||In-Flight Magnetometer Calibration with Temperature Compensation for PHOENIX CubeSat
||Department of Electrical Engineering
In-Flight Magnetometer Calibration
Attitude Control and Determination
Particle Swarm Optimization
PHOENIX is a 2U CubeSat in the QB50 project that is designed, assembled, integrated, tested and operated by National Cheng Kung University, Taiwan. After the deployment from International Space Station (ISS) in May 2017, extensive studies on magnetometer calibration have been conducted. The performance of attitude determination and control subsystem (ADCS) for PHOENIX depends on the reliability and accuracy of magnetometer calibration.
The thesis is concerned with the in-flight magnetometer calibration which will be naturally influenced by the variation of temperature during the course of orbiting around the earth. A temperature-dependent magnetometer model is proposed and a particle swarm optimization method is adopted in the estimate of calibration parameters. The proposed model and method are verified and tested by using in-flight data from PHOENIX. It has shown that the use of the proposed model together with the optimization method renders a closer match between the magnitudes of the measurement vector and IGRF model. Additionally, the calibration method can be extended to find the suboptimal solution for the satellites with magnetometers without the mechanism of temperature compensation. The proposed approach is believed to be beneficial for small satellites and CubeSats that rely on the use of magnetometer data for attitude determination, orbit determination, and attitude control.
List of Tables VIII
List of Figures IX
List of Abbreviations XI
Chapter 1 Introduction 1
1.1 Motivation and Objectives 1
1.2 Overview of PHOENIX Mission 2
1.2.1 QB50 Mission 2
1.2.2 Overview of PHOENIX 5
1.3 Thesis Overview 8
Chapter 2 PHOENIX ADCS 9
2.1 Attitude Determination and Control Subsystem 9
2.1.1 Coordination Definition 9
2.1.2 ADCS Module Specification 10
2.1.3 Control and Estimation Modes 12
2.2 In-Flight ADCS Experience 14
2.2.1 High Rate Detumbling 14
2.2.2 Y-Spin Control 16
2.2.3 Y-momentum Control 18
Chapter 3 In-Flight TAM Calibration Methods 21
3.1 Mathematical Model of Magnetometer 21
3.1.1 External Errors 21
3.1.2 Internal Errors 22
3.1.3 Measurement Model of 3-Axis Magnetometer 25
3.2 Review of Existing Calibration Methods 28
3.2.1 Least Square Method 28
3.2.2 TWOSTEP Algorithm 29
3.2.3 Nonlinear-Kalman-Filter Based Algorithm 31
3.2.4 Particle Swarm Optimization 32
3.3 PSO-Based Magnetometer Calibration 32
3.3.1 Particles Initialization 33
3.3.2 Particles Evaluation 34
3.3.3 Particles Update 34
Chapter 4 In-Flight TAM Calibration and Verification 37
4.1 Background 37
4.1.1 3-Axis Magnetometer of PHOENIX 37
4.1.2 Thermometers of PHOENIX 39
4.1.3 IGRF Model 41
4.1.4 In-Flight Data Collection 43
4.2 Ground-Calibration with In-Flight Data 45
4.2.1 CubeSupport Calibration 45
4.2.2 PSO-Based Calibration 46
188.8.131.52 Initial Parameters Setting 47
184.108.40.206 Comparison Test 49
220.127.116.11 Results of PSO-Based Calibration 49
4.3 In-Flight Test of Calibrated Parameters 59
4.4 Further Study of Magnetometer Calibration 63
4.4.1 The Setting of Temperature Reference T0 63
18.104.22.168 Comparison with Results from CubeSupport 65
4.4.2 Analysis of PSO-Based Calibration 68
22.214.171.124 Different Setting of Initial Boundary 68
126.96.36.199 Dynamic Weighting Parameters 71
Chapter 5 Conclusions and Future Works 74
5.1 Discussions 74
5.2 Future Works 76
QB50 Website, Available: http://www.qb50.eu, Accessed in 2018.
C. Underwood, “Development of the InflateSail (QB50 GB06) 3U CubeSat Technology Demonstrator and First Flight Results,” in 9th European CubeSat Symposium, Belgium, 2017.
T. C. Huang, Implementation and Verification of Reliable Flight Software for CubeSats, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2016.
C. H. Yeh, Estimation of Power Behavior in PHOENIX’s Electrical Power Subsystem, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2017.
