Thursday 25 August 2005

G1

PTH0005
Total least squares estimation of harmonic functions coefficients in Polar motion time series
Akyilmaz, Orhan¹, Kutterer, Hansjörg²
1 Ohio State University, Columbus, Ohio, USA
2 Geodetic Institute, University Of Hannover, Germany
Author email: kutterer@gih.uni-hannover.de
The classical estimation theory is based on least squares (LS) solution of a linearised system of equations. In this case, only the observation vector is assumed to be erroneous. The possible errors in design matrix of the estimation problem is usually ignored. However, in some cases, the design matrix elements are considered as stochastic as well. One way to take the errors in design matrix elements into account is the total least squares (TLS) estimation. TLS approach is quite new in mathematical literature as well as in geodetic science. The TLS solution of an estimation problem is based on the singular value decomposition properties in matrix algebra. It provides estimations not only for unit weighted problems but also for the problems where the covariances of observations as well as of the design matrix elements are different. In this study, the TLS approach was applied for the estimation of the coefficients of a harmonic function that describes the polar motion process. To this end, the C04 time series of the Earth rotation parameters broadcasted by the IERS (International Earth Rotation Service) was used as data set. In particular, the residuals of the estimated model coefficients were analysed in detail.

Return to Poster Presentations