Abstract

In most spacecraft, there is a need to know the craft’s angular rate. Approaches with least squares and an adaptive Kalman filter are proposed for estimating the angular rate directly from the star tracker measurements. In these approaches, only knowledge of the vector measurements and sampling interval is required. The designed adaptive Kalman filter can filter out noise without information of the dynamic model and inertia dyadic. To verify the proposed estimation approaches, simulations based on the orbit data of the challenging minisatellite payload (CHAMP) satellite and experimental tests with night-sky observation are performed. Both the simulations and experimental testing results have demonstrated that the proposed approach performs well in terms of accuracy, robustness, and performance.

© 2012 Optical Society of America

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References

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  1. M. A. Paluszek, J. B. Mueller, and M. G. Littman, “Optical navigation system,” in AIAA Infotech at Aerospace 2010, April 20, 2010–April 22, 2010 (American Institute of Aeronautics and Astronautics, 2010).
  2. H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
    [CrossRef]
  3. B. N. Agrawal and W. J. Palermo, “Angular rate estimation for gyroless satellite attitude control,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).
  4. M. D. Shuster, “A survey of attitude representations,” J. Astronautical Sciences 41, 439–517 (1993).
  5. Y. Oshman and F. Landis Markley, “Sequential attitude and attitude-rate estimation using integrated-rate parameters,” J. Guid. Control. Dyn. 22, 385–394 (1999).
    [CrossRef]
  6. I. Y. Bar-Itzhack, “Classification of algorithms for angular velocity estimation,” J. Guid. Control. Dyn. 24, 214–218 (2001).
    [CrossRef]
  7. I. Y. Bar-Itzhack, R. R. Harman, and D. Choukroun, “State-dependent pseudo-linear filters for spacecraft attitude and rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).
  8. I. Y. Bar-Itzhack, and R. R. Harman, “A feedback approach to spacecraft angular rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit21–24 August 2006 (Keystone, 2006).
  9. A. Carmi, and Y. Oshman, “Robust spacecraft angular-rate estimation from vector observations using fast interlaced particle filtering,” in AIAA Guidance, Navigation, and Control Conference and Exhibit15–18 August 2005 (AIAA, 2005).
  10. R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
    [CrossRef]
  11. J. L. Crassidis, “Angular velocity determination directly from star tracker measurements,” J. Guid. Control. Dyn. 25, 1165–1168 (2002).
    [CrossRef]
  12. H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
    [CrossRef]
  13. M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
    [CrossRef]
  14. G. Welch and G. Bishop, “An introduction to the Kalman filter,” SIGGRAPH 2001, Los Angeles, Calif., August 12–17 (SIGGRAPH, 2001).
  15. G. Nagendra Rao and T. K. Alex, “Incremental-angle and angular velocity estimation using a star sensor,” J. Guid. Control. Dyn. 25, 433–441 (2002).
    [CrossRef]
  16. 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, 23604–23608 (2011).
    [CrossRef]
  17. A. P. Sage and G. W. Husa, “Adaptive filtering with unknown prior statistics,” in Joint American Control Conference, 769–774 (1969).
  18. R. A. Singer, “Estimating optimal tracking filter performance for manned maneuvering targets,” IEEE Trans. on Aerospace and Electronic Systems AES-6, 473–483 (1970).
    [CrossRef]
  19. 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. Astronautical Sciences 32, 1190–1194 (2011).
  20. H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
    [CrossRef]
  21. C. Padgett and K. Kreutz-Delgado, “A grid algorithm for autonomous star identification,” IEEE Trans. on Aerospace and Electronic Systems 33, 202–212 (1997).
    [CrossRef]
  22. M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronautical Sciences 50, 113–123 (2002).
    [CrossRef]
  23. M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. on Aerospace and Electronic Systems 41, 1246–1254 (2005).
    [CrossRef]

2011

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, 23604–23608 (2011).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

2010

H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

2008

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[CrossRef]

2005

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

2002

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronautical Sciences 50, 113–123 (2002).
[CrossRef]