J. C. Liu, Mission Planning System for an Atmospheric Resarch CubeSat, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2017.
 T. Y. Lin, Design and Verification of the Control Procedure of Attitude Determination and Control Subsystem for Nanosatellite, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2014.
Vina, Attitude Determination and Control Subsystem for PHOENIX CubeSat: Design, Implementation and Testing, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2015.
S. H. Wu, Operating Strategy in PHOENIX’s Attitude Determination and Control Subsystem, M.S. Thesis, Department of Electrical Engineering, National Cheng Kung University, 2016.
L. Visagie and M. A. Kearney, “ADCS Interface Control Document ver. 3.2,” Surrey Space Centre, 2015.
L. Visagie, “QB50 ADCS Reference Manual ver. 2.0,” Surrey Space Centre, 2015.
L. Visagie, “QB50 ADCS Commissioning Manual ver. 1.0,” Surrey Space Centre, 2015.
H. Steyn and L. Visagie, “Final Lessons Learned from QB50 Precursor ADCS,” in 9th QB50 Workshop, 2015.
M. Y. Hong, K. C. Wu, and J. C. Juang, “Analysis of PHOENIX CubeSat under High Tumbling Rate,” in 9th European CubeSat Symposium, Belgium, 2017.
M. X. Huang, M. Y. Hong, and J. C. Juang, “Analysis of Tumbling Motions by Combining Telemetry Data and Radio Signal,” in 32th AIAA/USU Small Satellite Conference, USA, 2018.
M. Y. Hong and J. C. Juang, “Ground Based Angular Rate Reconstruction with Intermittent Magnetometer Data from PHOENIX CubeSat,” in 69th International Astronautical Congress, Germany, 2018.
V. Renaudin, M. H. Afzal, and G. Lachapelle, “Complete Triaxis Magnetometer Calibration in the Magnetic Domain,” Journal of Sensors, Vol. 2010, article ID 967245.
J. C. Springmann and J. W. Cutler, “Attitude-Independent Magnetometer Calibration with Time-Varying Bias,” Journal of Guidance, Control and Dynamics, Vol. 35, No. 4, July-August, 2012.
E. Kim, H. Bang, and S. H. Lee, “Attitude-Independent Magnetometer Calibration Considering Magnetic Torquer Coupling Effect,” Journal of Spacecraft and Rockets, Vol. 48, No. 4, July-August, 2011.
A. M. Bogatyrev, I. A. Lomaka, and P. N. Nikolayev, “Technology for Calibration of Measuring Instruments of SAMSAT Nanosatellites’ Family,” 24th Saint Petersburg International Conference on Integrated Navigation Systems, 2017.
M. Díaz-Michelena, R, Sanz, M. F. Cerdán, and A. B. Fernández, “Calibration of QW-MOURA Three-Axis Magnetometer and Gradiometer,” in Geoscientific Instrumentation, Methods and Data Systems, 2015.
Z. Liu and J. Xue, “New Calibration and Error Compensation for Strapdown Magnetometer,” in Proceedings of the 34th Chinese Control Conference, July 28-30, 2015.
C. C. Foster and G. H. Elkaim, “Extension of a Two-Step Calibration Methodology to Include Nonorthogonal Sensor Axes,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 3, July, 2008.
R. Alonso and M. D. Shuster, “Attitude-Independent Magnetometer Bias Determination: A Survey,” Journal of the Astronautical Sciences, Vol. 50, No. 4, October-December, 2002.
R. Alonso and M. D. Shuster, “TWOSTEP: A Fast Robust Algorithm for Attitude-Independent Magnetometer Bias Determination,” Journal of the Astronautical Sciences, Vol. 50, No. 4, October-December, 2002.
R. Alonso and M. D. Shuster, “Complete Linear Attitude-Independent Magnetometer Calibration,” Journal of the Astronautical Sciences, Vol. 50, No. 4, October-December, 2002.
J. L. Crassidis and K. L. Lai, “Real-Time Attitude-Independent Three-Axis Magnetometer Calibration,” Journal of Guidance, Control and Dynamics, Vol. 28, No. 1, January-February, 2005.
B. Grandvallet, A. Zemouche, M. Boutayeb, and S. Changey, “Real-Time Attitude-Independent Three-Axis Magnetometer Calibration for Spinning Projectiles: A Sliding Window Approach,” IEEE Transactions on Control Systems Technology, Vol 22, No. 1, January, 2014.
