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On the numerical solution of parameters of the least squares modification of stokes' formula
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment.
2005 (English)In: Window on the Future of Geodesy / [ed] Sanso, F, 2005, Vol. 128, 403-408 p.Conference paper (Refereed)
Abstract [en]

In regional gravimetric geoid determination, it has become customary to utilize the modified Stokes formula, which combines local terrestrial data with a global geopotential model (GGM). A modification method, proposed by L.E. Sjoberg in 1984 (with later developments), allows least squares minimization of the influence of any error source in geoid modelling. In this approach, depending on the local gravity data quality, the chosen radius of integration, and the characteristics ,of the used GGM, the modification parameters s(n) vary. New satellite gravity missions are expected to improve significantly the accuracy of geopotential models. Of particular interest of this study is to evaluate the impact of future (i.e. post-GOCE) geopotential coefficients. A set of least squares modification parameters is determined from the system of linear equations, aiming at minimizing the global mean square error of geoid estimator. Some difficulties may be encountered when practically computing the modification parameters. In particular, for certain parameters the design matrix suffers from numerical ill-conditioning. Importantly, Tikhonov regularization is satisfactory in providing a solution for the modification parameters. Numerical results are presented to illustrate the applicability of the obtained parameters in geoid modelling by comparing with GPS-levelling data.

Place, publisher, year, edition, pages
2005. Vol. 128, 403-408 p.
Keyword [en]
Stokes' formula, modification, regularization
National Category
Civil Engineering
URN: urn:nbn:se:kth:diva-42766ISI: 000229368000069ScopusID: 2-s2.0-84963995270ISBN: 3-540-24055-1OAI: diva2:447810
General Assembly of the International-Association-of-Geodesy Location: Sapporo, JAPAN Date: JUN 30-JUL 11, 2003
QC 20111013Available from: 2011-10-13 Created: 2011-10-12 Last updated: 2011-10-13Bibliographically approved

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