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

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

2001

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

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

1999

Y. Oshman and F. Landis Markley, “Sequential attitude and attitude-rate estimation using integrated-rate parameters,” J. Guid. Control. Dyn. 22, 385–394 (1999).
[CrossRef]

1997

C. Padgett and K. Kreutz-Delgado, “A grid algorithm for autonomous star identification,” IEEE Trans. on Aerospace and Electronic Systems 33, 202–212 (1997).
[CrossRef]

1993

M. D. Shuster, “A survey of attitude representations,” J. Astronautical Sciences 41, 439–517 (1993).

1970

R. A. Singer, “Estimating optimal tracking filter performance for manned maneuvering targets,” IEEE Trans. on Aerospace and Electronic Systems AES-6, 473–483 (1970).
[CrossRef]

Agrawal, B. N.

B. N. Agrawal and W. J. Palermo, “Angular rate estimation for gyroless satellite attitude control,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

Alex, T. K.

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

Azor, R.

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

Bar-Itzhack, I. Y.

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

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

I. Y. Bar-Itzhack, and R. R. Harman, “A feedback approach to spacecraft angular rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit21–24 August 2006 (Keystone, 2006).

I. Y. Bar-Itzhack, R. R. Harman, and D. Choukroun, “State-dependent pseudo-linear filters for spacecraft attitude and rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

Bishop, G.

G. Welch and G. Bishop, “An introduction to the Kalman filter,” SIGGRAPH 2001, Los Angeles, Calif., August 12–17 (SIGGRAPH, 2001).

Carmi, A.

A. Carmi, and Y. Oshman, “Robust spacecraft angular-rate estimation from vector observations using fast interlaced particle filtering,” in AIAA Guidance, Navigation, and Control Conference and Exhibit15–18 August 2005 (AIAA, 2005).

Choi, Y.

H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
[CrossRef]

Choukroun, D.

I. Y. Bar-Itzhack, R. R. Harman, and D. Choukroun, “State-dependent pseudo-linear filters for spacecraft attitude and rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

Crassidis, J. L.

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

Deutschmann, J. K.

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

Harman, R. R.

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

I. Y. Bar-Itzhack, and R. R. Harman, “A feedback approach to spacecraft angular rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit21–24 August 2006 (Keystone, 2006).

I. Y. Bar-Itzhack, R. R. Harman, and D. Choukroun, “State-dependent pseudo-linear filters for spacecraft attitude and rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

Husa, G. W.

A. P. Sage and G. W. Husa, “Adaptive filtering with unknown prior statistics,” in Joint American Control Conference, 769–774 (1969).

Jaroux, B. A.

H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
[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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

Junkins, J. L.

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. on Aerospace and Electronic Systems 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. Astronautical Sciences 50, 113–123 (2002).
[CrossRef]

Kolomenkin, M.

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[CrossRef]

Kreutz-Delgado, K.

C. Padgett and K. Kreutz-Delgado, “A grid algorithm for autonomous star identification,” IEEE Trans. on Aerospace and Electronic Systems 33, 202–212 (1997).
[CrossRef]

Landis Markley, F.

Y. Oshman and F. Landis Markley, “Sequential attitude and attitude-rate estimation using integrated-rate parameters,” J. Guid. Control. Dyn. 22, 385–394 (1999).
[CrossRef]

Leeghim, H.

H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
[CrossRef]

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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

Lindenbaum, M.

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[CrossRef]

Littman, M. G.

M. A. Paluszek, J. B. Mueller, and M. G. Littman, “Optical navigation system,” in AIAA Infotech at Aerospace 2010, April 20, 2010–April 22, 2010 (American Institute of Aeronautics and Astronautics, 2010).

Liu, H. B.

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

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, 23604–23608 (2011).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

Mortari, D.

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

Mueller, J. B.

M. A. Paluszek, J. B. Mueller, and M. G. Littman, “Optical navigation system,” in AIAA Infotech at Aerospace 2010, April 20, 2010–April 22, 2010 (American Institute of Aeronautics and Astronautics, 2010).

Oshman, Y.

