Abstract

Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient.

© 2011 Optical Society of America

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  1. C. C. Liebe, “Accuracy performance of star trackers—a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38, 587–599 (2002).
    [CrossRef]
  2. C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10, 10–16 (1995).
    [CrossRef]
  3. S. B. Grossman and R. B. Emmons, “Performance analysis and size optimization of focal planes for point-source tracking algorithm applications,” Opt. Eng. 23, 167–176 (1984).
  4. S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.
  5. S. Lee, “Pointing accuracy improvement using model-based noise reduction method,” Proc. SPIE 4635, 65–71 (2002).
    [CrossRef]
  6. G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53, 135–147 (2003).
    [CrossRef]
  7. B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
    [CrossRef]
  8. J. Yang, T. Zhang, J. Y. Song, and H. L. Zhu, “A new sub-pixel subdivision location algorithm for star image,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, M.Z.Nashed, ed. (IEEE, 2009), pp. 111–124.
  9. D. Motari, A. Romoli, and A. Difesa, “StarNav III: a three fields of view star tracker,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2002), pp. 47–57.
  10. H. Y. Kim, Novel Methods for Spacecraft Attitude Estimation (Texas A&M University, 2002).
  11. M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
    [CrossRef]
  12. J. Ares and J. Arines, “Influence of thresholding on centroid statistics: full analytical description,” Appl. Opt. 43, 5796–5805 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. I. Y. Bar-Itzhack and Y. Oshman, “Attitude determination from vector observations: quaternion estimation,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 128–136 (1985).
    [CrossRef]
  15. B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).
  16. S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
    [CrossRef]
  17. N. H. Smith, “Localized Distortion Estimation and Correction for the ICESat Star Trackers,” (University of Texas, 2006).
  18. H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
    [CrossRef]
  19. Y. Shi and X. Zhang, “Kalman-filtering-based angular velocity estimation using infrared attitude information of spacecraft,” Opt. Eng. 39, 551–557 (2000).
    [CrossRef]
  20. P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).
  21. M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. Aerosp. Electron. Syst. 41, 1246–1254 (2005).
    [CrossRef]
  22. D. M. Li, X. W. Wang, and M. Guo, “Image simulation of star sensor and movement characteristic analysis of background and target,” Optoelectron. Eng. 36, 40–44(2009).
  23. J. Keat, “Analysis of least squares attitude determination routine DOAOP,” CSC/TM-77/6034 (Computer Sciences Corporation, 1977).
  24. D. P. Woodbury and J. L. Junkins, “Improving camera intrinsic parameter estimates for star tracker applications,” in AIAA Guidance, Navigation, and Control Conference (AIAA, 2009), paper AIAA 2009-6312.
  25. H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
    [CrossRef]
  26. J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control. Dyn. 25, 1165–1168 (2002).
    [CrossRef]

2011 (1)

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

2010 (1)

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

2009 (2)

B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).

D. M. Li, X. W. Wang, and M. Guo, “Image simulation of star sensor and movement characteristic analysis of background and target,” Optoelectron. Eng. 36, 40–44(2009).

2007 (3)

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

N. Hagen, M. Kupinski, and E. L. Dereniak, “Gaussian profile estimation in one dimension,” Appl. Opt. 46, 5374–5383(2007).
[CrossRef] [PubMed]

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 (2)

J. Ares and J. Arines, “Influence of thresholding on centroid statistics: full analytical description,” Appl. Opt. 43, 5796–5805 (2004).
[CrossRef] [PubMed]

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

2003 (1)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53, 135–147 (2003).
[CrossRef]

2002 (4)

S. Lee, “Pointing accuracy improvement using model-based noise reduction method,” Proc. SPIE 4635, 65–71 (2002).
[CrossRef]

C. C. Liebe, “Accuracy performance of star trackers—a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38, 587–599 (2002).
[CrossRef]

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
[CrossRef]

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

2000 (1)

Y. Shi and X. Zhang, “Kalman-filtering-based angular velocity estimation using infrared attitude information of spacecraft,” Opt. Eng. 39, 551–557 (2000).
[CrossRef]

1995 (1)

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10, 10–16 (1995).
[CrossRef]

1985 (1)

I. Y. Bar-Itzhack and Y. Oshman, “Attitude determination from vector observations: quaternion estimation,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 128–136 (1985).
[CrossRef]

1984 (1)

S. B. Grossman and R. B. Emmons, “Performance analysis and size optimization of focal planes for point-source tracking algorithm applications,” Opt. Eng. 23, 167–176 (1984).

Accardo, D.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53, 135–147 (2003).
[CrossRef]

Ares, J.

Arines, J.

Bar-Itzhack, I. Y.

