Abstract

Benefiting from rapid development of imaging sensor technology, modern optical technology, and a high-speed computing chip, the star tracker’s accuracy, dynamic performance, and update rate have been greatly improved with low power consumption and miniature size. The star tracker is currently one of the most competitive attitude measurement sensors. However, due to restrictions of the optical imaging system, difficulties still exist in moving star spot detection and star tracking when in special motion conditions. An effective star tracking method based on optical flow analysis for star trackers is proposed in this paper. Spot-based optical flow, based on a gray gradient between two adjacent star images, is analyzed to distinguish the star spot region and obtain an accurate star spot position so that the star tracking can keep continuous under high dynamic conditions. The obtained star vectors and extended Kalman filter (EKF) are then combined to conduct an angular velocity estimation to ensure region prediction of the star spot; this can be combined with the optical flow analysis result. Experiment results show that the method proposed in this paper has advantages in conditions of large angular velocity and large angular acceleration, despite the presence of noise. Higher functional density and better performance can be achieved; thus, the star tracker can be more widely applied in small satellites, remote sensing, and other complex space missions.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Novel approach to improve the attitude update rate of a star tracker

Shuo Zhang, Fei Xing, Ting Sun, Zheng You, and Minsong Wei
Opt. Express 26(5) 5164-5181 (2018)

Simulation analysis of dynamic working performance for star trackers

Juan Shen, Guangjun Zhang, and Xinguo Wei
J. Opt. Soc. Am. A 27(12) 2638-2647 (2010)

Star spot location estimation using Kalman filter for star tracker

Hai-bo Liu, Jian-kun Yang, Jiong-qi Wang, Ji-chun Tan, and Xiu-jian Li
Appl. Opt. 50(12) 1735-1744 (2011)

References

  • View by:
  • |
  • |
  • |

  1. U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
    [Crossref]
  2. U. Schmidt, C. Elstner, and K. Michel, “ASTRO 15 star tracker flight experience and further improvements towards the ASTRO APS star tracker,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2008), paper 6649.
  3. U. Schmidt, “ASTRO APS-the next generation Hi-Rel star tracker based on active pixel sensor technology,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2005), p. 5925.
  4. L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.
  5. D. L. Michaels, “Ball aerospace star tracker achieves high tracking accuracy for a moving star field,” in Aerospace Conference (IEEE, 2005), pp. 1–7.
  6. L. W. Cassidy, “HDOS HD-1003 star tracker,” Proc. SPIE 2466, 93–99 (1995).
    [Crossref]
  7. F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.
  8. M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
    [Crossref]
  9. L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.
  10. T. E. Paulsen and L. Maresi, “Calibration and verification of the TERMA star tracker for the NEMO satellite,” in AIAA Space Conference and Exposition (American Institute of Aeronautics and Astronautics, 2000), p. 5338.
  11. P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.
  12. T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
    [Crossref]
  13. A. Katake and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
    [Crossref]
  14. F. Xing, Z. You, and T. Sun, “Method for determining attitude of star sensor based on rolling shutter imaging,” U.S. patent20140232867A1 (21August2014).
  15. T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
    [Crossref]
  16. L. Ma, F. Bernelli-Zazzera, G. Jiang, X. Wang, Z. Huang, and S. Qin, “Region-confined restoration method for motion-blurred star image of the star sensor under dynamic conditions,” Appl. Opt. 55, 4621–4631 (2016).
    [Crossref]
  17. T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
    [Crossref]
  18. J. Yan, J. Jiang, and G. Zhang, “Dynamic imaging model and parameter optimization for a star tracker,” Opt. Express 24, 5961–5983 (2016).
    [Crossref]
  19. L. Ma, D. Zhan, G. Jiang, S. Fu, H. Jia, X. Wang, Z. Huang, J. Zheng, F. Hu, W. Wu, and S. Qin, “Attitude-correlated frames approach for a star sensor to improve attitude accuracy under highly dynamic conditions,” Appl. Opt. 54, 7559–7566 (2015).
    [Crossref]
  20. L. Kazemi, J. Enright, and T. Dzamba, “Improving star tracker centroiding performance in dynamic imaging conditions,” in IEEE Aerospace Conference (IEEE, 2015), pp. 1–8.
  21. J. Zhang, Y. Hao, L. Wang, and D. Liu, “Studies on dynamic motion compensation and positioning accuracy on star tracker,” Appl. Opt. 54, 8417–8424 (2015).
    [Crossref]
  22. M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
    [Crossref]
  23. J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
    [Crossref]
  24. T. Ye and F. Zhou, “Autonomous space target recognition and tracking approach using star sensors based on a Kalman filter,” Appl. Opt. 54, 3455–3469 (2015).
    [Crossref]
  25. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
    [Crossref]
  26. B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
    [Crossref]
  27. G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
    [Crossref]
  28. B. D. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” in Proc. 7th International Joint Conference on Artificial Intelligence (IJCAI) (Morgan Kaufmann, 1981), pp. 674–679.
  29. J.-Y. Bouguet, Pyramidal Implementation of the Affine Lucas Kanade Feature Tracker Description of the Algorithm (Intel Corporation, 2001).
  30. T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21, 20096–20110 (2013).
    [Crossref]
  31. C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
    [Crossref]
  32. P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).
  33. I. Y. Bar-Itzhack, “Classification of algorithms for angular velocity estimation,” J. Guid. Control Dyn. 24, 214–218 (2001).
    [Crossref]
  34. J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control Dyn. 25, 1165–1168 (2002).
    [Crossref]
  35. S. Jo, Y. Choi, and H. Bang, “Optimal angular velocity estimation of spacecraft using only star tracker measurements,” J. Guid. Control Dyn. 38, 342–346 (2015).
    [Crossref]
  36. H. Liu, J. Yang, W. Yi, J. Wang, J. Yang, X. Li, and J. Tan, “Angular velocity estimation from measurement vectors of star tracker,” Appl. Opt. 51, 3590–3598 (2012).
    [Crossref]
  37. G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
    [Crossref]

