Abstract

The star tracker is widely used in attitude control systems of spacecraft for attitude measurement. The attitude update rate of a star tracker is important to guarantee the attitude control performance. In this paper, we propose a novel approach to improve the attitude update rate of a star tracker. The electronic Rolling Shutter (RS) imaging mode of the complementary metal-oxide semiconductor (CMOS) image sensor in the star tracker is applied to acquire star images in which the star spots are exposed with row-to-row time offsets, thereby reflecting the rotation of star tracker at different times. The attitude estimation method with a single star spot is developed to realize the multiple attitude updates by a star image, so as to reach a high update rate. The simulation and experiment are performed to verify the proposed approaches. The test results demonstrate that the proposed approach is effective and the attitude update rate of a star tracker is increased significantly.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (IEEE, 2000), pp. 299–313.
  2. F. H. Bauer and W. Dellinger, “Gyroless fine pointing on small explorer spacecraft,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 1993), pp. 492–506.
    [Crossref]
  3. T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
    [Crossref] [PubMed]
  4. T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
    [Crossref]
  5. T. Sun, F. Xing, X. Wang, J. Li, M. Wei, and Z. You, “Effective star tracking method based on optical flow analysis for star trackers,” Appl. Opt. 55(36), 10335–10340 (2016).
    [Crossref] [PubMed]
  6. G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
    [Crossref]
  7. W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
    [Crossref] [PubMed]
  8. 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(17), 20096–20110 (2013).
    [Crossref] [PubMed]
  9. H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).
  10. X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).
  11. A. B. Katake, “Modeling, image processing and attitude estimation of high speed star sensors,” Ph.D. dissertation (Texas A&M University, 2006).
  12. A. Katake and C. Bruccoleri, “StarCam SG100: a high update rate, high sensitivity stellar gyroscope for spacecraft,” Proc. SPIE 7536, 753608 (2010).
    [Crossref]
  13. W. Yu, J. Jiang, and G. Zhang, “Multiexposure imaging and parameter optimization for intensified star trackers,” Appl. Opt. 55(36), 10187–10197 (2016).
    [Crossref] [PubMed]
  14. M. Wei, F. Xing, and Z. You, “An implementation method based on ERS imaging mode for sun sensor with 1 kHz update rate and 1″ precision level,” Opt. Express 21(26), 32524–32533 (2013).
    [Crossref] [PubMed]
  15. Gpixel Inc, “4MP scientific image sensor for high speed imaging,” http://www.gpixelinc.com/en/Data/Uploads/file/14906056676139.pdf .
  16. J. Enright and T. Dzamba, “Rolling shutter compensation for star trackers,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 2012), p. 4839.
  17. C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
    [Crossref]
  18. G. Wahba, “A least squares estimate of spacecraft attitude,” SIAM Rev. 7(3), 409 (1965).
    [Crossref]
  19. D. Mortari, “A closed-form solution to the Wahba problem,” J. Astronaut. Sci. 45(2), 195–204 (1997).
  20. L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
    [Crossref]
  21. E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).
  22. F. L. Markley and J. L. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control (Springer, 2014).
  23. C. C. Liebe, “Accuracy of star tracker - a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
    [Crossref]
  24. G. Wang, F. Xing, M. Wei, and Z. You, “Rapid optimization method of the strong stray light elimination for extremely weak light signal detection,” Opt. Express 25(21), 26175–26185 (2017).
    [Crossref] [PubMed]
  25. J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
    [Crossref]
  26. F. L. Markley, “Attitude error representations for Kalman filtering,” J. Guid. Control Dyn. 26(2), 311–317 (2003).
    [Crossref]
  27. H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

2017 (1)

2016 (4)

J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
[Crossref]

T. Sun, F. Xing, X. Wang, J. Li, M. Wei, and Z. You, “Effective star tracking method based on optical flow analysis for star trackers,” Appl. Opt. 55(36), 10335–10340 (2016).
[Crossref] [PubMed]

W. Yu, J. Jiang, and G. Zhang, “Multiexposure imaging and parameter optimization for intensified star trackers,” Appl. Opt. 55(36), 10187–10197 (2016).
[Crossref] [PubMed]