I. Y. Bar-Itzhack and Y. Oshman, “Attitude determination from vector observations: quaternion estimation,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 128–136 (1985).
[CrossRef]

Crassidis, J. L.

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

Crenshaw, M.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Dereniak, E. L.

Difesa, A.

D. Motari, A. Romoli, and A. Difesa, “StarNav III: a three fields of view star tracker,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2002), pp. 47–57.

Downes, R.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Emmons, R. B.

S. B. Grossman and R. B. Emmons, “Performance analysis and size optimization of focal planes for point-source tracking algorithm applications,” Opt. Eng. 23, 167–176 (1984).

Griffith, D. T.

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

Grossman, S. B.

S. B. Grossman and R. B. Emmons, “Performance analysis and size optimization of focal planes for point-source tracking algorithm applications,” Opt. Eng. 23, 167–176 (1984).

Guo, M.

D. M. Li, X. W. Wang, and M. Guo, “Image simulation of star sensor and movement characteristic analysis of background and target,” Optoelectron. Eng. 36, 40–44(2009).

Hagen, N.

Hornsey, R.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

Jia, H.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Junkins, J. L.

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

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

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
[CrossRef]

D. P. Woodbury and J. L. Junkins, “Improving camera intrinsic parameter estimates for star tracker applications,” in AIAA Guidance, Navigation, and Control Conference (AIAA, 2009), paper AIAA 2009-6312.

Katake, A.

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

Katsanis, R.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Keat, J.

J. Keat, “Analysis of least squares attitude determination routine DOAOP,” CSC/TM-77/6034 (Computer Sciences Corporation, 1977).

Kim, H. Y.

H. Y. Kim, Novel Methods for Spacecraft Attitude Estimation (Texas A&M University, 2002).

Kraemar, S.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Kupinski, M.

Lee, S.

S. Lee, “Pointing accuracy improvement using model-based noise reduction method,” Proc. SPIE 4635, 65–71 (2002).
[CrossRef]

Li, B. H.

B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).

Li, D. M.

D. M. Li, X. W. Wang, and M. Guo, “Image simulation of star sensor and movement characteristic analysis of background and target,” Optoelectron. Eng. 36, 40–44(2009).

Li, X. J.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Liebe, C. C.

C. C. Liebe, “Accuracy performance of star trackers—a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38, 587–599 (2002).
[CrossRef]

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10, 10–16 (1995).
[CrossRef]

Liu, H. B.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Liu, J.

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

Liu, R.

B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).

Ma, Y. Y.

B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).

McGrath, M.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Mebrahtu, H.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

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]

Motari, D.

D. Motari, A. Romoli, and A. Difesa, “StarNav III: a three fields of view star tracker,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2002), pp. 47–57.

Oshman, Y.

I. Y. Bar-Itzhack and Y. Oshman, “Attitude determination from vector observations: quaternion estimation,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 128–136 (1985).
[CrossRef]

Pollock, T. C.

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
[CrossRef]

Quine, B. M.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

Robinson, R.

S. Kraemar, R. Downes, R. Katsanis, M. Crenshaw, M. McGrath, and R. Robinson, “STIS target acquisition,” in Proceedings of Hubble Space Telescope Calibration Workshop, (Space Telescope Science Institute, 1997), pp. 39–46, http://www.stsci.edu/~stefano/newcal97/pdf/kraemers.pdf.

Romoli, A.

D. Motari, A. Romoli, and A. Difesa, “StarNav III: a three fields of view star tracker,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2002), pp. 47–57.

Rufino, G.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53, 135–147 (2003).
[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]

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
[CrossRef]

Shi, Y.

Y. Shi and X. Zhang, “Kalman-filtering-based angular velocity estimation using infrared attitude information of spacecraft,” Opt. Eng. 39, 551–557 (2000).
[CrossRef]

Singla, P.

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

Smith, N. H.

N. H. Smith, “Localized Distortion Estimation and Correction for the ICESat Star Trackers,” (University of Texas, 2006).

Song, J. Y.

J. Yang, T. Zhang, J. Y. Song, and H. L. Zhu, “A new sub-pixel subdivision location algorithm for star image,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, M.Z.Nashed, ed. (IEEE, 2009), pp. 111–124.

Su, D. Z.

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Tan, J. C.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Tarasyuk, V.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

Tian, J. W.

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

Tian, Y. L.

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

Wang, C. H.

B. H. Li, Y. Y. Ma, R. Liu, and C. H. Wang, “A predictive centroiding algorithm of unmatched stars for star sensor,” Opt. Precis. Eng. 17, 191–195 (2009).

Wang, J. Q.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

Wang, X. W.

D. M. Li, X. W. Wang, and M. Guo, “Image simulation of star sensor and movement characteristic analysis of background and target,” Optoelectron. Eng. 36, 40–44(2009).

