Abstract

Under dynamic conditions, star spots move across the image plane of a star tracker and form a smeared star image. This smearing effect increases errors in star position estimation and degrades attitude accuracy. First, an analytical energy distribution model of a smeared star spot is established based on a line segment spread function because the dynamic imaging process of a star tracker is equivalent to the static imaging process of linear light sources. The proposed model, which has a clear physical meaning, explicitly reflects the key parameters of the imaging process, including incident flux, exposure time, velocity of a star spot in an image plane, and Gaussian radius. Furthermore, an analytical expression of the centroiding error of the smeared star spot is derived using the proposed model. An accurate and comprehensive evaluation of centroiding accuracy is obtained based on the expression. Moreover, analytical solutions of the optimal parameters are derived to achieve the best performance in centroid estimation. Finally, we perform numerical simulations and a night sky experiment to validate the correctness of the dynamic imaging model, the centroiding error expression, and the optimal parameters.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  5. B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
    [Crossref]
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    [Crossref]
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2015 (2)

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Z. Jun, H. Yuncai, W. Li, and L. Da, “Studies on dynamic motion compensation and positioning accuracy on star tracker,” Appl. Opt. 54(28), 8417–8424 (2015).
[Crossref] [PubMed]

2014 (5)

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(5), 6009–6024 (2014).
[Crossref] [PubMed]

W. Hou, H. Liu, Z. Lei, Q. Yu, X. Liu, and J. Dong, “Smeared star spot location estimation using directional integral method,” Appl. Opt. 53(10), 2073–2086 (2014).
[Crossref] [PubMed]

T. Dzamba and J. Enright, “Ground testing strategies for verifying the slew rate tolerance of star trackers,” Sensors (Basel) 14(3), 3939–3964 (2014).
[Crossref] [PubMed]

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

2012 (2)

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[Crossref] [PubMed]

2011 (2)

X. Wu and X. Wang, “Multiple blur of star image and the restoration under dynamic conditions,” Acta Astronaut. 68(11–12), 1903–1913 (2011).

J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

2010 (2)

J. Shen, G. Zhang, and X. Wei, “Simulation analysis of dynamic working performance for star trackers,” J. Opt. Soc. Am. A 27(12), 2638–2647 (2010).
[Crossref] [PubMed]

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

2009 (2)

X. Li and H. Zhao, “Analysis of star image centroid accuracy of an APS star sensor in rotation,” Aerospace Control Appl. 35(4), 11–16 (2009).

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

2004 (1)

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

2003 (1)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

2002 (2)

C. C. Liebe, “Accuracy performance of star trackers-a tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 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. 50(1), 113–123 (2002).

Accardo, D.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

Cheng, X.

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

Cunningham, T. J.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Da, L.

Dong, J.

Dzamba, T.

T. Dzamba and J. Enright, “Ground testing strategies for verifying the slew rate tolerance of star trackers,” Sensors (Basel) 14(3), 3939–3964 (2014).
[Crossref] [PubMed]

Enright, J.

T. Dzamba and J. Enright, “Ground testing strategies for verifying the slew rate tolerance of star trackers,” Sensors (Basel) 14(3), 3939–3964 (2014).
[Crossref] [PubMed]

Gromov, K.

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

Guo, L.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[Crossref] [PubMed]

Hancock, B. R.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Hao, Y.

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

Hou, W.

Hu, L. H.

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Jia, H.

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

Jun, Z.

Junkins, J. L.

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50(1), 113–123 (2002).

Lei, Z.

Li, A. J.

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Li, B.

Li, J.

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

Li, W.

Li, X.

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

X. Li and H. Zhao, “Analysis of star image centroid accuracy of an APS star sensor in rotation,” Aerospace Control Appl. 35(4), 11–16 (2009).

Liang, B.

J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

Liao, J.

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

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(1), 91–99 (2004).
[Crossref]

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

Lin, H.

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

Liu, C. S.

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Liu, G. B.

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Liu, H.

Liu, X.

Liu, Y.

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

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(1), 91–99 (2004).
[Crossref]

Pain, B.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[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. 50(1), 113–123 (2002).

Quan, W.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[Crossref] [PubMed]

Ringold, P. G.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Rufino, G.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

Samaan, M. A.

