Wave Summit Course

"Very Long Baseline Interferometer"

Fujinobu Takahashi, Tetsuro Kondo, Yukio Takahashi, and Yasuhiro Koyama
published by Ohmsha Ltd.

ISBN 4-274-9378-8
ISBN 1 58603 076 0 (IOS Press)

The authors are members of the research staff at the Communications Research Laboratory. This book explains VLBI technology comprehensively and is aimed at university students and graduate students of science and engineering. It should be useful for people who want to study space geodetic technology, not only VLBI but also GPS and SLR. Although the book was first published in Japanese in 1997, the description to the Key Stone Project (KSP) which CRL has promoted is more enriched in publication with the English version. The KSP is the project dedicated to measuring crustal deformation around the Tokyo metropolitan area using space geodetic techniques, such as VLBI, and the KSP implemented the world's first practical unmanned regular observations by the real-time VLBI technique.
The contents are as follows:
Chapter 1: Introduction
Chapter 2: Basic Concepts: A Quick Tour of VLBI
Chapter 3: Data Processing Techniques
Chapter 4: Data Analysis
Chapter 5: Geodetic VLBI Experiments
Chapter 6: Applications of VLBI Techniques
Chapter 7: In Conclusion

The book will be published in June, 2000 by Ohmsha and IOS Press.


IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
E-mail: market(AT)iospress.nl
3-1 Kanda Nishiki-cho,
Chiyoda-ku,Tokyo 101 Japan
E-mail: hanbaibu(AT)ohmsha.co.jp

Information in Detail


In October 1896, one year after the success of Marconi's wireless telegraphy experiments, Japan started research into wireless telegraphy at the Electrical Technical Laboratory of the Ministry of Communications. The following year, Mr. Matsunosuke Matsushiro found success in his wireless telegraphy experiments. The Radio Research Laboratories, Ministry of Posts and Telecommunications, was established in 1952 after some reorganization of the laboratories researching radio communication technology. The Radio Research Laboratories was renamed the Communications Research Laboratory in 1988 to reflect the change in the environment for research following the privatization of the Nippon Telegraph and Telephone Corporation in Japan.

To celebrate 100 years of radio communications, we have spent several years at the Communications Research Laboratory planning and preparing to publish in book from the results of the research so far conducted. Entitled the "Wave Summit Course", it will contain a series of papers on various aspects of radio communications technology and is aimed at students of both the senior and graduate levels, that is, the generation of scientists who will lead the way in the 21st century.

Now the time for publication has arrived. This series consists of seven volumes: 'Satellite Communications', 'Very Long Baseline Interferometer', 'Science of Space Environment', 'Modern Millimeter-Wave Technologies', 'Digital Broadcasting', 'Mobile Communications', and 'Global Environment Remote Sensing'. We hope that these volumes will be widely read as useful guides to the different fields in which radio waves are used.

Finally, I would like to extend my deep gratitude to all those involved in enabling this project to come to fruition, including the authors, editors, and successive Director-Generals of the CRL and chairpersons of the publications committee, and of course to Ohmsha, Ltd. for their untiring assistance and encouragement.

Dr. Takashi Iida
Communications Research Laboratory
Ministry of Posts and Telecommunications


This text, entitled "Very Long Baseline Interferometer", celebrates the 100th anniversary of the discovery of the wireless telegraph, and is one of the texts in the "Wave Summit Course" published by the Communications Research Laboratory (CRL), Ministry of Posts and Telecommunications. The material covered in this text is presented in as systematic a manner as is possible, and although aimed specifically for the student of VLBI, it should also be suitable for engineering school and graduate-level students as well.

VLBI is an acronym for Very Long Baseline Interferometer, and can be roughly divided into two areas of application. The first area is in geodesy, which is covered in considerable detail in the text. The second area is in astrometry, or radio astronomy, which is only briefly treated in this text.

Many people probably relate geodesy and land surveying more with geology and geography than with space-based measuring techniques; and at least up through the first half of the 20th century, geodesy was largely based on knowledge in these fields. Surveyors were generally considered as technicians or craftsmen. Modern GPS (Global Positioning Systems) is probably best known for its use in automobile navigation, but such space-based measuring systems have made tremendous advances in the field of geodesy as well.