Y. Oshman and F. Landis Markley, “Sequential attitude and attitude-rate estimation using integrated-rate parameters,” J. Guid. Control. Dyn. 22, 385–394 (1999).
[CrossRef]

A. Carmi, and Y. Oshman, “Robust spacecraft angular-rate estimation from vector observations using fast interlaced particle filtering,” in AIAA Guidance, Navigation, and Control Conference and Exhibit15–18 August 2005 (AIAA, 2005).

Padgett, C.

C. Padgett and K. Kreutz-Delgado, “A grid algorithm for autonomous star identification,” IEEE Trans. on Aerospace and Electronic Systems 33, 202–212 (1997).
[CrossRef]

Palermo, W. J.

B. N. Agrawal and W. J. Palermo, “Angular rate estimation for gyroless satellite attitude control,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

Paluszek, M. A.

M. A. Paluszek, J. B. Mueller, and M. G. Littman, “Optical navigation system,” in AIAA Infotech at Aerospace 2010, April 20, 2010–April 22, 2010 (American Institute of Aeronautics and Astronautics, 2010).

Pollak, S.

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[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. Astronautical Sciences 50, 113–123 (2002).
[CrossRef]

Rao, G. Nagendra

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

Sage, A. P.

A. P. Sage and G. W. Husa, “Adaptive filtering with unknown prior statistics,” in Joint American Control Conference, 769–774 (1969).

Samaan, M. A.

M. A. Samaan, D. Mortari, and J. L. Junkins, “Recursive mode star identification algorithms,” IEEE Trans. on Aerospace and Electronic Systems 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. Astronautical Sciences 50, 113–123 (2002).
[CrossRef]

Shimshoni, I.

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[CrossRef]

Shuster, M. D.

M. D. Shuster, “A survey of attitude representations,” J. Astronautical Sciences 41, 439–517 (1993).

Singer, R. A.

R. A. Singer, “Estimating optimal tracking filter performance for manned maneuvering targets,” IEEE Trans. on Aerospace and Electronic Systems AES-6, 473–483 (1970).
[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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

Welch, G.

G. Welch and G. Bishop, “An introduction to the Kalman filter,” SIGGRAPH 2001, Los Angeles, Calif., August 12–17 (SIGGRAPH, 2001).

Yang, J.

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, J. K. Yang, J. Q. Wang, J. C. Tan, and X. J. Li, “Star spot location estimation using Kalman filter for star tracker,” Appl. Opt. 50, 1735–1744 (2011).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

Acta Astronaut

H. Leeghim, Y. Choi, and B. A. Jaroux, “Uncorrelated unscented filtering for spacecraft attitude determination,” Acta Astronaut 67, 135–144 (2010).
[CrossRef]

Appl. Opt.

IEEE Trans, Aerosp. Electron. Syst.

M. Kolomenkin, S. Pollak, I. Shimshoni, and M. Lindenbaum, “Geometric voting algorithm for star trackers,” IEEE Trans, Aerosp. Electron. Syst. 44, 441–456 (2008).
[CrossRef]

IEEE Trans. on Aerospace and Electronic Systems

R. A. Singer, “Estimating optimal tracking filter performance for manned maneuvering targets,” IEEE Trans. on Aerospace and Electronic Systems AES-6, 473–483 (1970).
[CrossRef]

C. Padgett and K. Kreutz-Delgado, “A grid algorithm for autonomous star identification,” IEEE Trans. on Aerospace and Electronic Systems 33, 202–212 (1997).
[CrossRef]

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

J. Astronautical Sciences

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronautical Sciences 50, 113–123 (2002).
[CrossRef]

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. Astronautical Sciences 32, 1190–1194 (2011).

M. D. Shuster, “A survey of attitude representations,” J. Astronautical Sciences 41, 439–517 (1993).

J. Guid. Control. Dyn.

Y. Oshman and F. Landis Markley, “Sequential attitude and attitude-rate estimation using integrated-rate parameters,” J. Guid. Control. Dyn. 22, 385–394 (1999).
[CrossRef]

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

R. Azor, I. Y. Bar-Itzhack, J. K. Deutschmann, and R. R. Harman, “Angular-rate estimation using delayed quaternion measurements,” J. Guid. Control. Dyn. 24, 436–443 (2001).
[CrossRef]

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

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

Opt. Eng.