L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
[Crossref]

2015 (1)

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

2013 (3)

2012 (1)

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

2011 (2)

X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

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 (2)

H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

2003 (1)

F. L. Markley, “Attitude error representations for Kalman filtering,” J. Guid. Control Dyn. 26(2), 311–317 (2003).
[Crossref]

2002 (1)

C. C. Liebe, “Accuracy of star tracker - a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

1997 (2)

D. Mortari, “A closed-form solution to the Wahba problem,” J. Astronaut. Sci. 45(2), 195–204 (1997).

C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
[Crossref]

1982 (1)

E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).

1965 (1)

G. Wahba, “A least squares estimate of spacecraft attitude,” SIAM Rev. 7(3), 409 (1965).
[Crossref]

Anderson, E. H.

E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (IEEE, 2000), pp. 299–313.

Bauer, F. H.

F. H. Bauer and W. Dellinger, “Gyroless fine pointing on small explorer spacecraft,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 1993), pp. 492–506.
[Crossref]

Bettarini, R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

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]

Casini, R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Chang, L.

L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
[Crossref]

Dellinger, W.

F. H. Bauer and W. Dellinger, “Gyroless fine pointing on small explorer spacecraft,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 1993), pp. 492–506.
[Crossref]

Dzamba, T.

J. Enright and T. Dzamba, “Rolling shutter compensation for star trackers,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 2012), p. 4839.

Enright, J.

J. Enright and T. Dzamba, “Rolling shutter compensation for star trackers,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 2012), p. 4839.

Erwin, R. S.

E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (IEEE, 2000), pp. 299–313.

Fumo, J. P.

E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (IEEE, 2000), pp. 299–313.

Guo, L.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Hosonuma, T.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Ikari, S.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Inamori, T.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Jiang, J.

J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
[Crossref]

W. Yu, J. Jiang, and G. Zhang, “Multiexposure imaging and parameter optimization for intensified star trackers,” Appl. Opt. 55(36), 10187–10197 (2016).
[Crossref] [PubMed]

Kaidy, J. T.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

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]

Kreutz-Delgado, K.

C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
[Crossref]

Landi, A.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Lefferts, E. J.

E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).

Li, J.

Li, X. J.

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

Liang, W.

X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).

Liebe, C. C.

C. C. Liebe, “Accuracy of star tracker - a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

Liu, H. B.

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

Liu, L.

J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
[Crossref]

Lorenzini, S.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Lu, X.

H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).

Mao, X.

X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).

Markley, F. L.

F. L. Markley, “Attitude error representations for Kalman filtering,” J. Guid. Control Dyn. 26(2), 311–317 (2003).
[Crossref]

E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).

Mortari, D.

D. Mortari, “A closed-form solution to the Wahba problem,” J. Astronaut. Sci. 45(2), 195–204 (1997).

Nakasuka, S.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Padgett, C.

C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
[Crossref]

Qin, F.

L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
[Crossref]

Quan, W.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Rogers, G. D.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Saisutjarit, P.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Sako, N.

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Schwinger, M. R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Shuster, M. D.

E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).

Strikwerda, T. E.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Su, D. Z.

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

Sun, T.

Tan, J. C.

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

Udomkesmalee, S.

C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
[Crossref]

Wahba, G.

G. Wahba, “A least squares estimate of spacecraft attitude,” SIAM Rev. 7(3), 409 (1965).
[Crossref]

Wang, G.

Wang, X.

Wei, M.

Xing, F.

Yang, J. K.

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

Yang, M.

H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).

You, Z.

Yu, W.

Zha, F.

L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
[Crossref]

Zhang, G.

J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
[Crossref]

W. Yu, J. Jiang, and G. Zhang, “Multiexposure imaging and parameter optimization for intensified star trackers,” Appl. Opt. 55(36), 10187–10197 (2016).
[Crossref] [PubMed]

Zhang, W.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Zheng, X.

X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).

Zhong, H.

H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).