In a 1996 speech announcing the United States' policy regarding GPS, the US Vice President, Albert Gore, boasted to the world that, in addition to the Internet, the US had achieved a level of technology in space-based measuring systems far superior to any other country on earth. Given Japan's present status in the high-tech field of modern geodesy, it appears that we have been relegated to following the US's lead. This is paricularly true with regards to GPS, which can be considered as a large engineering conglomerate consisting of both space and terrestrial systems. Such a project requires large financial support, but if not correctly evaluated and prioritized, simply having the correct scientific knowledge will not necessarily produce successful results. The same can be said for VLBI: at first glance it is easy to mistake the motives and outcomes of research of being for a scientific project because it deals primarily with the sciences of astronomy and geodesy. As with GPS, VLBI should also be considered as a project yielding superb scientific results because of a well-financed, flawlessly operated engineering system which allows the melding of hardware and software technologies.

The CRL has provided an environment where hardware and software can be properly evaluated from an engineering standpoint, and scientists and engineers have cooperated in the development of the world's most advanced VLBI technologies.

The word "geodesy" in Japanese is a term composed of the words, measurement, earth, and studies. The word itself strongly embodies the engineering elements of metering distances and determination of precision values. The study you are about to embark on in space-based surveying encompasses VLBI techniques in this case, but as its name implies, is also a new world of science that combines hardware and software to create a megatechnology. Radio wave and microwave technology form the core of the VLBI system. One can thus immediately see that the late marriage of VLBI and wireless communications technology which is over 100 years old really means that VLBI has a connection to the past, present, and to the future.

The authors of this text are members of the research staff at the Communications Research Laboratory. We have also written this book from the perspective of a group of scientists who, until reaching the university level had never had the opportunity to utilize such technologies as we have available to us now. Consequently, we consider ourselves to be members of a group whose primary purpose is to determine how to best realize scientific results from the technology-heavy equipment found in VLBI systems.

The most notable results obtained by VLBI so far has been the global-scale measuring of the movements of the tectonic plates which cover the surface of the earth. Details of this achievement are discussed in the text, but the primary focus of the material covered here remains an investigation of how VLBI can conduct these measurements with such a high level of precision. The text also explains how the various aspects of system hardware, software, and data analysis techniques can be effectively combined to yield a measurement accuracy that is four orders in magnitude better than conventional surveying techniques. VLBI requires knowledge in many areas of science and engineering. To the students of this text: as you carefully study the processes by which these highly precise measurements are achieved, you should gain an appreciation of how each process relates to the various areas of engineering and science. We also believe that the text will be very useful to researchers having prior knowledge of GPS techniques.

If this text proves useful in overcoming to some degree the huge advantage that the US presently enjoys in GPS and other measuring technologies, we will be gratified beyond our expectations.

Finally, the authors wish to express our gratitude to Mr. Wayne Hughes, the translator of this text.

May 2000
Fujinobu Takahashi


Chapter 1 Introduction

1.1 The Birth of Radio Astronomy 1
1.2 The Concepts of Radio Interferometry 3
1.3 The Evolution of the Atomic Clock 4
1.4 Developments in Large-Scale Antenna Technology 6
1.5 Advances in Signal Processing Technology 7
1.6 The Advent of Geodetic VLBI 9
1.7 Chapter Outlines 11
. Chapter Questions 12
. Chapter References 12
Chapter 2 Basic Concepts: A Quick Tour of VLBI

2.1 The Basic Principles of Radio Interferometry 13
2.2 Galactic Radio Sources and Coordinate Systems 15
2.3 Observational Coordinate Systems 17

2.3.1 Surveying the Earth's Shape from Outside the Solar System 18
2.4 Propagation Delays 21

2.4.1 Atmospheric Propagation Delay 22
2.4.2 Solar and Planetary Effects 23
2.5 Basic Principles of VLBI 23
2.6 VLBI System Components: A Historical Sketch 27
2.7 VLBI Observations 33
2.7.1 Observation Equipment 33
2.7.2 Observation Schedules 37
2.8 Data Processing Flow in Geodetic VLBI 40
2.9 Collaboration in VLBI Experiments 41
. Chapter Questions 44
. Chapter References 44
Chapter 3 Data Processing Techniques

3.1 The Fourier Transform and Applications 45

3.1.1 Defining the Fourier Transform 46
3.1.2 Time Shifts and Fourier Transforms 47
3.1.3 Correlation Theorem 47
3.1.4 The Convolution Theorem 49
3.2 A VLBI Equivalent Signal Model 51
3.3 One-Bit Sampling 54
3.4 Maximum Likelihood Estimation of Delay 57

3.4.1 Maximum Likelihood Estimation Principle and Least- Squares Method 57
3.4.2 Cross-Correlation as the Maximum Likelihood Esti- mation of Delay: A Time-Domain Approach 59
3.4.3 Cross-Correlation as the Maximum Likelihood Esti- mation of Delay: A Frequency-Domain Approach 62
3.5 Cross-Correlation Function in VLBI 65