Woodbury, D. P.

D. P. Woodbury and J. L. Junkins, “Improving camera intrinsic parameter estimates for star tracker applications,” in AIAA Guidance, Navigation, and Control Conference (AIAA, 2009), paper AIAA 2009-6312.

Yang, J.

J. Yang, T. Zhang, J. Y. Song, and H. L. Zhu, “A new sub-pixel subdivision location algorithm for star image,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, M.Z.Nashed, ed. (IEEE, 2009), pp. 111–124.

Yang, J. K.

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Zhang, T.

J. Yang, T. Zhang, J. Y. Song, and H. L. Zhu, “A new sub-pixel subdivision location algorithm for star image,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, M.Z.Nashed, ed. (IEEE, 2009), pp. 111–124.

Zhang, X.

Y. Shi and X. Zhang, “Kalman-filtering-based angular velocity estimation using infrared attitude information of spacecraft,” Opt. Eng. 39, 551–557 (2000).
[CrossRef]

Zheng, S.

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

Zhu, H. L.

J. Yang, T. Zhang, J. Y. Song, and H. L. Zhu, “A new sub-pixel subdivision location algorithm for star image,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing, M.Z.Nashed, ed. (IEEE, 2009), pp. 111–124.

Acta Astronaut. (1)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53, 135–147 (2003).
[CrossRef]

Appl. Opt. (2)

Comput. Phys. Commun. (1)

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: a new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177, 700–706 (2007).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (4)

C. C. Liebe, “Accuracy performance of star trackers—a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38, 587–599 (2002).
[CrossRef]

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10, 10–16 (1995).
[CrossRef]

I. Y. Bar-Itzhack and Y. Oshman, “Attitude determination from vector observations: quaternion estimation,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 128–136 (1985).
[CrossRef]

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

J. Astronaut. Sci. (2)

P. Singla, D. T. Griffith, A. Katake, and J. L. Junkins, “Attitude and interlock angle estimation using split-field-of-view star tracker,” J. Astronaut. Sci. 55, 85–105 (2007).

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50113–123 (2002).
[CrossRef]

J. Guid. Control. Dyn. (1)

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

Opt. Eng. (5)

H. B. Liu, J. Q. Wang, J. C. Tan, J. K. Yang, H. Jia, and X. J. Li, “Autonomous on-orbit calibration of a star tracker camera,” Opt. Eng. 50, 023604 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 073601 (2010).
[CrossRef]

Y. Shi and X. Zhang, “Kalman-filtering-based angular velocity estimation using infrared attitude information of spacecraft,” Opt. Eng. 39, 551–557 (2000).
[CrossRef]

S. Zheng, Y. L. Tian, J. W. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43, 2796–2805 (2004).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Measurement model of star tracker.

Fig. 2
Fig. 2

Scheme of the proposed star spot location approach with the Kalman filter.

Fig. 3
Fig. 3

Flowchart of the proposed simulation.

Fig. 4
Fig. 4

Star track on the star tracker frame (in pixels).

Fig. 5
Fig. 5

Star spot location error in the conventional star acquisition process.

Fig. 6
Fig. 6

Final star spot location error with the Kalman filter.

Fig. 7
Fig. 7

Attitude angle errors using the measurement centroids achieved by conventional method.

Fig. 8
Fig. 8

Attitude angle errors using the star spot locations with Kalman filter.

Tables (2)

Tables Icon

Table 1 Star Spot Location Errors with Different Angular Velocity Accuracies (in Pixels)

Tables Icon

Table 2 Star Spot Location Errors with Different Data Rates of Star Tracker (in Pixels)

Equations (25)