Acta Astronaut. (1)

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut. 65(1–2), 61–74 (2009).
[Crossref]

Adv. Space Res. (1)

T. Inamori, T. Hosonuma, S. Ikari, P. Saisutjarit, N. Sako, and S. Nakasuka, “Precise attitude rate estimation using star images obtained by mission telescope for satellite missions,” Adv. Space Res. 55(4), 1199–1210 (2015).
[Crossref]

Appl. Opt. (2)

IEEE Sens. J. (1)

L. Chang, F. Qin, and F. Zha, “Pseudo open-loop unscented quaternion estimator for attitude estimation,” IEEE Sens. J. 16(11), 4460–4469 (2016).
[Crossref]

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

C. C. Liebe, “Accuracy of star tracker - a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

J. Astronaut. (1)

X. Mao, W. Liang, and X. Zheng, “A parallel computing architecture based image processing algorithm for star sensor,” J. Astronaut. 32, 613–619 (2011).

J. Astronaut. Sci. (2)

D. Mortari, “A closed-form solution to the Wahba problem,” J. Astronaut. Sci. 45(2), 195–204 (1997).

H. B. Liu, D. Z. Su, J. C. Tan, J. K. Yang, and X. J. Li, “An approach for star image simulation for star tracker considering satellite orbit motion and effect of image shift,” J. Astronaut. Sci. 32, 1190–1194 (2011).

J. Guid. Control Dyn. (3)

F. L. Markley, “Attitude error representations for Kalman filtering,” J. Guid. Control Dyn. 26(2), 311–317 (2003).
[Crossref]

E. J. Lefferts, F. L. Markley, and M. D. Shuster, “Kalman filtering for spacecraft attitude estimation,” J. Guid. Control Dyn. 5(4), 536–542 (1982).

C. Padgett, K. Kreutz-Delgado, and S. Udomkesmalee, “Evaluation of star identification techniques,” J. Guid. Control Dyn. 20(2), 259–267 (1997).
[Crossref]

Opt. Eng. (1)

J. Jiang, L. Liu, and G. Zhang, “Robust and accurate star segmentation algorithm based on morphology,” Opt. Eng. 55(6), 063101 (2016).
[Crossref]

Opt. Express (3)

Opt. Precis. Eng. (1)

H. Zhong, M. Yang, and X. Lu, “Increasing update rate for star sensor by pipelining parallel processing method,” Opt. Precis. Eng. 17, 2230–2235 (2009).

Proc. SPIE (1)

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

Sensors (Basel) (2)

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

SIAM Rev. (1)

G. Wahba, “A least squares estimate of spacecraft attitude,” SIAM Rev. 7(3), 409 (1965).
[Crossref]

Other (6)

F. L. Markley and J. L. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control (Springer, 2014).

E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (IEEE, 2000), pp. 299–313.

F. H. Bauer and W. Dellinger, “Gyroless fine pointing on small explorer spacecraft,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 1993), pp. 492–506.
[Crossref]

A. B. Katake, “Modeling, image processing and attitude estimation of high speed star sensors,” Ph.D. dissertation (Texas A&M University, 2006).

Gpixel Inc, “4MP scientific image sensor for high speed imaging,” http://www.gpixelinc.com/en/Data/Uploads/file/14906056676139.pdf .

J. Enright and T. Dzamba, “Rolling shutter compensation for star trackers,” in Proceedings of the AIAA Guidance, Navigation and Control Conference (AIAA, 2012), p. 4839.

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Figures (17)

Fig. 1
Fig. 1 Operations of GS and RS modes.
Fig. 2
Fig. 2 Processing procedure of attitude update based on RS mode.
Fig. 3
Fig. 3 Pixel architectures of GS and RS.
Fig. 4
Fig. 4 Vector observation model of star tracker.
Fig. 5
Fig. 5 Optical design of star tracker. (a) Imaging lens and light paths. (b) Point spread functions (PSFs) at different incident angles and wavelengths. The PSFs at different incident angles and wavelengths are analyzed by ZEMAX software. (c) Shape of a star spot in the star image.
Fig. 6
Fig. 6 Architecture of the designed star tracker.
Fig. 7
Fig. 7 Star image interfered by moonlight.
Fig. 8
Fig. 8 Definition of structuring elements.
Fig. 9
Fig. 9 Star extraction with stray light from the moon.
Fig. 10
Fig. 10 Attitude estimate errors with 3σ-error boundaries.
Fig. 11
Fig. 11 Synthetic star image with 15 star spots.
Fig. 12
Fig. 12 Attitude quaternion updates by the 15 star spots.
Fig. 13
Fig. 13 Number of attitude updates.
Fig. 14
Fig. 14 Laboratory experiment system.
Fig. 15
Fig. 15 Star tracker in the experiment.
Fig. 16
Fig. 16 Attitude estimate errors in the experiment.
Fig. 17
Fig. 17 Number of attitude updates in the experiment.

