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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 72–83 | Cite as

Kalman filter for attitude determination of a CubeSat using low-cost sensors

  • Leandro Baroni
Article

Abstract

Nanosatellites have become a common choice for certain space missions, principally in universities, due to their low production and launching costs and reduced developing time. However, they present some technological challenges. In a CubeSat, total mass and available electric power are very restricted. Therefore, subsystem components and payload must be designed to have the smallest size, mass, and power consumption possible for the mission. Regarding to Attitude Determination and Control System, one of restrictions in developing CubeSats is the need to use small and low-cost sensors which fulfill satellite building restrictions. Thus, commercial-off-the-shelf components are a common choice in CubeSat development, but these parts normally present high noise levels. Therefore, a multiplicative Kalman filter for attitude determination algorithm based on quaternions is proposed. Data are simulated using typical values for low-cost sensors, namely, 3-axes magnetometer, 3-axes gyroscope, and a sun sensor. Results are compared to the extended Kalman filter proposed for AAUSAT-3 satellite and to the QUEST method, showing a better precision and low execution time compared to other methods.

Keywords

Attitude determination Kalman filter Simulation CubeSat 

Mathematics Subject Classification

93E10 93E11 

References

  1. Bouwmeester J, Guo J (2010) Survey of worldwide pico- and nanosatellite missions, distributions and subsystem technology. Acta Astronautica 67(7–8):854–862CrossRefGoogle Scholar
  2. Carrara V, Kuga HK, Bringhenti PM, de Carvalho MJM (2014) Attitude determination, control and operating modes for CONASAT Cubesats. In: Proceedings of 24 International Symposium on Space Flight Dynamics (ISSFD 2014), Laurel, Maryland, USAGoogle Scholar
  3. Crassidis J, Junkins J (2012) Optimal estimation of dynamic systems. CRC, Boca RatonzbMATHGoogle Scholar
  4. Duarte RO, Martins-Filho LS, Kuga HK (2009) Performance comparison of attitude determination algorithms developed to run in a microprocessor environment. In: International Congress of Mechanical Engineering, 20th, Proceedings of COBEM 2009, ABCM, Gramado, RS, BrazilGoogle Scholar
  5. Duarte RO, Torres FE, Gomes FH, Martins-Filho LS, Kuga HK (2011) An attitude determination system implementation to low orbit small satellite with fault tolerant techniques. In: Proceedings of the 8th IAA Symposium on Small Satellites for Earth Observation, IAA, Berlin, pp 453–459Google Scholar
  6. Flenniken IV WS (2005) Modeling inertial measurement units and analyzing the effect of their errors in navigation applications. Master’s thesis, Auburn UniversityGoogle Scholar
  7. Garcia RV, Kuga HK, Zanardi MC (2012) Unscented Kalman filter applied to the spacecraft attitude estimation with Euler angles. Math Probl Eng 2012:1–12. doi: 10.1155/2012/985429 MathSciNetCrossRefzbMATHGoogle Scholar
  8. Garcia RV, Kuga HK, Zanardi MC (2016a) Unscented Kalman filter for determination of spacecraft attitude using different attitude parameterizations and real data. J Aerosp Technol Manag 8(1):82–90. doi: 10.5028/jatm.v8i1.509 CrossRefGoogle Scholar
  9. Garcia RV, Matos NFO, Kuga HK, Zanardi MC (2016b) Unscented Kalman filter for spacecraft attitude estimation using modified Rodrigues parameters and real data. Comput Appl Math 3:835–846MathSciNetCrossRefGoogle Scholar
  10. Gravdahl JT (2004) Magnetic attitude control for satellites. In: Proceedings of the 8th IEEE Conference on Decision and Control, IEEE, pp 261–266. doi: 10.1109/CDC.2004.1428640
  11. Jensen KF, Vinther K (2010) Attitude determination and control system for AAUSAT3. Master’s thesis, Aalborg University, AalborgGoogle Scholar
  12. Lefferts EJ, Markley FL, Shuster MD (1982) Kalman filtering for spacecraft attitude estimation. J Guid Control Dyn 5(5):417–429CrossRefGoogle Scholar
  13. Ovchinnikov MY, Penkov VI, Malphrus B, Brown K, Roldugin DS (2014) Active magnetic attitude control algorithms for a CubeSat for astrophysics research. Keldysh Institute Preprints 47. http://keldysh.ru/papers/2014/prep2014_47_eng.pdf. Accessed 9 Mar 2017
  14. Reda I, Andreas A (2008) Solar position algorithm for solar radiation applications. Tech. rep., National Renewable Energy Laboratory, NREL/TP-560-34302Google Scholar
  15. Selva D, Krejci D (2012) A survey and assessment of the capabilities of CubeSats for Earth observation. Acta Astronautica 74:50–68CrossRefGoogle Scholar
  16. Shuster MD, Oh SD (1981) Three-axis attitude determination from vector observations. J Guid Control 4(1):70–77CrossRefGoogle Scholar
  17. Swartwout M (2013) The long-threatened flood of university-class spacecraft (and CubeSats) has come: Analyzing the numbers. In: Proceedings of the AIAA/USU Small Satellite Conference, AAIA, Utah State University, Logan, UT, Standards and Education, SSC13-IX-01Google Scholar
  18. The CubeSat Program (2015) CubeSat design specification rev. 13. http://www.cubesat.org/s/cds_rev13_final2.pdf. Accessed 22 Feb 2017
  19. Thébault E et al (2015) International geomagnetic reference field: the 12th generation. Earth Planets Sp. doi: 10.1186/s40623-015-0228-9 CrossRefGoogle Scholar
  20. Theil S, Appel P, Schleicher A (2003) Low cost, good accuracy – attitude determination using magnetometer and simple sun sensor. In: Proceedings of the AIAA/USU Small Satellite Conference, AAIA, Logan, UT, SSC03-XI-7Google Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Center for Engineering, Modeling and Applied Social SciencesFederal University of ABC Rua ArcturusSão Bernardo do CampoBrazil

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