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v = [ cos α cos δ sin α cos δ sin δ ] ,
w = 1 x 2 + y 2 + f 2 [ x y f ] ,
w = M ( q ) v = [ q 1 2 + q 2 2 q 3 2 q 4 2 2 ( q 2 q 3 + q 1 q 4 ) 2 ( q 2 q 4 q 1 q 3 ) 2 ( q 2 q 3 q 1 q 4 ) q 1 2 q 2 2 + q 3 2 q 4 2 2 ( q 4 q 3 q 1 q 2 ) 2 ( q 2 q 4 q 1 q 3 ) 2 ( q 4 q 3 q 1 q 2 ) q 1 2 - q 2 2 q 3 2 + q 4 2 ] v ,
1 x 2 + y 2 + f 2 [ x y ] = M ( q ) v = [ q 1 2 + q 2 2 q 3 2 q 4 2 2 ( q 2 q 3 + q 1 q 4 ) 2 ( q 2 q 4 q 1 q 3 ) 2 ( q 2 q 3 q 1 q 4 ) q 1 2 q 2 2 + q 3 2 q 4 2 2 ( q 4 q 3 q 1 q 2 ) ] v .
1 ( x 2 + y 2 + f 2 ) 3 / 2 [ ( y 2 + f 2 ) x t ( x 2 + f 2 ) y t ] = [ A 1 A 2 A 3 A 4 ] q t v ,
A 1 = M q 1 = 2 [ q 1 q 4 q 3 q 4 q 1 q 2 ] ,
A 2 = M q 2 = 2 [ q 2 q 3 q 4 q 3 q 2 q 1 ] ,
A 3 = M q 3 = 2 [ q 3 q 2 q 1 q 2 q 3 q 4 ] ,
A 4 = M q 4 = 2 [ q 4 q 1 q 2 q 1 q 4 q 3 ] ,
q t = [ q 1 t q 2 t q 3 t q 4 t ] T .
[ x t y t ] = ( x 2 + y 2 + f 2 ) 3 / 2 [ 1 ( y 2 + f 2 ) 0 0 1 ( x 2 + f 2 ) ] { [ A 1 A 2 A 3 A 4 ] q t v } .
{ ( x 2 + y 2 + f 2 ) 3 / 2 y 2 + f 2 = f ( 1 + x 2 + y 2 f 2 ) 3 / 2 1 + y 2 f 2 f ( x 2 + y 2 + f 2 ) 3 / 2 x 2 + f 2 = f ( 1 + x 2 + y 2 f 2 ) 3 / 2 1 + x 2 f 2 f .
[ x t y t ] T = f [ A 1 A 2 A 3 A 4 ] q t v .
[ x ^ t + δ t y ^ t + δ t ] = [ x t y t ] + [ x t / t y t / t ] δ t ,
[ x ˜ y ˜ ] = [ x c y c ] [ δ x ˜ ( x c , y c ) δ y ˜ ( x c , y c ) ] = [ x c y c ] [ ( g 1 + g 3 ) x c 2 + g 4 x c y c + g 1 y c 2 + κ 1 x c x c 2 + y c 2 + κ 2 x c ( x c 2 + y c 2 ) + κ 3 x c ( x c 2 + y c 2 ) 3 2 g 2 x c 2 + g 3 x c y c + ( g 2 + g 4 ) y c 2 + κ 1 y c x c 2 + y c 2 + κ 2 y c ( x c 2 + y c 2 ) + κ 3 y c ( x c 2 + y c 2 ) 3 2 ] .
{ X ( t + δ t ) = I 2 × 2 X ( t ) + X ( t ) t δ t + N p Z ( t + δ t ) = I 2 × 2 X ( t + δ t ) + N m ,
{ X ( t + δ t ) = X ( t ) + X ( t ) t δ t P t + δ t = P t + Q e K t + δ t = P t + δ t [ P t + δ t + R e ] 1 X ( t + δ t ) = X ( t + δ t ) + K t + δ t [ Z ( t + δ t ) X ( t + δ t ) ] P t + δ t = [ I 2 × 2 K t + δ t ] P t + δ t ,
Q e = E [ ( X [ x y ] ) ( X [ x y ] ) T ] = [ E [ ( x ^ x ) 2 ] E [ ( x ^ x ) ( y ^ y ) ] E [ ( x ^ x ) ( y ^ y ) ] E [ ( y ^ y ) 2 ] ] ,
R e = [ ( Z [ x y ] ) ( Z [ x t y t ] ) T ] = [ E [ ( x ˜ x ) 2 ] E [ ( x ˜ x ) ( y ˜ y ) ] E [ ( x ˜ x ) ( y ˜ y ) ] E [ ( y ˜ y ) 2 ] ] ,
P = E [ ( X [ x y ] ) ( X [ x y ] ) T ] = [ E [ ( x ^ x ) 2 ] E [ ( x ^ x ) ( y ^ y ) ] E [ ( x ^ x ) ( y ^ y ) ] E [ ( y ^ y ) 2 ] ] ,
{ α = arctan ( Y / X ) , 0 ° α < 360 ° δ = arctan ( Z / X 2 + Y 2 ) , 90 ° δ 90 ° ,
M = [ cos θ sin δ cos α sin θ sin α cos θ sin δ sin α + sin θ cos α cos θ cos δ sin θ sin δ cos α cos θ sin α sin θ sin δ sin α + cos θ cos α sin θ cos δ cos δ cos α cos δ sin α sin δ ] ,
θ = arccos ( Y Z X 2 + Y 2 X 2 + Z 2 ) ,
R = [ sin φ cos γ sin φ sin γ cos φ sin γ cos γ 0 cos φ cos γ cos φ sin γ sin φ ] .
M = R × M .

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