2016 (2)

2015 (5)

2014 (2)

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
[Crossref]

2013 (3)

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
[Crossref]

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21, 20096–20110 (2013).
[Crossref]

2012 (1)

2010 (1)

A. Katake and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

2009 (1)

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

2006 (1)

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

2005 (1)

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
[Crossref]

2004 (1)

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
[Crossref]

2003 (1)

P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).

2002 (2)

J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control Dyn. 25, 1165–1168 (2002).
[Crossref]

G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
[Crossref]

2001 (1)

I. Y. Bar-Itzhack, “Classification of algorithms for angular velocity estimation,” J. Guid. Control Dyn. 24, 214–218 (2001).
[Crossref]

1995 (1)

L. W. Cassidy, “HDOS HD-1003 star tracker,” Proc. SPIE 2466, 93–99 (1995).
[Crossref]

1994 (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[Crossref]

1981 (1)

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[Crossref]

Accardo, D.

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

Airy, S. P.

F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.

Alex, T. K.

G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
[Crossref]

Bang, H.

S. Jo, Y. Choi, and H. Bang, “Optimal angular velocity estimation of spacecraft using only star tracker measurements,” J. Guid. Control Dyn. 38, 342–346 (2015).
[Crossref]

Bar-Itzhack, I. Y.

I. Y. Bar-Itzhack, “Classification of algorithms for angular velocity estimation,” J. Guid. Control Dyn. 24, 214–218 (2001).
[Crossref]

Barron, J. L.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[Crossref]

Beauchemin, S. S.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[Crossref]

Benzi, E.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

Bernelli-Zazzera, F.

Betto, M.

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

Bhat, M. S.

G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
[Crossref]

Blarre, L.

L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.

Boldrini, F.

F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.

Bouguet, J.-Y.

J.-Y. Bouguet, Pyramidal Implementation of the Affine Lucas Kanade Feature Tracker Description of the Algorithm (Intel Corporation, 2001).

Bruccoleri, C.

A. Katake and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Cassidy, L. W.

L. W. Cassidy, “HDOS HD-1003 star tracker,” Proc. SPIE 2466, 93–99 (1995).
[Crossref]

Choi, Y.

S. Jo, Y. Choi, and H. Bang, “Optimal angular velocity estimation of spacecraft using only star tracker measurements,” J. Guid. Control Dyn. 38, 342–346 (2015).
[Crossref]

Collingwood, C.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Crassidis, J. L.

P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).

J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control Dyn. 25, 1165–1168 (2002).
[Crossref]

Cropp, A.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Denver, T.

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

Dzamba, T.

L. Kazemi, J. Enright, and T. Dzamba, “Improving star tracker centroiding performance in dynamic imaging conditions,” in IEEE Aerospace Conference (IEEE, 2015), pp. 1–8.

Elstner, C.

U. Schmidt, C. Elstner, and K. Michel, “ASTRO 15 star tracker flight experience and further improvements towards the ASTRO APS star tracker,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2008), paper 6649.

Enright, J.

L. Kazemi, J. Enright, and T. Dzamba, “Improving star tracker centroiding performance in dynamic imaging conditions,” in IEEE Aerospace Conference (IEEE, 2015), pp. 1–8.