Tables (5)

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Table 1 Gauss radii of PSFs at different incident angles

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Table 2 Notations for the Pair of Star Spots in Two Successive Frames of Star Images

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Table 3 Parameters of Star Tracker

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Table 4 Positions of the 15 star spots

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Table 5 Parameters of the star tracker in the experiment

Equations (44)

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f GS = 1 t e +n t rd
t row = t rd
f ERS > m t e +n t rd =m f GS
A( q )=( q 4 2 q v 2 ) I 3 +2 q v q v T 2 q 4 [ q v × ]
[ q v × ]=[ 0 q 3 q 2 q 3 0 q 1 q 2 q 1 0 ]
q ˙ = 1 2 Ω( ω )q
Ω( ω )=[ [ ω× ] ω ω T 0 ]
q( t 2 )= Ω ¯ [ t 2 ,ω( t 1 ) ]q( t 1 )
Ω ¯ [ t 2 ,ω( t 1 ) ]=cos( 1 2 ω( t 1 ) ( t 2 t 1 ) ) I 4 +[ [ Ψ( t 2 , t 1 )× ] Ψ( t 2 , t 1 ) Ψ ( t 2 , t 1 ) T 0 ]
Ψ( t 2 , t 1 )= sin( ω( t 1 ) ( t 2 t 1 )/2 ) ω( t 1 ) ω( t 1 )
δq=q q ^ 1
q ^ ˙ = 1 2 Ω( ω ^ ) q ^
δ q ˙ = 1 2 { [ ω ^ 0 ]δqδq[ ω ^ 0 ] }+ 1 2 [ δω 0 ]δq
δq= [ θ/2 ψ/2 ϕ/2 1 ] T
x ˙ =[ ω ^ × ]x+δω
x( t 2 )=F( t 2 , t 1 )x( t 1 )+Γ( t 2 , t 1 )δω( t 1 )
F( t 2 , t 1 )=exp{ [ ω ^ ( t 1 )× ]( t 2 t 1 ) } = I 3 [ ω ^ ( t 1 )× ] ω ^ ( t 1 ) sin( ω ^ ( t 1 ) ( t 2 t 1 ) ) + [ ω ^ ( t 1 )× ] 2 ω ^ ( t 1 ) 2 [ 1cos( ω ^ ( t 1 ) ( t 2 t 1 ) ) ]
Γ( t 2 , t 1 )= 0 t 2 t 1 exp{ [ ω ^ ( t 1 )× ]t }dt =( t 2 t 1 ) I 3 [ ω ^ ( t 1 )× ] ω ^ ( t 1 ) 2 [ 1cos( ω ^ ( t 1 ) ( t 2 t 1 ) ) ] + [ ω ^ ( t 1 )× ] 2 ω ^ ( t 1 ) 2 [ t 2 t 1 sin( ω ^ ( t 1 ) ( t 2 t 1 ) ) ω ^ ( t 1 ) ]
r=[ cosαcosβ sinαcosβ sinβ ]
b= 1 x ¯ 2 + y ¯ 2 + f 2 [ x ¯ y ¯ f ]
I( x,y )= I 0 2π σ PSF 2 exp[ ( x x ¯ ) 2 2 σ PSF 2 ]exp[ ( y y ¯ ) 2 2 σ PSF 2 ]
g( x,y )=f( x,y ) B s min{ f( x,y )ΔBΘ B o ,f( x,y ) B s }
