Uncertainties in GPS Positioning ：A Mathematical Discourse

Publication subTitle ：A Mathematical Discourse

Author： Oxley   Alan  

Publisher： Elsevier Science‎

Publication year： 2017

E-ISBN: 9780128097878

P-ISBN(Paperback): 9780128095942

Subject： O29 applied mathematics

Keyword： 数学

Language： ENG

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Description

Uncertainties in GPS Positioning: A Mathematical Discourse describes the calculations performed by a GPS receiver and the problems associated with ensuring that the derived location is a close match to the actual location. Inaccuracies in calculating a location can have serious repercussions, so this book is a timely source for information on this rapidly evolving technology.

  • Covers how a GPS receiver works and how the earth is modeled so position data can be calculated
  • Discusses the different signals and clock speeds of the satellites, the receivers, and sources of inaccuracy
  • Examines how the errors are distributed in the data and provides examples

Chapter

Front Cover

Uncertainties in GPS Positioning: A Mathematical Discourse

Copyright

Contents

List of Figures

List of Tables

Preface

Chapter 1: Positioning and Navigation Systems

Navigation

Wireless Positioning Systems

Positioning Techniques

Limits in the Accuracy of Wireless Positioning

Innovative Positioning Techniques

Further Reading

Reference

Chapter 2: Introduction to GPS

Satellite-Based Systems

GPS

Context and Applications

Surveying

Location-Based Services

Map Making

Sports Data

Uncertainty in GPS Positioning

GNSSs Usage Patterns

Nonpositioning Uses of GPS

Time and Frequency Measurements

GPS Receivers

Measurement Techniques

One-Way

Common-View

Carrier-Phase Common-View

Further Information

Estimating the Distance to a Golf Flagstick

GPS

Laser Ranging

Comparison Between GPS and Laser Ranging

Receiver Specifics

An Interesting Aside

Further Reading

References

Chapter 3: Basic GPS Principles

Clocks

Ground Segment

Space Segment

User Segment

GPS Services

Performance of GPS

GLONASS

Galileo

Referencing a Position

Inertial Reference Frame

Earth-Centered, Earth Fixed (ECEF)

Geographic Coordinates

Satellites in Orbit

Kepler’s Laws and Orbital Dynamics

Navigation Signals

Navigation Signal

Navigation Data

Data Content

Differential Positioning

Classifications of Differential Positioning

Absolute/Relative Differential Positioning

Real-Time/Postprocessed Differential Positioning

Large-Scale DGPSs

The Process of Differencing

Single Difference

Double Difference

Triple Difference

Relativity

The Ionosphere and the Troposphere

Ionospheric Scintillation

Further Reading

References

Chapter 4: Signals From Satellites to Receiver—GPS

GPS Signal Structure

Carrier Signal

Exercises

C/A and P(Y) Codes

Data

Navigation Processing

Further Reading

Chapter 5: GPS Modernization

Frequency Plan

Multiple Access

C/A, L1 P(Y)

L2 P(Y)

Improved Pseudodistance Calculations

GPS Receiver

Signal Acquisition

Signal Tracking

Code Delay Tracking: The DLL

Reference

Chapter 6: Signals From Satellites to Receiver—Other Satellite Navigation Systems

Galileo Signal Structure

Frequency Plan

Galileo E1

GLONASS

System Characteristics

GLONASS Ground Segment

GLONASS Space Segment

GLONASS Navigation Signals

Compass/BeiDou and Regional GPSSs

Chapter 7: Solution of an Idealized Problem

The Competition

Satellites

Pseudodistances

Further Assumptions

Challenges

Solutions

Solutions to Problem 1

Suggested Result

Note on Problem Posed

Problem 1: Methodology

Variation of Coordinates

Solution to Problem 2

Reference

Chapter 8: Sources of Inaccuracy

Deliberate Interference With GPS Signals

Degradation of Physical Equipment

Other Vulnerabilities

Inertial Navigation System

Accuracy

Errors and Error Corrections

Scope of Errors

Sources of Errors

Ground Segment

Ephemeris Errors

Space Segment

Satellite Clock Error

User Segment

Navigation Receiver

Signal Propagation

Data Content

Data Structure

Error Detection and Correction

Error Identification

Syndrome

Example

Symbol Rate

Error Magnitudes

Ranging and Positioning

Ranging

Positioning

GPS UERE Budgets

Differential Positioning

Overview of Differential Corrections

Error Review

Common Errors (ε0)

Correlated Errors (εc)

Uncorrelated Errors (εuc)

Further Reading

Reference

Chapter 9: Learning From Experience

Studying Past Data

Mitigating Risks

Reducing Error Magnitudes When Surveying

Reference

Chapter 10: Error Distribution in Data

Solutions

Suggested Result

Supplementary Result

Problem 2: Methodology

References

Chapter 11: Improving Accuracy With GPS Augmentation

Using Two GNSSs

Single-Epoch Ambiguity Resolution

Landing Aircraft

Augmentation Complications

Other Augmentation Systems and Assisted GNSS

Satellite-Based Augmentation Systems

Network RTK

Assisted GNSS

Assisted GPS Standards

References

Chapter 12: GPS Disciplined Oscillators

How a GPSDO Works

GPSDO Performance

Choosing Between a GPSDO and a Rubidiumor Cesium Standard

References

Appendix A: Calibration of a GPS Receiver Used as a Time Reference

Reference

Appendix B: Comparing Time and Frequency Standards Between Laboratories

Reference

Appendix C: Calibration of GPS Receivers: Comparing Laboratories

Reference

Appendix D: Possible Use of a GPS Receiver as an Acceleration Sensor

Reference

Appendix E: Notes on the Error Distribution in Data

Problem 2: Notes

Bibliography

Index

Back Cover

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