Fasano, G.

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

Fellowes, S.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Fiksel, T.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

Fleet, D. J.

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[Crossref]

Fu, S.

Giulicchi, L.

F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.

Gleason, S.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Grassi, M.

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

Gromov, K.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
[Crossref]

Hao, Y.

Horn, B. K. P.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[Crossref]

Hu, F.

Huang, Z.

Jia, H.

Jiang, G.

Jiang, J.

J. Yan, J. Jiang, and G. Zhang, “Dynamic imaging model and parameter optimization for a star tracker,” Opt. Express 24, 5961–5983 (2016).
[Crossref]

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

Jo, S.

S. Jo, Y. Choi, and H. Bang, “Optimal angular velocity estimation of spacecraft using only star tracker measurements,” J. Guid. Control Dyn. 38, 342–346 (2015).
[Crossref]

Jørgensen, J. L.

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

Jørgensen, P. S.

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

Junkins, J. L.

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
[Crossref]

P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).

Kanade, T.

B. D. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” in Proc. 7th International Joint Conference on Artificial Intelligence (IJCAI) (Morgan Kaufmann, 1981), pp. 674–679.

Katake, A.

A. Katake and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Kazemi, L.

L. Kazemi, J. Enright, and T. Dzamba, “Improving star tracker centroiding performance in dynamic imaging conditions,” in IEEE Aerospace Conference (IEEE, 2015), pp. 1–8.

Kwiatkowski, A.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

Lalani, S.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Li, B.

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
[Crossref]

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

Li, X.

H. Liu, J. Yang, W. Yi, J. Wang, J. Yang, X. Li, and J. Tan, “Angular velocity estimation from measurement vectors of star tracker,” Appl. Opt. 51, 3590–3598 (2012).
[Crossref]

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

Liebe, C. C.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
[Crossref]

Liu, D.

Liu, H.

Lucas, B. D.

B. D. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” in Proc. 7th International Joint Conference on Artificial Intelligence (IJCAI) (Morgan Kaufmann, 1981), pp. 674–679.

Ma, L.

Maresi, L.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

T. E. Paulsen and L. Maresi, “Calibration and verification of the TERMA star tracker for the NEMO satellite,” in AIAA Space Conference and Exposition (American Institute of Aeronautics and Astronautics, 2000), p. 5338.

Martinez, P.

L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.

Meller, D. M.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
[Crossref]

Michaels, D. L.

D. L. Michaels, “Ball aerospace star tracker achieves high tracking accuracy for a moving star field,” in Aerospace Conference (IEEE, 2005), pp. 1–7.

Michel, K.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

U. Schmidt, C. Elstner, and K. Michel, “ASTRO 15 star tracker flight experience and further improvements towards the ASTRO APS star tracker,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2008), paper 6649.

Mikkelsen, O.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

Mortari, D.

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
[Crossref]

Nielsen, R.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

Noteborn, R.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

Oddos-Marcel, L.

L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.

Oosthuizen, P.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Ouaknine, J.

L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.

Paulsen, T.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

Paulsen, T. E.

T. E. Paulsen and L. Maresi, “Calibration and verification of the TERMA star tracker for the NEMO satellite,” in AIAA Space Conference and Exposition (American Institute of Aeronautics and Astronautics, 2000), p. 5338.

Pradarutti, B.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

Procopio, D.

F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.

Qin, S.

Rao, G. N.

G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
[Crossref]

Rufino, G.

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

Samaan, M. A.

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
[Crossref]

Schmidt, U.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

U. Schmidt, “ASTRO APS-the next generation Hi-Rel star tracker based on active pixel sensor technology,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2005), p. 5925.

U. Schmidt, C. Elstner, and K. Michel, “ASTRO 15 star tracker flight experience and further improvements towards the ASTRO APS star tracker,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2008), paper 6649.

Schunck, B. G.

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[Crossref]

Singla, P.

P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).

Steinbach, I.

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

Sun, T.

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
[Crossref]

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
[Crossref]

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21, 20096–20110 (2013).
[Crossref]

F. Xing, Z. You, and T. Sun, “Method for determining attitude of star sensor based on rolling shutter imaging,” U.S. patent20140232867A1 (21August2014).

Tan, J.

Wang, J.

Wang, L.

Wang, X.

Wei, M.

Wei, X.

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

Wu, W.

Xing, F.

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
[Crossref]

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
[Crossref]

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21, 20096–20110 (2013).
[Crossref]

F. Xing, Z. You, and T. Sun, “Method for determining attitude of star sensor based on rolling shutter imaging,” U.S. patent20140232867A1 (21August2014).

Yan, J.

Yang, J.

