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Design and Performance Analysis of a Low-Cost Aided Dead Reckoning Navigator

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Design and Performance Analysis of a Low-Cost Aided Dead Reckoning Navigator DESIGN AND PERFORMANCE ANALYSIS OF A LOW-COST AIDED DEAD RECKONING NAVIGATOR a dissertation submitted to the department of aeronautics and astronautics and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy Demoz Gebre-Egziabher February 2004 c Copyright 2004 by Demoz Gebre-Egziabher All Rights Reserved ii I certify that I have read this thesis and that in my opin- ion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. Professor J. David Powell (Principal Advisor) I certify that I have read this thesis and that in my opin- ion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. Professor Per K. Enge I certify that I have read this thesis and that in my opin- ion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. Professor Bradford W. Parkinson Approved for the University Committee on Graduate Studies: Dean of Graduate Studies iii Abstract The Federal Aviation Administration is leading the National Airspace System modernization effort, in part, by supplanting traditional air traffic services with the Global Positioning System (GPS) aided by the Wide and Local Area Augmentation Systems (WAAS & LAAS). Making GPS the primary-means of navigation will en- hance safety, flexibility and efficiency of operations for all aircraft ranging from single engine general aviation aircraft to complex commercial jet-liners. This transformation of the National Airspace System will be gradual and the build-up to a primary-means GPS capability is expected to occur concurrently with the de-commissioning of a sig- nificant number of existing ground-based navigational facilities. If an alternate means of navigation is not available during this transition period, temporary interruptions of GPS services due to intentional or unintentional interference could present significant problems for aircraft lacking backup navigation capability. To successfully deal with such outage scenarios, this thesis outlines an architec- ture of a skeletal network of existing radio-navigation aids, the Distance Measuring Equipment (DME), that should be left in place to provide a redundant navigation ca- pability alongside GPS/WAAS during this transition period. When the information from the proposed skeletal network of DME is fused with a low cost dead-reckoning system in terminal areas, performance comparable to VOR and LORAN based nav- igation can be achieved. This navigation scheme allows reduction of the number of operational radio-navigation aids required while still providing adequate coverage for navigation during the transition to a primary-means GPS National Airspace System. The dead-reckoning navigation system is based on the fusion of a single low-end DME receiver with low cost inertial, air-data and magnetic sensors. These sensors are already part of the newer general aviation aircraft’s suite of navigation sensors. iv Estimator architectures for fusing the information from the various sensors is pre- sented. The performance of this navigator depends on the calibration and on-line estimation of sensor errors. Accordingly, various algorithms for estimating sensor errors in the low cost inertial sensors and magnetometers were developed. In particu- lar, a novel non-linear estimation algorithm for calibrating the errors in a strapdown magnetometer is presented. It is shown that a navigator based on airspeed and magnetometer-derived heading information, augmented by intermittent range measurements from a skeletal network of DME, can provide a backup navigation capability with accuracies better than 0.5 nautical miles. v Acknowledgments I thank my dissertation adviser, Prof. J. David Powell, for his guidance and mentoring. He fostered a research environment which made the Ph.D. process both fruitful and enjoyable. He gave me the freedom to direct my research in areas that were more aligned with my interests, shared my enthusiasm for the research and, above all, was always within reach and unselfish with his time when I needed help. I thank Prof. Per Enge whose infectious enthusiasm for GPS related research made the Stanford GPS Laboratory a fun place in which to work. His advice and guidance were indispensable for my research and I also thank him for extending me the opportunity to teach AA272D–an invaluable experience for one aspiring a future academic career. I thank Prof. Bradford Parkinson for his advice on various issues ranging from the finer points of inertial navigation to things to consider when looking for a faculty job. His careful reading of this dissertation and his feedback are greatly appreciated. Flight testing was