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2016 | Buch

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GPS

Theory, Algorithms and Applications

verfasst von: Guochang Xu, Yan Xu

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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, the basics 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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The Global Positioning System (GPS) is a navigation system based on satellite technology. Its fundamental technique involves measuring the ranges between the receiver and a few simultaneously observed satellites, and the positions of the satellites are forecasted and broadcasted along with the GPS signal to the user. Through several known positions (of the satellites) and the measured distances between the receiver and the satellites, the position of the receiver can be determined. The position change, which can also be determined, is then the velocity of the receiver. The most important applications of GPS are positioning and navigation.

Guochang Xu, Yan Xu

Chapter 2. Coordinate and Time Systems

Abstract

GPS satellites orbit the earth over time. GPS surveys are conducted mostly on land. To describe the GPS observation (distance) as a function of GPS orbit (satellite position) and the measuring position (station location), suitable coordinate and time systems must be defined.

Guochang Xu, Yan Xu

Chapter 3. Satellite Orbits

Abstract

The principle of the GPS system is to measure the signal transmission paths from the satellites to the receivers. Therefore, the satellite orbits are very important topics in GPS theory. In this chapter, the basic orbits theory is briefly described.

Guochang Xu, Yan Xu

Chapter 4. GPS Observables

Abstract

The basic GPS observables are code pseudoranges and carrier phases as well as Doppler measurements. The principle of the GPS measurements and their mathematical expressions are described.

Guochang Xu, Yan Xu

Chapter 5. Physical Influences of GPS Surveying

Abstract

This chapter covers all physical influences of GPS observations, including ionospheric effects, tropospheric effects, relativistic effects, earth tide and ocean loading tide effects, clock errors, antenna mass centre and phase centre corrections, multipath effects, anti-spoofing and historical selective availability, and instrumental biases. Theories, models, and algorithms are discussed in detail.

Guochang Xu, Yan Xu

Chapter 6. GPS Observation Equations and Equivalence Properties

Abstract

In this chapter, we begin with a discussion of the general mathematical model of GPS observation and its linearisation. All partial derivatives of the observation function are given in detail. These are necessary for forming GPS observation equations. We then outline the linear transformation and covariance propagation. In the section on data combinations, we discuss all meaningful and useful data combinations, such as ionosphere-free, geometry-free, code–phase combinations, and ionospheric residuals, as well as differential Doppler and Doppler integration. In the data differentiation section, we discuss single, double, and triple differences and their related observation equations and weight propagation. The parameters in the equations are greatly reduced through difference forming; however, the covariance derivations are tedious. In the last two sections, we discuss the equivalent properties between the uncombined and combining and the undifferenced and differencing algorithms. We propose a unified GPS data processing method, which is described in detail. The method is selectively equivalent to the zero-, single-, double-, triple-, and user-defined differential methods.

Guochang Xu, Yan Xu

Chapter 7. Adjustment and Filtering Methods

Abstract

In this chapter, we outline the most useful and necessary adjustment and filtering algorithms for statistical and kinematic as well as dynamic GPS data processing. We derive the necessary estimators, and provide a detailed discussion of the relationships between the methods presented.

Guochang Xu, Yan Xu

Chapter 8. Cycle Slip Detection and Ambiguity Resolution

Abstract

Ambiguity problems can arise during phase measurement when the receiver loses its lock on the signal, and phase measurement must be reinitiated. This phenomenon is called cycle slip, i.e. the cycle count must begin again because of a signal interruption. The consequence of a cycle slip is an observable jump by an integer number of cycles in the adjacent carrier phase, and a new ambiguity parameter is required in the related observation model. Accurate cycle slip detection thus ensures correct ambiguity parameterisation. Here, we begin with a discussion of cycle slip detection, after which we will focus on integer ambiguity resolution, including integer ambiguity search criteria. We also provide an outline and discussion of the historical ambiguity function method.

Guochang Xu, Yan Xu

Chapter 9. Parameterisation and Algorithms of GPS Data Processing

Abstract

The parameterisation problems of the bias parameters in the GPS observation model are outlined in Sect. 12.1 of the first edition of this book.

Guochang Xu, Yan Xu

Chapter 10. Applications of GPS Theory and Algorithms

Abstract

In this chapter, we discuss software development using GPS theory and algorithms, and present a concept of precise kinematic positioning and flight-state monitoring of an airborne remote sensing system.

Guochang Xu, Yan Xu

Chapter 11. Perturbed Orbit and Its Determination

Abstract

Satellites are attracted not only by the central force of the earth, but also by the non-central force, the attraction forces of the sun and the moon, and the drag force of the atmosphere. They are also affected by solar radiation pressure, earth and ocean tides, general relativity effects (cf. Chap. 5), and coordinate perturbations. Equations of satellite motion must be represented by perturbed equations. In this chapter, after discussions of the perturbed equations of motion and the attraction forces, for convenience of the earth tide and ocean loading tide computations, the ephemerides of the sun and the moon are described. Orbit correction is discussed based on an analysis solution of the \( \overline{C}_{20} \) perturbation. Emphasis is given to the precise orbit determination, which includes the principle of orbit determination, algebraic solution of the variation equation, numerical integration, and interpolation algorithms, as well as the related partial derivatives.

Guochang Xu, Yan Xu

Chapter 12. Singularity-Free Orbit Theory

Abstract

The previous chapter (Chap. 11) of this book covered the most important content regarding numerical satellite orbit determination theory and algorithms. In this chapter, the emphasis will be on singularity-free orbit theory.

Guochang Xu, Yan Xu

Chapter 13. Discussions

Abstract

The previous chapters of this book covered the most important material regarding static, kinematic, and dynamic GPS, including theory, algorithms, and applications.

Guochang Xu, Yan Xu

Backmatter

Titel: GPS
verfasst von: Guochang Xu
Yan Xu
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-662-50367-6
Print ISBN: 978-3-662-50365-2
DOI: https://doi.org/10.1007/978-3-662-50367-6