b ˜ ( t 2 )=A( q( t 2 ) )r( t 2 )+v( t 2 )
b ˜ ( t 2 )=A( δq( t 2 ) q ^ ( t 2 | t 1 ) )r( t 2 )+v( t 2 ) =A( δq( t 2 ) )A( q ^ ( t 2 | t 1 ) )r( t 2 )+v( t 2 ) ( I 3 [ x( t 2 )× ] )A( q ^ ( t 2 | t 1 ) )r( t 2 )+v( t 2 ) =A( q ^ ( t 2 | t 1 ) )r( t 2 )+[ A( q ^ ( t 2 | t 1 ) )r( t 2 )× ]x( t 2 )+v( t 2 )
y( t 2 )=H( t 2 )x( t 2 )+v( t 2 )
y( t 2 )= b ˜ ( t 2 )A( q ^ ( t 2 | t 1 ) )r( t 2 )
H( t 2 )=[ A( q ^ ( t 2 | t 1 ) )r( t 2 )× ]
b ˜ i ( 2 ) b ˜ i ( 1 ) =[ A( q i ( 2 ) )A( q i ( 1 ) ) ] r i + v i ( 2 ) v i ( 1 )
A( q i ( 2 ) )( I 3 ( t i ( 2 ) t i ( 1 ) )[ ω× ] )A( q i ( 1 ) )
b ˜ i ( 2 ) b ˜ i ( 1 ) =( t i ( 2 ) t i ( 1 ) )[ ω× ]A( q i ( 1 ) ) r i + v i ( 2 ) v i ( 1 ) =( t i ( 2 ) t i ( 1 ) )[ ω× ]( b ˜ i ( 1 ) v i ( 1 ) )+ v i ( 2 ) v i ( 1 )
( b ˜ i ( 2 ) b ˜ i ( 1 ) )/ ( t i ( 2 ) t i ( 1 ) ) =[ b ˜ i ( 1 ) × ]ω+ w i
w i =[ ω× ] v i ( 1 ) + ( v i ( 2 ) v i ( 1 ) )/ ( t i ( 2 ) t i ( 1 ) )
E{ w i }=0 E{ w i w i T }= σ 2 [ ω× ] [ ω× ] T +[ 2 σ 2 / ( t i ( 2 ) t i ( 1 ) ) 2 ] I 3
E{ w i w i T }[ 2 σ 2 / ( t i ( 2 ) t i ( 1 ) ) 2 ] I 3
ω ^ = ( i=1 N B i ) 1 i=1 N 1 t i ( 2 ) t i ( 1 ) [ b ˜ i ( 1 ) × ] T b ˜ i ( 2 )
δω=ω ω ^ = ( i=1 N Β i ) 1 i=1 N [ b ˜ i ( 1 ) × ] T w i
E{ δω }=0 Q=E{ δωδ ω T }= ( i=1 N B i ) 1 ( i=1 N 2 σ 2 ( t i ( 2 ) t i ( 1 ) ) 2 B i ) ( i=1 N B i ) 1
q ^ ( t 2 | t 1 )= Ω ¯ [ t 2 , ω ^ ( t 1 ) ] q ^ ( t 1 )
P( t 2 | t 1 )=F( t 2 , t 1 )P( t 1 )F ( t 2 , t 1 ) T +Γ( t 2 , t 1 )Q( t 1 )Γ ( t 2 , t 1 ) T
K( t 2 )=P( t 2 | t 1 )H ( t 2 ) T [ H( t 2 )P( t 2 | t 1 )H ( t 2 ) T +R ] 1
x ^ ( t 2 )=K( t 2 )y( t 2 )
P( t 2 )=[ I 3 K( t 2 )H( t 2 ) ]P( t 2 | t 1 )
q ^ ( t 2 )=[ 1 2 x ^ ( t 2 ) 1 ] q ^ ( t 2 | t 1 )
q ^ ( 0 )= [ 0 0 1 0 ] T ω ^ ( 0 )= [ 0.0177 0.0173 0.0185 ] T P( 0 )=0.1 I 3 Q( 0 )= 10 3 I 3

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