About this Journal Submit a Manuscript Table of Contents
International Journal of Aerospace Engineering
Volume 2012 (2012), Article ID 910496, 13 pages
http://dx.doi.org/10.1155/2012/910496
Research Article

Implementation of a Differential Geometric Filter for Spacecraft Formation Orbit Estimation

1MEEM Department, Michigan Technological University, Houghton, MI 49931, USA
2ECE Department, Michigan Technological University, Houghton, MI 49931, USA

Received 31 May 2011; Revised 31 August 2011; Accepted 11 October 2011

Academic Editor: Srinivas R. Vadali

Copyright © 2012 Shu Ting Goh 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. P. A. Bernhardt, C. Siefring, J. Huba, and C. Selcher, “CITRIS: the COSMIC companion for LEO radio occultation,” in Proceedings of the COSMIC Radio Occultation Workshop, 2002.
  2. C. P. Escoubet, “Cluster-II: scientific objectives and data dissemination,” European Space Agency Bulletin, vol. 102, pp. 54–60, 2000.
  3. G. Purcell, D. Kuang, S. Lichten, S. C. Wu, and L. Young, “Autonomous formation flyer (AFF) sensor technology development,” in Proceedings of the Guidance and Control Conference, 1998, AAS 98-062.
  4. T. Corazzini, A. Robertson, J. C. Adams, A. Hassibi, and J. P. How, “GPS sensing for spacecraft formation flying,” in Proceedings of the 10th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS '97), pp. 735–744, September 1997.
  5. S. G. Kim, J. L. Crassidis, Y. Cheng, A. M. Fosbury, and J. L. Junkins, “Kalman filtering for relative spacecraft attitude and position estimation,” in Proceedings of the AIAA Guidance, Navigation, and Control Conference, pp. 2518–2535, August 2005.
  6. K. K. Gunnam, D. C. Hughes, J. L. Junkins, and N. Kehtarnavaz, “A vision-based DSP embedded navigation sensor,” IEEE Sensors Journal, vol. 2, no. 5, pp. 428–441, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Valasek, K. Gunnam, J. Kimmett, M. D. Tandale, J. L. Junkins, and D. Hughes, “Vision-based sensor and navigation system for autonomous air refueling,” Journal of Guidance, Control, and Dynamics, vol. 28, no. 5, pp. 979–989, 2005. View at Scopus
  8. J. Junkins, D. Hughes, K. Wazni, and V. Pariyapong, “Vision-based navigation for rendezvous, docking and proximity operations,” in Proceedings of the 22nd Annual AAS Guidance and Control Conference, Breckenridge, Colo, USA, 1999.
  9. M. L. Psiaki, “Autonomous orbit determination for two spacecraft from relative position measurements,” Journal of Guidance, Control, and Dynamics, vol. 22, no. 2, pp. 305–312, 1999. View at Scopus
  10. N. K. Philip and M. R. Ananthasayanam, “Relative position and attitude estimation and control schemes for the final phase of an autonomous docking mission of spacecraft,” Acta Astronautica, vol. 52, no. 7, pp. 511–522, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. D. J. McTavish, R. Schumacher, and G. Okouneva, “Kalman filtering for dynamic pose and relative motion estimation in orbit,” Canadian Aeronautics and Space Journal, vol. 53, no. 3-4, pp. 95–105, 2007. View at Scopus
  12. S. T. Goh, O. Abdelkhalik, and S. A. Zekavat, “Spacecraft constellation orbit estimation via a novel wireless positioning system,” in Proceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting, Savannah, Ga, USA, 2009.
  13. D. Lee and H. Pernicka, “Vision-based relative state estimation using the unscented Kalman filter,” in Proceedings of the 19th AAS/AIAA Space Flight Mechanics Meeting, Savannah, Ga, USA, 2009.
  14. S. T. Goh, Unscented Kalman filtering for relative attitude and position estimation, M.S. thesis, University at Buffalo, 2007.
  15. J. L. Crassidis and F. L. Markley, “Unscented filtering for spacecraft attitude estimation,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 4, pp. 536–542, 2003. View at Scopus
