Table of Contents Author Guidelines Submit a Manuscript
Journal of Sensors
Volume 2017, Article ID 9560108, 9 pages
https://doi.org/10.1155/2017/9560108
Research Article

Linear Kalman Filter for Attitude Estimation from Angular Rate and a Single Vector Measurement

1College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2School of Automation, University of Electronic Science and Technology of China, Chengdu, China

Correspondence should be addressed to Jin Wu; moc.liamtoh@ctseu_uw_nij

Received 7 May 2017; Accepted 20 July 2017; Published 18 October 2017

Academic Editor: Mohannad Al-Durgham

Copyright © 2017 Shangqiu Shan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Zhu, Z. Zhou, Y. Li, C. Rizos, and X. Wang, “Further development of the attitude difference method for estimating deflections of the vertical in real time,” Measurement Science and Technology, vol. 27, no. 7, Article ID 075004, 2016. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Zhou, Y. Li, J. Zhang, and C. Rizos, “Integrated navigation system for a low-cost quadrotor aerial vehicle in the presence of rotor influences,” Journal of Surveying Engineering, vol. 143, no. 1, 2017. View at Publisher · View at Google Scholar · View at Scopus
  3. Z. Zhou, Y. Li, J. Liu, and G. Li, “Equality constrained robust measurement fusion for adaptive kalman-filter-based heterogeneous multi-sensor navigation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 49, no. 4, pp. 2146–2157, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Yun, J. Calusdian, E. R. Bachmann, and R. B. McGhee, “Estimation of human foot motion during normal walking using inertial and magnetic sensor measurements,” IEEE Transactions on Instrumentation and Measurement, vol. 61, no. 7, pp. 2059–2072, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. W. T. Higgins Jr., “A comparison of complementary and Kalman filtering,” IEEE Transactions on Aerospace and Electronic Systems, vol. 11, no. 3, pp. 321–325, 1975. View at Google Scholar · View at Scopus
  6. R. E. Kalman and R. S. Bucy, “New results in linear filtering and prediction theory,” Transactions of the ASME D, vol. 83, pp. 95–108, 1961. View at Google Scholar · View at MathSciNet
  7. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of Fluids Engineering, vol. 82, no. 1, pp. 35–45, 1960. View at Publisher · View at Google Scholar
  8. G. Ligorio and A. M. Sabatini, “A novel kalman filter for human motion tracking with an inertial-based dynamic inclinometer,” IEEE Transactions on Biomedical Engineering, vol. 62, no. 8, pp. 2033–2043, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. A. M. Sabatini, “Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing,” IEEE Transactions on Biomedical Engineering, vol. 53, no. 7, pp. 1346–1356, 2006. View at Google Scholar
  10. W. Li and J. Wang, “Effective adaptive Kalman filter for MEMS-IMU/magnetometers integrated attitude and heading reference systems,” Journal of Navigation, vol. 66, no. 1, pp. 99–113, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. S. Suh, “Orientation estimation using a quaternion-based indirect Kalman filter with adaptive estimation of external acceleration,” IEEE Transactions on Instrumentation and Measurement, vol. 59, no. 12, pp. 3296–3305, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. R. G. Valenti, I. Dryanovski, and J. Xiao, “A linear Kalman filter for MARG orientation estimation using the algebraic quaternion algorithm,” IEEE Transactions on Instrumentation and Measurement, vol. 65, no. 2, pp. 467–481, 2016. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Euston, P. Coote, R. Mahony, J. Kim, and T. Hamel, “A complementary filter for attitude estimation of a fixed-wing UAV,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '08), pp. 340–345, IEEE, Nice, France, September 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. J. Cockcroft, J. H. Muller, and C. Scheffer, “A complementary filter for tracking bicycle crank angles using inertial sensors, kinematic constraints, and vertical acceleration updates,” IEEE Sensors Journal, vol. 15, no. 8, pp. 4218–4225, 2015. View at Publisher · View at Google Scholar · View at Scopus
  15. C. K. Chui and G. Chen, Kalman Filtering: with Real-Time Applications, Springer Science & Business Media, Berlin, Germany, 2008.