Ye, T.

Yi, W.

You, Z.

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Smearing model and restoration of star image under conditions of variable angular velocity and long exposure time,” Opt. Express 22, 6009–6024 (2014).
[Crossref]

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
[Crossref]

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21, 20096–20110 (2013).
[Crossref]

F. Xing, Z. You, and T. Sun, “Method for determining attitude of star sensor based on rolling shutter imaging,” U.S. patent20140232867A1 (21August2014).

Zhan, D.

Zhang, G.

J. Yan, J. Jiang, and G. Zhang, “Dynamic imaging model and parameter optimization for a star tracker,” Opt. Express 24, 5961–5983 (2016).
[Crossref]

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

Zhang, J.

Zheng, J.

Zhou, F.

Acta Astronaut. (1)

M. Betto, J. L. Jørgensen, P. S. Jørgensen, and T. Denver, “Advanced stellar compass deep space navigation, ground testing results,” Acta Astronaut. 59, 1020–1028 (2006).
[Crossref]

Adv. Astronaut. Sci. (1)

P. Singla, J. L. Crassidis, and J. L. Junkins, “Spacecraft angular rate estimation algorithms for star tracker-based attitude determination,” Adv. Astronaut. Sci. 114, 1303–1316 (2003).

Appl. Opt. (5)

Artif. Intell. (1)

B. K. P. Horn and B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[Crossref]

CEAS Space J. (1)

U. Schmidt, T. Fiksel, A. Kwiatkowski, I. Steinbach, B. Pradarutti, K. Michel, and E. Benzi, “Autonomous star sensor ASTRO APS: flight experience on Alphasat,” CEAS Space J. 7, 237–246 (2015).
[Crossref]

IEEE Aerosp. Electron. Syst. Mag. (1)

J. Jiang, G. Zhang, X. Wei, and X. Li, “Rapid star tracking algorithm for star sensor,” IEEE Aerosp. Electron. Syst. Mag. 24(9), 23–33 (2009).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (1)

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
[Crossref]

Int. J. Comput. Vis. (1)

J. L. Barron, D. J. Fleet, and S. S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis. 12, 43–77 (1994).
[Crossref]

J. Guid. Control Dyn. (5)

I. Y. Bar-Itzhack, “Classification of algorithms for angular velocity estimation,” J. Guid. Control Dyn. 24, 214–218 (2001).
[Crossref]

J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control Dyn. 25, 1165–1168 (2002).
[Crossref]

S. Jo, Y. Choi, and H. Bang, “Optimal angular velocity estimation of spacecraft using only star tracker measurements,” J. Guid. Control Dyn. 38, 342–346 (2015).
[Crossref]

G. N. Rao, T. K. Alex, and M. S. Bhat, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control Dyn. 25, 433–441 (2002).
[Crossref]

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27, 91–99 (2004).
[Crossref]

Meas. Sci. Technol. (1)

T. Sun, F. Xing, Z. You, X. Wang, and B. Li, “Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions,” Meas. Sci. Technol. 25, 085003 (2014).
[Crossref]

Opt. Express (3)

Proc. SPIE (2)

L. W. Cassidy, “HDOS HD-1003 star tracker,” Proc. SPIE 2466, 93–99 (1995).
[Crossref]

A. Katake and C. Bruccoleri, “StarCam SG100: a high-update rate, high-sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
[Crossref]

Sensors (2)

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors 13, 4598–4623 (2013).
[Crossref]

G. Fasano, G. Rufino, D. Accardo, and M. Grassi, “Satellite angular velocity estimation based on star images and optical flow techniques,” Sensors 13, 12771–12793 (2013).
[Crossref]

Other (12)

B. D. Lucas and T. Kanade, “An iterative image registration technique with an application to stereo vision,” in Proc. 7th International Joint Conference on Artificial Intelligence (IJCAI) (Morgan Kaufmann, 1981), pp. 674–679.

J.-Y. Bouguet, Pyramidal Implementation of the Affine Lucas Kanade Feature Tracker Description of the Algorithm (Intel Corporation, 2001).

L. Kazemi, J. Enright, and T. Dzamba, “Improving star tracker centroiding performance in dynamic imaging conditions,” in IEEE Aerospace Conference (IEEE, 2015), pp. 1–8.

F. Xing, Z. You, and T. Sun, “Method for determining attitude of star sensor based on rolling shutter imaging,” U.S. patent20140232867A1 (21August2014).

F. Boldrini, D. Procopio, S. P. Airy, and L. Giulicchi, “Miniaturised star tracker (AA-STR) ready to fly,” in Proceedings of the 4S Symposium: Small Satellites, Systems and Services (ESA SP-571), La Rochelle, France, 2004, p. 571.

