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Clock Synchronization and Navigation in the Vicinity of the Earth
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Authors: Thomas B. Bahder (Army Aviation and Missile Research, Development, and Engineering Center, Redstone Arsenal, Alabama) 
Book Description:
Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over satellite-to-ground
and satellite-to-satellite distances requires the use of general relativistic concepts. The role of geometrical optics and antenna phase center approximations are discussed in high accuracy work. The clock synchronization problem is explored from a general
relativistic point of view, with emphasis on the local measurement process and the use of the tetrad formalism as the correct model of relativistic measurements. The treatment makes use of J. L. Synge’s world function of space-time as a basic coordinate independent geometric concept. A metric is used for space-time in the vicinity of the Earth, where coordinate time is proper time on the geoid. The problem of satellite clock syntonization is analyzed by numerically integrating the geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit (GEO), and highly elliptical orbit (HEO) satellites. Proper time minus coordinate time is computed for satellites in these orbital regimes. The frequency shift as a function of time is computed for a signal observed on the Earth’s geoid from a LEO, GEO, and HEO satellite. Finally, the problem of geolocation in curved space-time is briefly explored using the world function formalism.

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Table of Contents:

1. Introduction, pp. 1-4

2. Hardware Time, Proper Time, and Coordinate Time, pp. 5-8
2.1 Synchronization versus Syntonization

3. Choice of a Physical Theory, pp. 9-17
3.1 Electromagetic Waves
3.2 The Geometrical Optics Approximation
3.3 Signal Detection and Use of Antenna Phase Center

4. World Function of Space-Time, pp. 19-22
4.1 Navigation in Curved Space-time

5. Physical Measurements, pp. 23-31
5.1 Observations and Measurements
5.2 Tetrad Formalism

6. Reference Frames and Coordinate Systems, pp. 33-36
6.1 Gravitational Warping of Coordinates

7. Clock Synchronization, pp. 37-45
7.1 Eddington Slow Clock Transport
7.2 Einstein Synchronization
7.3 GPS Clock Synchronization
7.4 Quantum Synchronization

8. The Syntonization Problem, pp. 47-71
8.1 Choice of Metric in Vicinity of the Earth
8.2 Integration of Geodesic Equations
8.3 Proper Time Minus Coordinate Time for Various Orbits
8.4 Proper Time Minus Coordinate Time: Numerical Results for Various Orbits
8.5 Observed Doppler and Gravitational Frequency Shift
8.6 Doppler Plus Gravitational Frequency Shift: Numerical Results for Various Orbits

9. Geolocation in Curved Space-Time, pp. 73-84
9.1 Time Difference of Arrival (TDOA) Geolocation
9.2 Doppler Effect in a Gravitational Field
9.3 Observed Doppler Shifts
9.4 Frequency Difference of Arrival (FDOA) Geolocation

10. Summary, pp. 85

Appendix. , pp. 87-91
A: Significance of Accurate Clock Synchronization for Geolocation
B: Conventions and Notation
C: Acknowledgment

References pp.93-99
Index pp.100-105

   Binding: Softcover
   Pub. Date: 2011 - 1st Quarter
   Pages: pp.105
   ISBN: 978-1-60692-114-2
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
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Clock Synchronization and Navigation in the Vicinity of the Earth