  16. S. O. H. Madgwick, A. J. L. Harrison, and R. Vaidyanathan, “Estimation of IMU and MARG orientation using a gradient descent algorithm,” in Proceedings of the IEEE International Conference on Rehabilitation Robotics (ICORR '11), pp. 1–7, Zurich, Switzerland, July 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Tian, H. Wei, and J. Tan, “An adaptive-gain complementary filter for real-time human motion tracking with MARG sensors in free-living environments,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 21, no. 2, pp. 254–264, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Marantos, Y. Koveos, and K. J. Kyriakopoulos, “UAV state estimation using adaptive complementary filters,” IEEE Transactions on Control Systems Technology, vol. 24, no. 4, pp. 1214–1226, 2016. View at Publisher · View at Google Scholar · View at Scopus
  19. J. F. Vasconcelos, B. Cardeira, C. Silvestre, P. Oliveira, and P. Batista, “Discrete-time complementary filters for attitude and position estimation: design, analysis and experimental validation,” IEEE Transactions on Control Systems Technology, vol. 19, no. 1, pp. 181–198, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Mahony, T. Hamel, and J.-M. Pflimlin, “Nonlinear complementary filters on the special orthogonal group,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203–1218, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  21. G. Wahba, “A least squares estimate of satellite attitude,” SIAM Review, vol. 7, no. 3, p. 409, 1965. View at Publisher · View at Google Scholar
  22. M. D. Shuster and S. D. Oh, “Three-axis attitude determination from vector observations,” Journal of Guidance and Control, vol. 4, no. 1, pp. 70–77, 1981. View at Publisher · View at Google Scholar · View at Scopus
  23. F. L. Markley, “Attitude determination using vector observations: a fast optimal matrix algorithm,” The Journal of the Astronautical Sciences, vol. 41, no. 2, pp. 261–280, 1993. View at Google Scholar · View at MathSciNet
  24. Attitude determination and parameter estimation using vector observations and the Singular Value Decomposition, p. 245258, 1988.
  25. Y. Yang and Z. Zhou, “An analytic solution to Wahbas problem,” Aerospace Science and Technology, vol. 30, no. 1, pp. 46–49, 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. D. Mortari, “ESOQ: a closed-form solution to the Wahba problem,” The Journal of the Astronautical Sciences, vol. 45, no. 2, pp. 195–204, 1997. View at Google Scholar · View at MathSciNet
  27. F. L. Markley and D. Mortari, “How to estimate attitude from vector observations,” Advances in the Astronautical Sciences, vol. 103, no. 3, pp. 1979–1996, 2000. View at Google Scholar · View at Scopus
  28. J. Wu, Z. Zhou, J. Chen, H. Fourati, and R. Li, “Fast complementary filter for attitude estimation using low-cost MARG sensors,” IEEE Sensors Journal, vol. 16, no. 18, pp. 6997–7007, 2016. View at Publisher · View at Google Scholar
  29. J. Wu, Z. Zhou, B. Gao, R. Li, Y. Cheng, and H. Fourati, “Fast linear quaternion attitude estimator using vector observations,” IEEE Transactions on Automation Science and Engineering, no. 99, pp. 1–13, 2017. View at Publisher · View at Google Scholar
  30. J. Wu, Z. Zhou, R. Li, L. Yang, and H. Fourati, “Attitude determination using a single sensor observation: analytic quaternion solutions and property discussion,” IET Science, Measurement & Technology, vol. 11, no. 6, article 731, 2017. View at Publisher · View at Google Scholar
  31. J. Farrell, Aided Navigation: GPS with High Rate Sensors, McGraw-Hill Education, New York, NY, USA, 2008.
  32. A. Makni, H. Fourati, and A. Y. Kibangou, “Energy-aware adaptive attitude estimation under external acceleration for pedestrian navigation,” IEEE/ASME Transactions on Mechatronics, vol. 21, no. 3, pp. 1366–1375, 2016. View at Publisher · View at Google Scholar · View at Scopus
  33. D. Titterton and J. Weston, Strapdown Inertial Navigation Technology, IET Digital Library, Stevenage, UK, 2nd edition, 2004. View at Publisher · View at Google Scholar
  34. F. H. Schlee, C. J. Standish, and N. F. TODA, “Divergence in the Kalman filter,” AIAA Journal, vol. 5, no. 6, pp. 1114–1120, 1967. View at Publisher · View at Google Scholar
  35. N. A. Carlson, “Federated square root filter for decentralized parallel processes,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 3, pp. 517–525, 1990. View at Publisher · View at Google Scholar · View at Scopus
  36. A. M. Sabatini, “Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation,” Sensors, vol. 11, no. 10, pp. 9182–9206, 2011. View at Publisher · View at Google Scholar · View at Scopus