3.5.1 Cross-Correlation Function (without frequency conversion) 65
3.5.2 Cross-Correlation Function of the Video Signal 67
3.6 Correlator Processing 70

3.6.1 Correlation Processing Principles 70
3.6.2 Delay Tracking 72
3.6.3 Fringe Stopping 75
3.6.4 Bit Shifts and 90-degree Phase Jumps 79
3.6.5 Fractional Bit Correction 83
3.6.6 Phase Calibration Signal Detection 84
3.7 Precise Determination of Delay and Delay Rates 85

3.7.1 Normalizing Correlator Output 86
3.7.2 Coarse Delay Search 88
3.7.3 Precise Delay Search using Bandwidth Synthesis 91
3.7.4 Ambiguities in Bandwidth Synthesis 93
3.8 Verification of VLBI Measurement Precision 96

3.8.1 Scattering and Bias of Measurement Values 96
3.8.2 Signal-to-Noise Analysis 96
3.8.3 Theoretical Delay Errors 100
3.8.4 Error Verification using Independent Correlation Systems 104
3.9 Real-Time VLBI 105
. Chapter Questions 107
. Chaptert References 107
Chapter 4 Data Analysis

4.1 Overview of Data Analysis 109
4.2 VLBI Reference Frames 114

4.2.1 Inertial Reference Frame of the Solar System 114
4.2.2 Terrestrial Reference Frame 116
4.2.3 Time Systems 118
4.3 The Physical Models 119

4.3.1 The Earth's Rotation 119
4.3.2 Propagation Delay Corrections 128
4.3.3 Tidal Corrections 132
4.3.4 Relativistic Effects 134
4.3.5 Other Physical Effects 135
4.4 Estimating Parameters 138
4.5 Analytical Methods 139

4.5.1 Analysis Procedures 139
4.5.2 Kalman Filter Estimations 142
4.5.3 Analysis Procedures 144
4.6 VLBI Errors 147

4.6.1 Observation Errors 147
4.6.2 Errors of Estimated Values 149
4.7 Improving Analysis Procedures 150
. Chapter Questions 151
. Chapter References 151
Chapter 5 Geodetic VLBI Experiments

5.1 The Japanese Geodetic Coordinate System 155
5.2 Plate Tectonics and Earthquakes 158
5.3 Measuring Plate Motions 161
5.4 Crustal Deformations near Plate Boundaries 164
5.5 The Himalayan Collision Zone and the Japan-China Converging Zone 165
5.6 Plate Motion near Japan 166
5.7 VLBI Experiments in Japan 168
5.8 VLBI Experiments in Antarctica 171
5.9 Earth Rotation 172

5.9.1 Earth Rotation Observations 172
5.9.2 Results of Earth Rotation Observations 173
5.10 Other Experiments 178
. Chapter Questions 179
. Chapter References 179
Chapter 6 Applications of VLBI Techniques

6.1 Radio Astronomy 181

6.1.1 Determining Radio Source Positions 181
6.1.2 Radio Source Structures 186
6.2 Precise Measurements of Earth Rotation 191

6.2.1 Measuring Polar Motions and Fluctuations in Earth Rotation 191
6.2.2 Fluctuations in Earth Rotation Speed and Atmospheric Angular Momentum 193
6.3 Regional Deformation Monitoring System for the Tokyo Metropolitan Area 195

6.3.1 Geographical Locations of Observation Stations 196
6.3.2 Observation System 197
6.3.3 Automation of Data Analysis 203
6.4 Deep-Space Measurements 207
6.5 Applications in Ionospheric Measurements 208

6.5.1 Correcting for Ionospheric Delay 208
6.5.2 Using Least-Squares Estimation to Determine Total Electron Content of the Ionosphere 212
. Chapter Questions 216
. Chapter References 216
Chapter 7 In Conclusion

7.1 The Transition from Centimeter Accuracies to Millimeter Accuracies 219
7.2 Beyond the Earth 220

Table 1 Wahr Nutation Model Coefficients 221
Table 2 Yoder UT1 Earth Tides Correction Coefficients 223
Table 3 Dickman UT1 Earth Tides Correction Coefficients 224
Table 4 VLBI Station Positions in the ITRF Coordinate Frame 226
Table 5 Selected Radio source Positions for VLBI Observations 228
Answers to Chapter Questions 229
Postscript 234
Author's Profile 235
Index 237

Corrigenda for 'Very Long Baseline Interferometer'(as of May 17, 2008)

updated on May 17, 2008