Abstract
We propose an attitude filtering and magnetometer calibration approach for nanosatellites. Measurements from magnetometers, Sun sensor and gyros are used in the filtering algorithm to estimate the attitude of the satellite together with the bias terms for the gyros and magnetometers. In the traditional approach for the attitude filtering, the attitude sensor measurements are used in the filter with a nonlinear vector measurement model. In the proposed algorithm, the TRIAD algorithm is used in conjunction with the unscented Kalman filter (UKF) to form the nontraditional attitude filter. First the vector measurements from the magnetometer and Sun sensor are processed with the TRIAD algorithm to obtain a coarse attitude estimate for the spacecraft. In the second phase the estimated coarse attitude is used as quaternion measurements for the UKF. The UKF estimates the fine attitude, and the gyro and magnetometer biases. We evaluate the algorithm for a hypothetical nanosatellite by numerical simulations. The results show that the attitude of the satellite can be estimated with an accuracy better than 0.5\({^{\circ }}\) and the computational load decreases more than 25% compared to a traditional UKF algorithm. We discuss the algorithm’s performance in case of a time-variance in the magnetometer errors.
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References
Poghosyan A, Golkar A (2017) CubeSat evolution: analyzing CubeSat capabilities for conducting science missions. Prog Aerosp Sci 88:59–83. https://doi.org/10.1016/j.paerosci.2016.11.002
Ran D, Sheng T, Cao L, Chen X, Zhao Y (2014) Attitude control system design and on-orbit performance analysis of nano-satellite—"tian Tuo 1". Chin J Aeronaut 27:593–601. https://doi.org/10.1016/j.cja.2013.11.001
Busch S, Bangert P, Dombrovski S, Schilling K (2015) UWE-3, in-orbit performance and lessons learned of a modular and flexible satellite bus for future pico-satellite formations. Acta Astronaut 117:73–89. https://doi.org/10.1016/j.actaastro.2015.08.002
Lee H, Choi Y-H, Bang H-C, Park J-O (2008) Kalman filtering for spacecraft attitude estimation by low-cost sensors. Int J Aeronaut Space Sci 9:147–161. https://doi.org/10.5139/IJASS.2008.9.1.147
Yoo Y, Kim S, Suk J, Kim J (2016) Attitude control system design and verification for CNUSAIL-1 with solar/ drag sail. Int J Aeronaut Space Sci 17:579–92. https://doi.org/10.5139/IJASS.2016.17.4.579
Asundi S, Latchman H, Fitz-Coy N. Attitude estimation for picosatellites with distributed computing platform using Murrell’s algorithm of the extended Kalman filter. In: 21st AAS/AIAA Space Flight Mechanics Meeting, New Orleans, Louisiana, pp 1–14. https://doi.org/10.13140/RG.2.1.1821.6162
Pham MD, Low KS, Goh ST, Chen S (2015) Gain-scheduled extended kalman filter for nanosatellite attitude determination system. IEEE Trans Aerosp Electron Syst 51:1017–1028. https://doi.org/10.1109/TAES.2014.130204
Kiani M, Pourtakdoust SH, Sheikhy AA (2015) Consistent calibration of magnetometers for nonlinear attitude determination. Measurement, vol 73, pp 180–190. Elsevier Ltd. https://doi.org/10.1016/j.measurement.2015.05.005
Soken HE, Hajiyev C. Reconfigurable UKF for in-flight magnetometer calibration and attitude parameter estimation. In: IFAC Proceedings Volumes (IFAC-PapersOnline). https://doi.org/10.3182/20110828-6-IT-1002.00330
Inamori T, Sako N, Nakasuka S. Strategy of magnetometer calibration for nano-satellite missions and in-orbit performance. AIAA Guidance, Navigation, and Control Conference, American Institute of Aeronautics and Astronautics, Toronto. https://doi.org/10.2514/6.2010-7598
Springmann JC, Cutler JW (2012) Attitude-independent magnetometer calibration with time-varying bias. J Guid Control Dyn 35:1080–1088. https://doi.org/10.2514/1.56726
Kim E, Bang H, Lee S-H (2011) Attitude independent magnetometer calibration considering magnetic torquer coupling effect. J Spacecr Rockets 48:691–694. https://doi.org/10.2514/1.52634
Cilden D, Hajiyev C, Soken HE. Attitude and attitude rate estimation for a nanosatellite using SVD and UKF. In: RAST 2015—Proceedings of 7th International Conference on Recent Advances in Space Technologies. https://doi.org/10.1109/RAST.2015.7208431
Cilden D, Soken HE, Hajiyev C (2017) Nanosatellite attitude estimation from vector measurements using SVD-AIDED UKF algorithm. Metrol Measure Syst. https://doi.org/10.1515/mms-2017-0011
Soken HE, Cilden D, Hajiyev C. Integration of single-frame and filtering methods for nanosatellite attitude estimation. Multisensor Attitude Estimation. CRC Press. pp 463–484. https://doi.org/10.1201/9781315368795-27
Hajiyev C, Bahar M (2003) Attitude determination and control system design of the ITU-UUBF LEO1 satellite. Acta Astronaut 52:493–499. https://doi.org/10.1016/S0094-5765(02)00192-3
Mimasu BY, JC Van Der Ha (2008) Attitude determination concept for QSAT. pp 1–6. https://doi.org/10.2322/tstj.7.Pd_63
Nakajima Y, Murakami N, Ohtani T, Nakamura Y, Hirako K, Inoue K. SDS-4 attitude control system: in-flight results of three axis attitude control for small satellites. In: 19th IFAC Symposium on Automatic Control in Aerospace, IFAC. pp 283–238. https://doi.org/10.3182/20130902-5-DE-2040.00077
Markley FL, Crassidis JL (2014) Fundamentals of spacecraft attitude determination and control. Springer New York, New York, NY. https://doi.org/10.1007/978-1-4939-0802-8
Crassidis J, Markley FL (2003) Unscented filtering for spacecraft attitude estimation. J Guid Control Dyn 26:536–42. https://doi.org/10.2514/2.5102
Vallado DA (2001) Fundamentals of astrodynamics and applications. Springer, The Netherlands
Julier SJ, Uhlmann JK, Durrant-Whyte HF (1995) A new approach for filtering nonlinear systems. In: Proceedings of 1995 American Control Conference—ACC’95, vol 3. https://doi.org/10.1109/ACC.1995.529783
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This research is supported by JSPS KAKENHI Grant number 16K18313.
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An earlier version of this paper was presented at APISAT 2017, Seoul, Korea, October 2017.
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Söken, H.E. An Attitude Filtering and Magnetometer Calibration Approach for Nanosatellites. JASS 19, 164–171 (2018). https://doi.org/10.1007/s42405-018-0020-8
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DOI: https://doi.org/10.1007/s42405-018-0020-8