J. C. Juang, Y. F. Tsai, and C. T. Tsai, “Design and Verification of a Magnetometer-Based Orbit Determination and Sensor Calibration Algorithm,” in Aerospace Science and Technology, 2012.
Z. Wu, Y. Wu, X. Hu, and M. Wu, “Calibration of Three-axis Strapdown Magnetometers Using Particle Swarm Optimization Algorithm,” in Proceedings of IEEE International Symposium on Robotic and Sensors Environments, 2011.
B. A. Riwanto, T. Tikka, A. Kestilä, and J. Praks, “Particle Swarm Optimization with Rotation Axis Fitting for Magnetometer Calibration,” IEEE Transactions of Aerospace and Electronic Systems, Vol. 53, No. 2, 2017.
“1, 2 and 3-Axis Magnetic Sensors HMC1051/HMC1052L/HMC1053,” Honeywell, 2010.
AGI STK, Available: http://www.agi.com/resources, Accessed in 2018.
L. Visagie, “QB50 ADCS CubeSupport User Manual ver. 2.0,” Surrey Space Centre, 2015.
H. Steyn and L. Visagie, “In-Orbit Results of the ADCS Commissioning of nSight-1 (a QB50 CubeSat),” in 9th European CubeSat Symposium, Belgium, 2017.
M. Y. Hong, K. C. Wu, and J. C. Juang, “RSAT Pre-Mission Analysis: De-Orbiting Strategy and Simulation with VR technology,” in 11th IAA Symposium on Small Satellite for Earth Observation, Berlin, Germany, 2017.
M. M. Roh, S. Y. Park, and K. H. Choi, “Orbit Determination Using the Geomagnetic Field Measurements via the Unscented Kalman Filter,” Journal of Spacecraft and Rockets, Vol. 44, No.1, January-February 2007.
K. C. Wu, Earth Re-Entry CubeSat Mission Attitude Control Simulation and Mission Analysis, M.S. Thesis, Department of Aeronautics and Astronautics, National Cheng Kung University, 2017.
A. Ali, S. Siddharth, Z. Syed, and N. E. Sheimy, “Swarm Optimization-Based Magnetometer Calibration for Personal Handheld Devices,” in Sensors (Basel, Switzerland), 2012.
E. Carrubba, A. Junge, F. Marliani, and A. Monorchio, “Particle Swarm Optimization for Multiple Dipole Modeling of Space Equipments,” IEEE Transactions on Magnetics, Vol. 50, No. 12, December, 2014.
R. C. Eberhart and Y. Shi, “Particle Swarm Optimization: Developments, Applications and Resources,” in Proceedings of the IEEE Conference on Evolutionary Computation, 2001.
D. Bratton and J. Kennedy, “Defining a Standard for Particle Swarm Optimization,” in Proceedings of the IEEE Swarm Intelligence Symposium, 2007.
Bala VenKata Rama Kishore Killada, GPU Enabled Particle Swarm Optimization, M. S. Thesis, North Dakota State University of Agriculture amd Applied Science, 2017.
V. Roberge and M. Tarbouchi, “Parallel Particle Swarm Optimization on Graphical Processing Unit for Pose Estimation,” in Proceedings of WSEAS Transactions on Computers, 2012.
Parallel Particle Swarm for CUDA Accelerated Models, Available: http://parallelpso.blogspot.com/, Accessed in 2018.
Mitigation Risks with Hands-On Training (3-DoF Air Bearing Platform), Available: http://www.satmagazine.com/story.php?number=108332957, Accessed in 2018.
Embedded Navigation Solutions (3-axis Helmholtz Coil Platform), Available: https://www.vectornav.com/support/library/calibration, Accessed in 2018.
K. K. Tan, S. Huang, W. Liang, A. A. Mamun, E. K. Koh, and H. Zhou, “Development of a Spherical Air Bearing Positioning System,” IEEE Transactions on Industrial Electronics, Vol. 59, No. 9, pp. 3501-3509, 2012.
S. Chesi, O. Perez, and M. Romano, “A Dynamic, Hardware-in-the-Loop, Three-Axis Simulator of Spacecraft Attitude Maneuvering with Nanosatellite Dimensions,” Journal of Small Spacecraft, 2015.
F. L. Markley and J. L. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control, New York, NY, USA: Springer, 2014.