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, 23604–23608 (2011).
[CrossRef]

H. B. Liu, X. J. Li, J. C. Tan, J. K. Yang, J. Yang, D. Z. Su, and H. Jia, “Novel approach for laboratory calibration of star tracker,” Opt. Eng. 49, 73601–73609 (2010).
[CrossRef]

Other

A. P. Sage and G. W. Husa, “Adaptive filtering with unknown prior statistics,” in Joint American Control Conference, 769–774 (1969).

G. Welch and G. Bishop, “An introduction to the Kalman filter,” SIGGRAPH 2001, Los Angeles, Calif., August 12–17 (SIGGRAPH, 2001).

B. N. Agrawal and W. J. Palermo, “Angular rate estimation for gyroless satellite attitude control,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

I. Y. Bar-Itzhack, R. R. Harman, and D. Choukroun, “State-dependent pseudo-linear filters for spacecraft attitude and rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit5–8 August 2002 (AIAA, 2002).

I. Y. Bar-Itzhack, and R. R. Harman, “A feedback approach to spacecraft angular rate estimation,” in AIAA Guidance, Navigation, and Control Conference and Exhibit21–24 August 2006 (Keystone, 2006).

A. Carmi, and Y. Oshman, “Robust spacecraft angular-rate estimation from vector observations using fast interlaced particle filtering,” in AIAA Guidance, Navigation, and Control Conference and Exhibit15–18 August 2005 (AIAA, 2005).

M. A. Paluszek, J. B. Mueller, and M. G. Littman, “Optical navigation system,” in AIAA Infotech at Aerospace 2010, April 20, 2010–April 22, 2010 (American Institute of Aeronautics and Astronautics, 2010).

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Figures (8)

Fig. 1.
Fig. 1.

Measurement model of star tracker.

Fig. 2.
Fig. 2.

Scheme of the angular velocity estimate with the adaptive Kalman filter.

Fig. 3.
Fig. 3.

True values of the three-axis body angular velocity.

Fig. 4.
Fig. 4.

Estimation errors with the least-squares approach.

Fig. 5.
Fig. 5.

Estimation errors with the adaptive Kalman filter.

Fig. 6.
Fig. 6.

One of the night-sky images with highlighted centroid locations of the available stars.

Fig. 7.
Fig. 7.

Angular velocity estimation results with the least-squares approach.

Fig. 8.
Fig. 8.

Angular velocity estimation results with the adaptive Kalman filter.

Tables (2)

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Table 1. Star Identification Results in Epoch 2000 Reference Frame

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Table 2. Statistical Analysis of the Last 300 Images

Equations (36)

