Far Eastern Mathematical Journal

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Establishment of a global three-dimensional kinematic reference frame using VLBI and DORIS data


M. D. Gerasimenko, A. G. Kolomiets, M. Kasahara, J.-F. Cr?taux, L. Soudarin

2005, issue 1-2, Ñ. 3–13


Abstract
The main aim of this paper is to provide an algorithm to combine VLBI (Very Long Baseline Interferometry) and DORIS (Doppler Orbitography and Radio positioning Integrated by Satellite) data sets into the same kinematics reference frame. In a first stage of computation the VLBI and DORIS networks are knitted together using the velocities of each station with their covariance matrices that were obtained from individual solutions. A sequential least squares adjustment was used. In a second stage of computation a method of iterative weighted similarity transformation has been elaborated. In order to fix the three-dimensional kinematic reference frame (KRF), a system of constraints or datum equations based on vertical component of some quasi-stable reference stations are used. This strategy provides a datum that is robust to unstable reference points and gives less distorted displacements. This method has been applied to the VLBI and DORIS data collected during the last decades. Without survey ties available, and consequently without relative velocities between collocated VLBI and DORIS points, we forced the velocities of collocated sites to the same value and constrained their root mean squares to be equal to zero. As VLBI information is formally for some stations ten times more precise than the DORIS information, reference frame and precision of the VLBI stations were practically not affected by this computation. But precision of DORIS station velocities of the joint network is improved by almost 15% and fairly close agreement between ITRF2000 solution, NNR Nuvel-1A model predictions, and our solution has been found. The technique presented provides a method to define KRF without any information from a geological plate motion model. It is thus possible to verify any geological model using only geodetic information itself.

Keywords:
linear transformations, matrix inversion, general inversion, kinematic reference frame, NNR NUVEL-1A plate model, VLBI, DORIS, ITRF2000

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