Embedded Avionics with Kalman State Estimation for a Novel Micro-Scale Unmanned Aerial Vehicle by Theodore Tzanetos B.S. Electrical Engineering and Computer Science Massachusetts Institute of Technology, 2012 SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2013 @Massachusetts Institute of Technology This work is sponsored by the Department of the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government. Signature of Author: Department of Electrical Eifineering and Computer Science May 24, 2013 Certified by: JamesT. Roberge Professor of Electrical Engineering Thesis Supervisor Certified by: Ryan D. Eubank MIT Lincoln Laboratory Technical Staff Thesis Co-Supervisor Accepted by: Dennis MIWeman Professor of Electrical Engineering Chairman, Masters of Engineering Thesis Committee 1 Embedded Avionics with Kalman State Estimation for a Novel Micro-Scale Unmanned Aerial Vehicle by Theodore Tzanetos Submitted to the Department of Electrical Engineering and Computer Science on May 24, 2013 in Partial Fulfillment of the Requirements for the Degree of Master of Engineering in Electrical Engineering and Computer Science ABSTRACT An inertial navigation system leveraging Kalman estimation techniques and quaternion dynamics is devel- oped for deployment to a micro-scale unmanned aerial vehicle (UAV). The capabilities, limitations, and requirements of existing navigation solutions motivate the need for an integrated solution that can be read- ily applied to small embedded systems and still provide reasonably accurate results. Methods to calibrate and compensate systemic inaccuracies in microelectromechanical systems (MEMS) sensors, commonly used in micro-scale UAV applications, are also developed. The problems associated with attitude determination and system localization are analyzed in isolation with incremental simulation and field testing. Performance is evaluated against commercially available inertial navigation system solutions. The result is a capable navigation system that, by its structure, trades a small measure of accuracy in order to be easily adapted to the embedded computing constraints of unmanned vehicles in the micro-scale. Thesis Supervisor: James K. Roberge Title: Professor of Electrical Engineering 2 Acknowledgments First, I would like to thank all my friends and family for their support during my research. This includes my academic adviser Professor Christopher J. Terman who has been an invaluable guide during my time at MIT. I would like to thank my thesis supervisors Prof. James Roberge and Dr. Ryan Eubank for their time and guidance throughout my research. I am deeply indebted to the MIT Lincoln Laboratory staff who helped me achieve my success, specifically Josh Manore, Sam Stambler, Kenneth Chadwick, Andrew Kopeikin, Matthew Lowe, and Ronald Hoffeld. Special thanks is given to Mark Cutler of the MIT Aerospace Controls Lab for his help. Finally, I would also like to thank Tony Tao and Professor Hansman for their excellent engineering which laid the foundation for this project. 3 Contents 1 Introduction 11 1.1 Motivation . . . . . . 11 1.2 Novel Micro-UAS Platform . . . . . . . . . . . . . . . . . . ... . . . .. . 1 2 1.3 Problem Statement and Research Objectives . . . . . . . . . . . . . . . . . . 1 4 1.4 O utline . . . . . . . . . . . . . . . . . . . . ..-..... ..-.... 1 7 2 Avionics Systems 18 2.1 Primary Avionics . . . . . . . . . . . . . . . 18 2.2 Sensor Systems . . . . . . . . . . . . . . . . 20 2.3 Calibration . . . . . . . . . . . . . . . . . . 22 2.3.1 Six-Point Accelerometer Calibration 23 2.3.2 Gyroscope Rate Table Calibration 25 2.3.3 Hard Iron and Soft Iron Calibration 25 3 Inertial Navigation 31 3.1 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 3.2 Rotational Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 Euler Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.2 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . - . . . .... . . . 36 3.3 The Discrete Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... 40 3.4 The Indirect State Feedback Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4.1 One Dimensional Unaided Inertial Navigation System . . . . . . . 47 4 3.4.2 Indirect Filter Derivation . ..... ................. 50 5 3.4.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Navigation Development and Testing 61 4.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Navigation Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.2 Four Degree of Freedom Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3 Attitude and Heading Reference System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3.1 Aiding Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3.2 Quaternion Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.3.3 AHRS Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 INS Test Aircraft Results 89 5.1 Flat and Level Flight Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2 GPS Blackout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6 Conclusions and Future Work 105 Bibliography 106 5 List of Figures 1.1 Locust pUAS and flare canister housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Locust pUAS Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Closed-Loop pUAS GNC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 SBG-500N (L) and VectorNav VN-200 OEM(R) . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1 Locust avionics board and internals[35l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 MEMS Output Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Six-Point Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 HI/SI Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5 HI/SI with Spheroid Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.1 ECEF and local NEU frames[40] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 Aircraft Coordinate Frame [21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Kalman filter operation time-line[18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Prediction-Correction Cycle of the Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.5 Indirect Feedback Architecture[181 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.6 Sinusoidal Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.7 Position Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.8 Bias Results . . . . . . . . . . . . . . . ..... . . . . . . . . . . .. .. . .. .. .. . .. .. 58 3.9 Estimate Errors and 1-a Bounds on Error Covariance . . . . . . . . . . . . . . . . . . . . . . 59 3.10 Auto-correlation of Position and Velocity Innovation Processes . . . . . . . . . . . . . . . . . 59 3.11 1-D Kalman Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1 INS Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Navigation Filter Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3 3-DOF Simulated Acceleration Inputs (Non-Inertial) . . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Google Earth Plot of 3-DOF Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 4-DOF Test Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.6 Close up of SBG Systems INS and pUAS Avionics housing . . . . . . . . . . . . . . . . . . . . 71 4.7 4-DOF Test with Yaw Aiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.8 4-DOF Boolean Flag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.9 4-DOF Yaw Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.10 AHRS Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 77 4.11 AHRS Test Rotation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.12 AHRS Boolean Flag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.13 AHRS Bias Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.1 GII Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2 Flat and Level Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6 5.3 Flat and Level Flight Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.4 Flat and Level Flight Attitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.5 GII Reported Ground Speed(L) and Altitude(R) . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.6 Flat and Level Flight Bias Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.7 Flat and Level Flight Accelerometer Bias Initialization . . . . . . . . . . . . . . . . . . . . . . 96 5.8 NF Innovation Auto-correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.9 Kalman Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.10 GPS Blackout t=200s LLA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.11 GPS Blackout t=680 3D Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.12 Velocity Estimate(L) and LLA(R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.13 Locust INS Yaw and GPS Yaw Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7 List of Tables 1.1 Locust pUAS Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1 Analog Devices ADXL345 Accelerometer Specifications [7] . . . . . . . . . . . . . . . 21 2.2 ST L3G4200D Gyroscope Specifications 133] . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Honeywell HMC5883L Magnetometer Specifications [171 . . . . . . . . . . . . . . . . 22 2.4 u-blox MAX-6Q Specifications 1371 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Six-Point Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 1-D Indirect Kalman Filter RMS Errors . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.1 Commercial INS Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.2 4-DOF Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.1 Nominal Locust INS Performance Statistics . . . . . . . . . . . . . . . 10 2 5.2 Dynamic Locust INS Performance Statistics . . . . . . . . . . . . . . . 10 3 5.3 INS Test Noise Values . . . . . . . . . . . . . . . . . . . . . . . 104 8 This page is intentionally left blank. 9 This page is intentionally left blank. 10