Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 9-15-2016 Absolute Positioning Using the Earth's Magnetic Anomaly Field Aaron J. Canciani Follow this and additional works at: https://scholar.afit.edu/etd Part of the Electromagnetics and Photonics Commons Recommended Citation Canciani, Aaron J., "Absolute Positioning Using the Earth's Magnetic Anomaly Field" (2016). Theses and Dissertations. 251. https://scholar.afit.edu/etd/251 This Dissertation is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. ABSOLUTE POSITIONING USING THE EARTH'S MAGNETIC ANOMALY FIELD DISSERTATION Aaron J. Canciani, Capt, USAF AFIT-ENG-DS-16-S-074 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENG-DS-16-S-074 ABSOLUTE POSTIONING USING THE EARTH'S MAGNETIC ANOMALY FIELD DISSERTATION Presented to the Faculty Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Aaron J. Canciani, B.S.E.E., M.S.E.E. Capt, USAF September 2016 DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENG-DS-16-S-074 ABSOLUTE POSTIONING USING THE EARTH'S MAGNETIC ANOMALY FIELD DISSERTATION Aaron J. Canciani, B.S.E.E., M.S.E.E. Capt, USAF Committee Membership: John Raquet, PhD Chairman Matthew Fickus, PhD Member Maj Scott Pierce, PhD Member ADEDEJI B. BADIRU, PhD Dean, Graduate School of Engineering and Management AFIT-ENG-DS-16-S-074 Abstract Achieving worldwide dependable alternatives to GPS is a challenging engineering problem. Current GPS alternatives often suffer from limitations such as where and when the systems can operate. Navigation using the Earth's magnetic anomaly field, which is globally available at all times, shows promise to overcome many of these limitations. We present a navigation filter which uses the Earth's magnetic anomaly field as a navigation signal to aid an inertial navigation system (INS) in an aircraft. The filter utilizes highly-accurate optically pumped cesium (OPC) magnetometers to make scalar intensity measurements of the Earth's magnetic field and compare them to a map using a marginalized particle filter approach. The accuracy of these mea- surements allows observability of not only the INS errors, but also long-wavelength errors in the measurements. We demonstrate navigation accuracy of 13 meters DRMS with a high quality magnetic anomaly map at low altitudes with real flight data. We identify altitude and map quality as the two largest variables which effect naviga- tion accuracy. We further demonstrate navigation accuracies of several kilometers over a cross-country flight at 3000 meters altitude with a continental-sized magnetic anomaly map. We demonstrate that the majority of this error is caused by poor map quality. We predict navigation accuracies of a high altitude cross-country flight with an improved continental-sized map through simulation and show a range of accuracies from tens of meters to hundreds of meters, depending on altitude. We then conduct a simulation over the continental United States to predict accuracies with respect to variables like location, altitude, and velocity. Finally, we address the problem of map availability by presenting a method for a self-building world magnetic anomaly map which uses Gaussian process regression to model the error in existing large-scale mag- iv netic anomaly maps. We use real data to demonstrate the benefit in map accuracy that a few flight lines can provide to a large area. v Table of Contents Page Abstract . iv List of Figures . .x List of Tables . xvii List of Abbreviations . xix I. Introduction . .1 1.1 Technical Motivation. .2 1.2 Claimed Contributions . .2 1.3 Literature Review . .4 Aerial Magnetic Navigation . .4 Magnetic Ground Navigation . .7 Magnetic Space Navigation . .8 Magnetic Underwater Navigation . .8 Magnetic Indoor Navigation . .9 Gravity Navigation . 10 Cramer-Rao Lower Bound For Map-Matching Algorithms . 10 Literature Review Conclusion . 11 1.4 Dissertation Organization . 11 II. BACKGROUND . 13 2.1 Components of the Earth's Magnetic Field . 13 Core Field . 13 Crustal Field . 15 Induced Field . 16 External Fields. 16 Ionospheric Effects on the Magnetic Field . 17 Magnetospheric Effects on the Magnetic Field . 19 Coupling Currents . 21 2.2 Earth's Magnetic Anomaly Field . 21 International Geomagnetic Reference Field . 22 Anomaly Definition and Assumptions . 25 2.3 Magnetic Anomaly Modeling and Transforms . 29 Upward Continuation . 29 Magnetic Map Time Projections . 34 Modeling Magnetic Anomaly Fields . 38 Map Pre-Conditioning . 43 vi Page 2.4 Magnetic Anomaly Maps . 46 Flying Over a Modern Map At Map Altitude - The Ideal Case . 48 North American Magnetic Anomaly Map . 51 World Digital Magnetic Anomaly Map . 51 2.5 Types of Magnetic Measurements . 54 Scalar Intensity Measurements . 54 Intensity Gradient Measurements . 56 Vector Measurements . 59 Tensor Measurements . 60 2.6 Magnetic Sensors . 60 Optically Pumped / Alkali-Vapor Magnetometers . 61 Fluxgate Sensors . 67 2.7 Obtaining Accurate Magnetic Measurements . 68 Aircraft Sources . 69 Aircraft Magnetic Compensation Systems . 71 Temporal Variations . 74 2.8 Creating Magnetic Anomaly Maps . 75 Flight Path . 75 Data Processing . 79 2.9 Rao-Blackwellized Particle Filtering . 82 2.10 Background Conclusion . 89 III. Filter Design . 90 3.1 Temporal Variation Modeling . 90 Types of Temporal Variations . 90 Characterizing Temporal Variations as a Random Process . 92 Temporal Variation Variables . 100 3.2 Temporal Variation Observability Analysis . 104 Temporal Variation Frequencies . 104 Anomaly Field Frequencies . 107 3.3 Measuring the Magnetic Anomaly . 109 Map Quality . 110 Altitude Dependent Variations . 110 Corrupting Sources . 111 Measurement Equation . ..