U. Schmidt, C. Elstner, and K. Michel, “ASTRO 15 star tracker flight experience and further improvements towards the ASTRO APS star tracker,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2008), paper 6649.

U. Schmidt, “ASTRO APS-the next generation Hi-Rel star tracker based on active pixel sensor technology,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2005), p. 5925.

L. Blarre, J. Ouaknine, L. Oddos-Marcel, and P. Martinez, “High accuracy Sodern star trackers: recent improvements proposed on SED36 and HYDRA star trackers,” in AIAA Guidance, Navigation, and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6046.

D. L. Michaels, “Ball aerospace star tracker achieves high tracking accuracy for a moving star field,” in Aerospace Conference (IEEE, 2005), pp. 1–7.

L. Maresi, R. Noteborn, O. Mikkelsen, R. Nielsen, and T. Paulsen, “A compact autonomous medium resolution, high accuracy star tracker for earth remote sensing spacecraft,” in 4th ESA International Conference on Spacecraft Guidance, Navigation and Control Systems (European Space Agency, 2000), pp. 531–536.

T. E. Paulsen and L. Maresi, “Calibration and verification of the TERMA star tracker for the NEMO satellite,” in AIAA Space Conference and Exposition (American Institute of Aeronautics and Astronautics, 2000), p. 5338.

P. Oosthuizen, S. Fellowes, C. Collingwood, S. Lalani, A. Cropp, and S. Gleason, “Development and on-orbit results of the SSTL low cost commercial star tracker,” in AIAA Guidance, Navigation and Control Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2006), p. 6045.

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (15771 KB)      Continuous results of the optical flow analysis.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1. Flow chart of the proposed star tracking method.
Fig. 2.
Fig. 2. Pyramid decomposition diagram.
Fig. 3.
Fig. 3. Adaptive reference window setting. (a) is the result of optical flow analysis; (b) is the window setting result.
Fig. 4.
Fig. 4. Star tracker in the experiment.
Fig. 5.
Fig. 5. Real night sky experiment of the star tracker with turntable.
Fig. 6.
Fig. 6. Star spot of two adjacent star images (a) and (b) (with no additional angular velocity).
Fig. 7.
Fig. 7. Star spot of two adjacent dynamic star images (a) and (b).
Fig. 8.
Fig. 8. Successive star images under conditions of large angular acceleration.
Fig. 9.
Fig. 9. Star spot distinguish based on optical flow analysis; (a) is enlarged optical flow field combined with the original star image, and (b) is color display of the optical flow field of the whole star image.
Fig. 10.
Fig. 10. Angular velocity measurement by the star tracker with different rotation mode; (a) 1.4776°/s in maximum, (b) 1.6856°/s in maximum, (c) 1.9018°/s in maximum, and (d) 2.1192°/s in maximum.
Fig. 11.
Fig. 11. Measurement error of angular velocity by the star tracker with angular velocity of 2.1192°/s in maximum.
Fig. 12.
Fig. 12. Comparison and analysis between the common-used star tracking method and the proposed star tracking method.

Tables (1)

Tables Icon

Table 1. Parameters of the Star Tracker in the Experiment

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

E ( x , y , t ) = E ( x + d x , y + d y , t + d t ) .
E x d x d t + E y d y d t + E t = 0 .
[ E x , E y ] · [ u v ] = E t .
[ u v ] = [ i = 1 n E x ( q i ) 2 i = 1 n E x ( q i ) E y ( q i ) i = 1 n E y ( q i ) E x ( q i ) i = 1 n E y ( q i ) 2 ] 1 [ i = 1 n E x ( q i ) E t ( q i ) i = 1 n E y ( q i ) E t ( q i ) ] .
ω ( t ) = 1 Δ t { n = 1 N σ ¯ n 2 [ w ( t ) n × ] T [ w ( t ) n × ] } 1 × n = 1 N σ ¯ n 2 [ w ( t ) n × ] T w ( t Δ t ) n ,
x k = [ ω 1 ω 2 ω 3 ] T .
{ x k = f ( x k 1 , γ k 1 ) z k = h ( x k , χ k ) .
x k = f ( x k 1 , γ k 1 ) = I 3 × 3 · x k 1 + γ k 1 .
z k = 1 Δ t { n = 1 N σ ¯ n 2 [ w k n × ] T [ w k n × ] } × n = 1 N σ ¯ n 2 [ w k n × ] T w ( k 1 ) n .
{ p ( γ k 1 ) N ( 0 , Q k 1 ) p ( χ k ) N ( 0 , R k ) .

Metrics