an important and rewarding aspect of my thesis work. I thank the members of the flight testing team (Keith Alter, Andy Barrows, Christopher Comp, Rich Fuller, Andrew Hansen, Chad Jennings, Roger Hayward, Sharon Houck and Todd Walter) and the test pilots from Sky Research Inc. (Sky, Ben Hovelman and Kevin McCoy) for their help and hard work which made flight testing a success. I am also grateful for the help and friendship of all my colleagues, past and present, in the GPS laboratory (Dennis Akos, Doug Archdeacon, Frank Bauregger, Dave Bevly, Lee Boyce, Donghai Dai, Gabriel Elkaim, Jennifer Evans, Konstantin Gromov, Andrew Hansen, Roger Hayward, Sharon Houck, James Shau-Shiun Jan, Chad Jennings, Ping-Ya Ko, Sherman Lo, Eric Phelts and Todd Walter). I gratefully acknowledge their assistance, which ranged from building hardware to discussions which were the catalysts for many research ideas. I owe special thanks to Roger Hayward and Gabriel vi Elkaim. Roger designed and built the short baseline GPS attitude determination and sensor data collection systems. Without these systems flight testing would have been impossible. Gabriel’s collaboration was instrumental in the development of attitude determination and magnetometer calibration algorithms. I thank Dr. Zeev Berman for his help and very informative lectures on inertial navigation given when he was a visiting scholar in the Stanford GPS laboratory. The work in this thesis was sponsored by a research grant from the Federal Avia- tion Administration Satellite Program Office and a NASA-Langley technology trans- fer grant from Seagull Technology Inc. The support of these organizations is gratefully acknowledged. Finally, I owe a debt of gratitude to my older siblings Sam and Brikti. They have always been a source of inspiration and I was fortunate to have them as role models for my academic career and life in general. I thank my younger sisters, Meaza and Rahwa. I have benefited greatly from their advice and encouragement over the years. Above all, my deepest thanks go to my parents, Semainesh and Ytbarek. Their unending support and encouragement have been invaluable through out my life. Although in comparison it is significantly smaller to all that they have given me, it is to them, with heartfelt thanks, that I dedicate this thesis. vii Contents Abstract iv Acknowledgments vi 1 Introduction 1 1.1Overview.................................. 1 1.2TheNationalAirspaceSystem...................... 3 1.2.1 NavigationintheCurrentNAS................. 3 1.2.2 NavigationintheFutureNAS.................. 6 1.3TheNeedforaBackupNavigationSystem............... 7 1.4ResearchinthisThesis.......................... 9 1.5PreviousResearch............................. 10 1.6ThesisContributions........................... 11 1.7ThesisOrganization............................ 12 2 The DME-Based Navigator 14 2.1Introduction................................ 14 2.2 Justification of a DME-Based Navigation System . 14 2.3 Operation of the Backup Navigation System . 16 2.4ArchitectureoftheBackupNavigationSystem............. 19 2.5EquipmentInstalledontheAircraft................... 20 2.5.1 GPS/WAAS Receiver . 21 2.5.2 InertialSensors.......................... 22 2.5.3 AirDataSystems......................... 24 2.5.4 HeadingSensors.......................... 26 viii 2.5.5 Distance Measuring Equipment (DME) Receiver . 28 2.6 Ground Based Infrastructure: A Skeletal Network of DME . 31 2.7CostoftheNavigationSystem...................... 36 3 Sensor Error Models 38 3.1Introduction................................ 38 3.2AGeneralInertialSensorErrorModel................. 38 3.3RateGyroErrorModels......................... 41 3.3.1 VibratingStructureRateGyros................. 41 3.3.2 FiberOpticRateGyroErrorModels.............. 51 3.3.3 Summary of Low-Performance Rate Gyro Error Models . 53 3.4 Accelerometer Error Models . 54 3.5InertialNavigationSystemErrorModels................ 56 3.6MagnetometerErrorModels....................... 56 3.6.1 Background............................ 57 3.6.2 GeneralErrorEquation..................... 58 3.6.3 Hard Iron Errors: δB b ...................... 59 3.6.4 Soft Iron Errors: Csi ....................... 59 3.6.5 Scale Factor Errors: Csf ..................... 62 3.6.6 Misalignment Errors: Cm ..................... 62 3.7AirDataSystemErrors......................... 63 3.7.1 AirspeedMeasurementErrors.................. 63 3.7.2 AltitudeMeasurementErrors.................. 65 3.8WindErrorModel............................ 66 3.9DMEErrorModels............................ 68 3.10 GPS/WAASErrors............................ 72 3.11MagnetometerCalibration........................ 72 3.11.1 Calibration In the Heading Domain . 73 3.11.2 2-D Calibration in the Magnetic Field Domain . 78 3.11.3
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