8&*(5HSRUWV 1XPEHU Department of Geomatics Engineering Improving the Accuracy and Resolution of SINS/DGPS Airborne Gravimetry (URL: http://www.geomatics.ucalgary.ca/GradTheses.html) by Alexander Mark Bruton December 2000 UNIVERSITY OF CALGARY Improving the Accuracy and Resolution of SINS/DGPS Airborne Gravimetry by Alexander Mark Bruton A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF GEOMATICS ENGINEERING CALGARY, ALBERTA December, 2000 © Alexander Mark Bruton 2000 Abstract This dissertation describes improvements made to a system for airborne mapping of the gravity field of the Earth. The research is carried out using an airborne gravity system that is based on a Strapdown Inertial Navigation System (SINS) and receivers of the Global Positioning System in differential mode (DGPS). The objective of the research is to optimize the performance of the system, especially for geodesy and geophysics. An introduction to the field of airborne gravimetry is given and the state of current research in the field is surveyed. Data from recent airborne gravity campaigns is used to provide a detailed analysis of the DGPS error budget for airborne positioning, providing a realistic evaluation of the accuracy of current kinematic carrier phase techniques. A fundamental consideration of the various processes of differentiation is given and particular differentiating filters are proposed for the determination of high precision velocity and acceleration. A detailed analysis is given in the frequency domain of the DGPS error budget for acceleration determination. This provides an understanding of the characteristics of each of the relevant error sources for spatial resolutions up to 500 m and forms the basis for a set of recommendations regarding acceleration determination for airborne gravimetry. The limitations of the SINS gravimeter that are imposed by the accelerometer biases are analyzed and quantified. A thorough analysis is provided of the dynamics experienced by survey aircraft. The high-frequency errors affecting airborne gravimetry are analyzed in detail and methods for reducing them are proposed and implemented with success. An improvement to the performance of the system for medium-resolution applications is achieved and it is demonstrated for the first time that the SINS/DGPS system can be used for high-resolution applications. Major results include a demonstrated accuracy of 1.5 mGal for a spatial resolution of 2.0 km and an accuracy of 2.5 mGal for a resolution of 1.4 km. Improvements to processing methods have yielded slightly better performance than the LaCoste and Romberg gravimeter on a common flight. A method for removing the effect of the Phugoid motion has been proposed and implemented with success. iii Acknowledgements Graduate studies has been a wonderful experience for me. It has allowed me to learn, to travel to faraway places like Greenland and Brazil, and perhaps most importantly, to make some lasting friendships. I would like to express appreciation for the support I have received over the last four years: • To Dr. Klaus-Peter Schwarz, thank you for the opportunity to work within such a world-class research group during my graduate studies. Your support, encouragement, trust and technical leadership have made it a truly enjoyable and invaluable experience. • To those organizations whose financial support has made my graduate studies possible, especially the Natural Sciences and Research Council (NSERC) of Canada, whose support has been fundamental. Thanks to the Government of Alberta for support in the form of an Alberta Government Graduate Scholarship, to the University of Calgary for support in the form of the Helmut Moritz Graduate Scholarship and to the Department of Geomatics Engineering for financial support on several occasions. Also, thanks go to those organizations that improved my graduate experience in the form of awards and travel grants. • To past and present members of our research group at the University of Calgary. To Dr. Ming Wei, thank you for your generosity and for the practical work that has created the framework upon which many students at the University of Calgary have built, myself included. Although there are many others, I would like especially to thank Jan Skaloud, Craig Glennie, Yecai Li, Mohamed Mostafa, Michael Kern, Kris Keller, Fadi Bayoud and Sandy Kennedy for their help and partnership on many occasions. Craig is also thanked for thoroughly testing the first version of GREATGUN in his thesis work. • To my unofficial examining committee: Michael Kern, Jason Innes and especially Len Bruton. The quality of this dissertation was greatly improved as a result of iv the discussions we had and as a result of your thoughtful criticism of the first draft. Your encouragement and the time you spent to help me is truly appreciated. • Thanks goes to the Geomatics for Informed Decisions (GEOIDE) Network Centre of Excellence for financing my position at the University of Calgary for the last year and a half and for the great environment for collaboration that they helped create. Also, other members of the Airborne Gravity for Exploration and Mapping Project are thanked for enriching my learning experience. • To Rene Forsberg of the Danish National Survey and Cadastre (KMS), for the invitation to participate in the workshop and field test in Greenland, in June 1998. Greenland was an unforgettable experience! • To Hugh Martell and Darren Cosandier of Waypoint Consulting Ltd., for the loan of GrafNav 6.02. It made data processing a pleasure. • To Keith Tennant, for your feedback and the useful discussions we had. • To Intermap Technologies Corporation for the loan of the Honeywell Laseref III on many occasions and for the flight services that were provided. • To Steve Ferguson for your hospitality and for always being willing to help. • To Sander Geophysics Ltd. for the flight services that were provided during the two testing periods that I joined them in Ottawa. • To Vladimir Argeseanu for providing the upward continued reference gravity field for the Kananaskis campaign. • To Paul Mrstik for his generosity and help. • To the members of my examining committee for their advice: J.M. Brozena, M.G. Sideris, M.E. Cannon and J.W. Haslett. • To the staff in the main office of Geomatics Engineering, especially Anne Gehring. Your help is appreciated. On a more personal note, I would like to express appreciation to my family and friends who have been so supportive over the last four years, especially: • To Mum, Dad, Michelle, Nicole and Adrian, thank you for your friendship and your support. • Finally, thanks to my best friend Krista for sharing and dreaming with me. v Dedication This work is dedicated to my parents who teach me every day by example. To Mum, whose arms are always open, making ours the luckiest family in the world, and to Dad, whose love for us is evident in everything that he does. Thank you for your support, your strength, your patience, your friendship and your love. vi Table of Contents Abstract.............................................................................................................................iii Acknowledgements...........................................................................................................iv Dedication .........................................................................................................................vi Table of Contents ............................................................................................................vii List of Figures...................................................................................................................xi Notation, Symbols and Acronyms ................................................................................xiii Notation xiii List of acronyms xv List of symbols xvi Introduction ....................................................................................................................... 1 PART 1: BACKGROUND AND JUSTIFICATION ..................................................... 3 1 Background and Research Objectives..................................................................... 4 1.1 Gravimetry, airborne gravimetry and the SINS gravimeter 5 1.2 Why are airborne gravity measurements needed? 9 1.3 Related research 13 1.4 Statement of the problem 21 1.4.1 Objectives...................................................................................................... 22 1.4.2 Assumptions.................................................................................................. 22 2 Airborne Gravimetry Using a SINS ...................................................................... 24 2.1 The measurement model of airborne gravimetry 24 2.2 The error model of airborne gravimetry 26 2.3 The estimation process, the observables and the measuring systems 27 2.3.1 The process of estimating the gravity disturbance........................................ 28 2.3.2 The SINS as a measuring system .................................................................. 30 2.3.3 The GPS as a measuring system ................................................................... 34 2.3.4 The effects of other sources of error on gravity disturbance estimation....... 37 vii 2.4 Contributions of this dissertation 37 PART 2: DGPS FOR AIRBORNE GRAVITY MAPPING........................................ 39 3 On the Positioning Accuracy of Kinematic Carrier