literature. Highlights during the period of work have been (i) integer least-squares applied to
GPS-double difference carrier phase observations, (ii) random tensor statistics for stress and strain, (iii) variance-covariance component estimation, (iv) Kalman-Bucy filtering of geodetic data, (v) robust estimations, (vi) Kolmogorov structure function/Krige variogram/variance-covariance functions of higher order increments, (vii) weak unbiasedness, (viii) Bayesian estimation and (ix) statistics of geodetic datum transformations.

Both quoted reports are published in SC#1-Bulletin 1999.2. Particularly, Lubomir and Ludmila Kubacek have to be mentioned, our liaison professors to Mathematical Statistics who supported Subcommission 1 ("Statistics ) by book and paper reviews on non-linear regression.

Subcommission 2 ("Numerical and Approximations Methods ) chaired by W. Freeden, The University of Kaiserslautern/Germany, presented a great review paper entitled "Constructive Approximation and Numerical Methods in Geodetic Research Today - An Attempt of a Categorization Based on an Uncertainty Principle which has been accepted by Journal of Geodesy as a review paper on the topics of Subcommission 2. In addition the SC#1 president added an extensive literature list to SC#1-Bulletin 1999.1.

Subcommission 3 ("Boundary Value Problems ) was chaired by SC#1 president. He presented three review papers entitled (i) The spheroidal fixed-free two-boundary value problem for geoid determination (The spheroidal Bruns transform) by E. Grafarend, A. Ardalan (Stuttgart University/Germany) and M.G. Sideris (University of Calgary/Canada), (ii) The form parameters of the Sonigliana-Pizzetti level ellipsoid from current best estimates of fundamental geodetic parameters based on a functional analytic review of the Sonigliana-Pizzetti gravitational field by E. Grafarend and A. Ardalan (Stuttgart University/Germany) and (III) Boundary value problems in the complex world of geodetic measurements by R. Lehmann (Dresden Polytechnion/Germany).

All three review papers will be published in the Journal of Geodesy on behalf of SC#1. The topics include two-boundary value problems, the Somigliana-Pizzetti level ellipsoid boundary value problem, altimetry-gravimetry boundary value problems, gravitational boundary value problems, pseudo-boundary value problems, overdetemined and constrained boundary value problems. The Subcommission Chairman has added an impressive list of reference papers. Particular mention has to be made to the Slepian problem on the sphere introduced by A. Albertella, N. Sueeuw and F. Sanso. In the report period with support from SC#1 two books appeared, namely (i) A. Marchenko: Parameterization of the Earth’s gravity field and (ii) Z. Martinec: Boundary-value problems for gravimetric determination of a precise geoid.

Unfortunately from the Subcommission 4, chairman J. Zund/Las Cruces/USA, no report reached SC#1. A review of Subcommission 4 ("Geometry, relativity, cartography ) activities has accordingly been given by SC#1 president. He gave an extensive update of extractive highlighting the following research items: (i) map projections of the reference ellipsoid of revolutions, (ii) boundary value problems of the Korn-Lichtenstein equations which generate conformal mapping, (iii) datum transformation of UTM and Gauss-Krueger coordinates, (iv) pseudo-Riemann geometry of 1-PN-space-time, (v) relativistic equations of multibody dynamics.

Finally Subcommission 5 ("Theory of orbits and dynamics of systems ) under its chairman R.J. You/Tainan University/Taiwan focussed on (i) gravity field determination by dynamic satellite geodesy, (ii) precise orbit computation, (iii) relativistic orbit computation and (iv) modelling of non-gravitational forces on satellite motions. R.J. You presented an extensive review on the highlights of Subcommission 5 with an extensive reference list.

All quoted references and reports can be asked from SC#1/President 1991-1999/Erik W. Grafarend, Department of Geodesy and GeoInformatics, Stuttgart University, Geschwister-Scholl-Str. 24D, D-70174 Stuttgart, Germany, fax +49-711-121-3285,

e-mail: grafarend