Theory and Realization of Reference Systems
After a short introduction on the basics of reference system theory and its application for the description of earth rotation, the problem of establishing a reference system for the discrete stations of a geodetic network is studied, from both a theoretic
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference Systems in Motion: Generalized Euler Kinematic Equations – The Rotation Vector Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference Systems for the Description of Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . . The Realization of a Reference System Within Data Analysis, in the Case of Rigid Geodetic Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Least Squares Estimation for Models Without Full Rank Utilizing Minimal Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematical Modeling of Spatiotemporal Reference Systems for a Deformable Geodetic Network: Deterministic Aspects and Reference System Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reference System Definition in the Analysis of Coordinate Time Series . . . . . . . . . . . . Various Types of Minimal Constraints for the Definition of a Spatiotemporal Reference System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Posteriori Change of the Spatiotemporal Reference System . . . . . . . . . . . . . . . . . . . . 9.1 Conversion to a Solution Satisfying Some Type of Inner Constraints . . . . . . . . . 9.2 Conversion to a Solution Satisfying Some Type of Partial Inner Constraints . . . . 9.3 Conversion to a Solution Satisfying Different Constraints for Initial Coordinates and Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematic Minimal Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transforming a Network Reference System into an (Approximate) Earth Reference System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formulation of the International Terrestrial Reference Frame: Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basics of Data Set Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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This chapter is part of the series Handbuch der Geodäsie, volume “Mathematical Geodesy/ Mathematische Geodäsie”, edited by Willi Freeden, Kaiserslautern. A. Dermanis () Department of Geodesy and Surveying (DGS), Aristotle University of Thessaloniki, Thessaloniki, Greece E-Mail: [email protected]
© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 W. Freeden, R. Rummel (Hrsg.), Handbuch der Geodäsie, Springer Reference Naturwissenschaften, https://doi.org/10.1007/978-3-662-46900-2_107-1
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