Guochang Xu

This reference and handbook describes the functional software library of the Global Positioning System (GPS/Galileo). It is the original software source-code of many functions, models, algorithms and tools described in the textbook "GPS – Theory, Algorithms and Applications" written by the same author published by Springer. The software functions are parts of the KSGsoft and MFGsoft programs developed by the author at the GFZ in Potsdam. All the source-code are verified by real GPS data processing applications. The software uses the books "GPS – Theory, Algorithms and Applications" as its theoretical description. The functional library covers physical models, disturbance models, mathematical methods, adjustment and filtering algorithms, the transformation, interpolation, integration methods, and numerous tools.

This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Glonass/Galileo/Compass). It is primarily based on source-code descriptions of the KSGsoft program developed at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multi-functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method, the diagonalisation algorithm, the adaptive Kalman filter, the general ambiguity search criteria, and the algebraic solution of variation equation reported in the first edition, the equivalence theorem of the GPS algorithms, the independent parameterisation method, and the alternative solar radiation model reported in the second edition, the modernisation of the GNSS system, the new development of the theory and algorithms, and research in broad applications are supplemented in this new edition. Mathematically rigorous, the book begins with the introduction, thebasics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, software development and data processing and the determination of perturbed orbits.

This reference and handbook describes theory, algorithms and applications of the Global Positioning System (GPS/Glonass/Galileo/Compass). It is primarily based on source-code descriptions of the KSGsoft program developed at the GFZ in Potsdam. The theory and algorithms are extended and verified for a new development of a multi-functional GPS/Galileo software. Besides the concepts such as the unified GPS data processing method, the diagonalisation algorithm, the adaptive Kalman filter, the general ambiguity search criteria, and the algebraic solution of variation equation reported in the first edition, the equivalence theorem of the GPS algorithms, the independent parameterisation method, and the alternative solar radiation model reported in the second edition, the modernisation of the GNSS system, the new development of the theory and algorithms, and research in broad applications are supplemented in this new edition. Mathematically rigorous, the book begins with the introduction, thebasics of coordinate and time systems and satellite orbits, as well as GPS observables, and deals with topics such as physical influences, observation equations and their parameterisation, adjustment and filtering, ambiguity resolution, software development and data processing and the determination of perturbed orbits.

The development of the orbits theory lags behind the development of satellite technology. This book provides, for the first time in the history of human satellite development, the complete third order solution of the orbits under all possible disturbances. It describes the theory of satellite orbits, derives the complete solutions of the orbital disturbances, describes the algorithms of orbits determination based on the theory, describes the applications of the theory to the phenomenon of the satellite formation physically. The subjects include: Orbits Motion Equations, Disturbance theory, Solutions of the differential Equations, Algorithms of Orbits determinations, Applications of the theory to the satellite formation.

The development of the orbits theory lags behind the development of satellite technology. This book provides, for the first time in the history of human satellite development, the complete third order solution of the orbits under all possible disturbances. It describes the theory of satellite orbits, derives the complete solutions of the orbital disturbances, describes the algorithms of orbits determination based on the theory, describes the applications of the theory to the phenomenon of the satellite formation physically. The subjects include: Orbits Motion Equations, Disturbance theory, Solutions of the differential Equations, Algorithms of Orbits determinations, Applications of the theory to the satellite formation.

The purpose of this reference and handbook is to describe and to derive the analytic solutionsoftheequationsofsatellitemotionperturbedbyextraterrestrialandgeo- tential disturbances of the second order. The equations of satellite motion perturbed by extraterrestrial disturbances are solved by means of discretization and appr- imated potential function as well as Gaussian equations. The equations perturbed by geopotential disturbances are solved by symbolic mathematical operations. The traditional problem of singularity in the solutions is solved by so-called singulari- free orbit theory. Simpli?ed disturbed equations of motion are proposed to simplify the solutions. Applications of the theory for analytic orbit determination are also discussed. Indeed, this is the ?rst book since the satellite era, which describes s- tematically the orbit theory with analytical solutions, with respect to all of extrat- restrial and geopotential disturbances of the second order, and the solutions are free of singularity. Based on such a theory, the algorithms of orbit determination can be renewed; deeper insight into the physics of disturbances becomes possible; the way to a variety of new applications and re?nements is opened. My primary knowledge of the orbit theory came from my education of mat- matics while studying physics and theoretical mechanics (1981). My ?rst practical experience with orbit came from the research activity at the Technical University (TU) Berlin on orbit corrections of the satellite altimetry data (1988–1992). The extensive experience on orbit came from the GPS/Galileo software development for orbit determination and geopotential mapping at the GFZ (2001–2004).

After the first edition of this book was published at the end of 2003, I was very happy to put the hard work of book writing behind me and concentrate myself with my small team on the development of a multi-functional GPS/Galileo software (MFGsoft). The experiences from the practice and the implementation of the theory and algorithms into the high standard software gave me a strong feeling that I would very much like to revise and to supplement the original book, to modify parts of the contents and to - port on the new progress and knowledge. Furthermore, with the EU Galileo system now being realised and the Russian GLONASS system under development; the GPS theory and algorithms should be re-described so that they are also valid for the Galileo and GLONASS systems. Therefore, I am grateful to all of the readers of this book, whose int- est made it possible so that the Springer asked me to complete this second edition. I remember that I was in a hurry during the last check of the layout of the first edition. The description of a numerical solution of the variation equation in Sect. 11. 5. 1 was added to the book at the last minute in a limited extension of exactly one page.