  16. J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2004.
  17. A. A. Agrachev and R. V. Gamkrelidze, “Feedback-invariant optimal control theory and differential geometry. I. Regular extremals,” Journal of Dynamical and Control Systems, vol. 3, no. 3, pp. 343–389, 1997. View at Scopus
  18. A. P. Krishchenko, V. I. Kushnarev, A. N. Nazarenko, and S. B. Tkachev, “Numerical methods in a differential geometry approach to problems in nonlinear control theory,” Soviet journal of computer and systems sciences, vol. 29, no. 6, pp. 104–114, 1991.
  19. O. Ariff, R. Zbikowski, A. Tsourdos, and B. A. White, “Differential geometric guidance based on the involute of the target's trajectory: 2-D aspects,” in Proceedings of the American Control Conference, pp. 3640–3645, Boston, Mass, USA, July 2004.
  20. C. Li, W. Jing, H. Wang, and Z. Qi, “Analytical solution to 3D differential geometric guidance problem,” in Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics, pp. 647–652, January 2006.
  21. C.-Y. Kuo, D. Soetanto, and Y.-C. Chiou, “Geometric analysis of flight control command for tactical missile guidance,” IEEE Transactions on Control Systems Technology, vol. 9, no. 2, pp. 234–243, 2001. View at Publisher · View at Google Scholar
  22. P. K. Menon, “Differential geometric estimators for nonlinear dynamic systems,” in Proceedings of the AIAA Guidance, Navigation and Control Conference, Honolulu, Hawaii, USA, 2008.
  23. H. Tong, J. Pourrostam, and S. A. Zekavat, “LCMV beamforming for a novel wireless local positioning system: nonstationarity and cyclostationarity analysis,” Eurasip Journal on Advances in Signal Processing, vol. 2007, Article ID 98243, 12 pages, 2007. View at Publisher · View at Google Scholar
  24. H. Tong and S. A. Zekavat, “A novel wireless local positioning system via a merger of DS-CDMA and beamforming: probability-of-detection performance analysis under array perturbations,” IEEE Transactions on Vehicular Technology, vol. 56, no. 3, pp. 1307–1320, 2007. View at Publisher · View at Google Scholar
  25. L. C. Godara, “Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations,” Proceedings of the IEEE, vol. 85, no. 8, pp. 1195–1245, 1997. View at Scopus
  26. Z. Wang and S. Zekavat, “Comparison of semidistributed multinode TOA-DOA fusion localization and GPS-Aided TOA (DOA) fusion localization for MANETs,” Eurasip Journal on Advances in Signal Processing, vol. 2008, Article ID 439523, 2008. View at Publisher · View at Google Scholar
  27. Z. Wang and S. A. Zekavat, “MANET localization via multi-node TOA-DOA optimal fusion,” in Proceedings of the IEEE Milcom, Washington, DC, USA, 2006.
  28. S. T. Park and J. G. Lee, “Improved Kalman filter design for three-dimensional radar tracking,” IEEE Transactions on Aerospace and Electronic Systems, vol. 37, no. 2, pp. 727–739, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. R. R. Bate, D. D. Mueller, and J. E. White, Fundamentals of Astroydnamics, Dover, New York, NY, USA, 1971.
  30. C. F. Van Loan, “Computing integrals involving the matrix exponential,” IEEE Transactions on Automatic Control, vol. 23, no. 3, pp. 395–404, 1978. View at Scopus
  31. C.-T. Chen, Linear System Theory and Design, Oxford University Press, New York, NY, USA, 1999.
  32. H. Schaub and J. L. Junkins, Analytical Mechanics of Aerospace Systems, American Institute of Aeronautics and Astronautics, New York, NY, USA, 2003.
  33. A. Gasparri, “Sensor networks localization: a computational complexity analysis of an extended Kalman filter vs. an extended information filter,” Tech. Rep., Dipartimento di Informatica ed Automazione (DIA), Universita degli Studi “Roma Tre ”, Roma, Italy, 2007.