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v(t)=M(t)r,
v(t)=1x2(t)+y2(t)+f2[x(t)y(t)f]
r=[cosαcosδsinαcosδsinδ].
v(t)t=M(t)tr=[ωs(t)×]M(t)r.
v(t)t=[ωs(t)×]v(t)=[v(t)×]ωs(t).
v(t)tv(t+Δt)v(t)Δt,
v(t+Δt)v(t)Δt=[v(t)×]ωs(t).
ω^s(t)=1Δt{k=1nσ¯k2[v(t)k×]T[v(t)k×]}1k=1nσ¯k2[v(t)k×]Tv(t+Δt)k,
P(t)=E{[ω^s(t)ωs(t)][ω^s(t)ωs(t)]T}={k=1nσ¯k2[v(t)k×]T[v(t)k×]}1,
v(t)tv(t)v(tΔt)Δt.
v(t)v(tΔt)Δt=[v(t)×]ωs(t).
ω^s(t)=1Δt{k=1nσ¯k2[v(t)k×]T[v(t)k×]}1k=1nσ¯k2[v(t)k×]Tv(tΔt)k.
X(t)k=I3×3X(t)k1+W1(t)k1,
Z1(t)k=H1(t)kX(t)k+V1(t)k,
Z1(t)k=v(t)kv(tΔt)kΔt,
H1(t)k=[v(t)k×]=1x2(t)k+y2(t)k+f2[0fy(t)kf0x(t)ky(t)kx(t)k0].
V1(t)k=ωs(t)×δv(t)k+1Δt[δv(t)kδv(tΔt)k],
E{V1(t)}=[ωs(t)×]E{δv(t)}+1Δt[E{δv(t)}E{δv(tΔt)}]=[ωs(t)×]E{δv(t)},
E{[V1(t)E{V1(t)}][V1(t)kE{V1(t)}]T}=E{V1(t)V1(t)T}E{V1(t)}E{V1(t)T}=[ωs(t)×]E{δv(t)δv(t)T}[ωs(t)×]T[ωs(t)×]E{δv(t)}E{δv(t)T}[ωs(t)×]T+2Δt2E{δv(t)δv(t)T}.
[ωs(t)×]×E{δv(t)}E{δv(t)T}×[ωs(t)×]T[ωs(t)×]×E{δv(t)δv(t)T}×[ωs(t)×]T=ωs(t)Δt2Δt2×E{δv(t)δv(t)T}1Δt2E{δv(t)δv(t)T}
E{V1(t)}ωs(t)ΔtΔt×E{δv(t)}1ΔtE{δv(t)δv(t)T},
E{[V1(t)E{V1(t)}][V1(t)E{V1(t)}]T}2Δt2E{δv(t)δv(t)T}.
E{V1(t)}E{[V1(t)E{V1(t)}][V1(t)kE{V1(t)}]T}.
Z2(t)k=H2(t)kX(t)k+V2(t)k,
Z2(t)k=1x2(t)k+y2(t)k+f2[x(t)ky(t)k]1x2(t)k1+y2(t)k1+f2[x(t)k1y(t)k1],
H2(t)k=1x2(t)k+y2(t)k+f2[0fy(t)kf0x(t)k].
{P(t)k=P(t)k1+Q1εk=Z2(t)kH2(t)kX(t)k1R(t)k=(1dk)R(t)k1+dk{εkεkTH2(t)kP(t)kH2(t)kT}Kk=P(t)kH2(t)kT[H2(t)kP(t)kH2(t)kT+R(t)k]1P(t)k=[I3×3KkH2(t)k]P(t)kX(t)k=X(t)k1+Kkεkdk=(1b)/(1bk+1),
P(t)0=E{[X(t)0ωs(t)]T[X(t)0ωs(t)]}.
X(t)0ω(t)=2X(tΔt)X(t2Δt)ωs(t)=X(tΔt)+X(tΔt)X(t2Δt)ΔtΔtωs(t)=X(tΔt)+ω˙sΔtωs(t)+o(Δt2)=[X(tΔt)ωs(tΔt)]+[ωs(tΔt)+ϖ˙Δtωs(t)]+(ω˙sϖ˙)Δt+o(Δt2)=[X(tΔt)ωs(tΔt)]+(ω˙sϖ˙)Δt+o(Δt2)[X(tΔt)ωs(tΔt)]+(ω˙sϖ˙)Δt,
P(t)0=E{[X(t)0ωs(t)]T[X(t)0ωs(t)]}=E{[X(tΔt)ωs(tΔt)]T[X(tΔt)ωs(tΔt)]}+E{[(ω˙sϖ˙)T(ω˙sϖ˙)]}Δt2=P(tΔt)+Δt2Λ,
Λ=diag{σ12,σ22,σ32}.
ϖ˙=ωs(tΔt)ωs(t2Δt)Δt.
σi2=ω˙i23(1+4pMip0i).
X0=1Δt{k=1n[v(t0+Δt)k×]T[v(t0+Δt)k×]}1k=1n[v(t0+Δt)k×]Tv(t0)k,
R0=[Z2(t0+Δt)kH2(t0+Δt)1X0][Z2(t0+Δt)kH2(t0+Δt)1X0]T,
P0=[H2(t0+Δt)1TR01H2(t0+Δt)1]1.

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