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50(1), 113–123 (2002).

Shen, B.

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

Shen, J.

Song, J.

J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

Stirbl, R. C.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Sun, T.

Tan, J.

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

Tan, W.

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

Wang, H.

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

Wang, X.

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(5), 6009–6024 (2014).
[Crossref] [PubMed]

X. Wu and X. Wang, “Multiple blur of star image and the restoration under dynamic conditions,” Acta Astronaut. 68(11–12), 1903–1913 (2011).

Wei, X.

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

J. Shen, G. Zhang, and X. Wei, “Simulation analysis of dynamic working performance for star trackers,” J. Opt. Soc. Am. A 27(12), 2638–2647 (2010).
[Crossref] [PubMed]

Wrigley, C. J.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

Wu, X.

X. Wu and X. Wang, “Multiple blur of star image and the restoration under dynamic conditions,” Acta Astronaut. 68(11–12), 1903–1913 (2011).

Xing, F.

Xu, J.

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

Yan, J.

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

Yang, B.

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Yang, J.

J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

Yang, M.

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

You, Z.

Yu, Q.

Yuncai, H.

Zhang, G.

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

J. Shen, G. Zhang, and X. Wei, “Simulation analysis of dynamic working performance for star trackers,” J. Opt. Soc. Am. A 27(12), 2638–2647 (2010).
[Crossref] [PubMed]

Zhang, T.

J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

Zhang, W.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[Crossref] [PubMed]

Zhao, H.

X. Li and H. Zhao, “Analysis of star image centroid accuracy of an APS star sensor in rotation,” Aerospace Control Appl. 35(4), 11–16 (2009).

Zhou, W.

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

Acta Astronaut. (3)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

X. Wei, J. Xu, J. Li, J. Yan, and G. Zhang, “S-curve centroiding error correction for star sensor,” Acta Astronaut. 99, 231–241 (2014).
[Crossref]

X. Wu and X. Wang, “Multiple blur of star image and the restoration under dynamic conditions,” Acta Astronaut. 68(11–12), 1903–1913 (2011).

Aerospace Control Appl. (1)

X. Li and H. Zhao, “Analysis of star image centroid accuracy of an APS star sensor in rotation,” Aerospace Control Appl. 35(4), 11–16 (2009).

Appl. Opt. (2)

Chin. J. Aeronauti. (1)

H. Wang, W. Zhou, X. Cheng, and H. Lin, “Image smearing modeling and verification for strapdown star sensor,” Chin. J. Aeronauti. 25(1), 115–123 (2012).
[Crossref]

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

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

J. Astronaut. Sci. (1)

M. A. Samaan, T. C. Pollock, and J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50(1), 113–123 (2002).

J. Guid. Control Dyn. (1)

C. C. Liebe, K. Gromov, and D. M. Meller, “Toward a stellar gyroscope for spacecraft attitude determination,” J. Guid. Control Dyn. 27(1), 91–99 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

C. S. Liu, L. H. Hu, G. B. Liu, B. Yang, and A. J. Li, “Kinematic model for the space-variant image motion of star sensors under dynamical conditions,” Opt. Eng. 54(6), 063104 (2015).
[Crossref]

Opt. Express (1)

Opto-Electron. Eng. (1)

B. Shen, J. Tan, J. Yang, and J. Liao, “Exposure Time Optimization of the Star Sensor,” Opto-Electron. Eng. 12, 008 (2009).

Sci. China Technol. Sci. (1)

H. Jia, J. Yang, X. Li, J. Yang, M. Yang, Y. Liu, and Y. Hao, “Systematic error analysis and compensation for high accuracy star centroid estimation of star tracker,” Sci. China Technol. Sci. 53(11), 3145–3152 (2010).
[Crossref]

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J. Yang, B. Liang, T. Zhang, and J. Song, “A novel systematic error compensation algorithm based on least squares support vector regression for star sensor image centroid estimation,” Sensors (Basel) 11(12), 7341–7363 (2011).
[Crossref] [PubMed]

X. Wei, W. Tan, J. Li, and G. Zhang, “Exposure Time Optimization for Highly Dynamic Star Trackers,” Sensors (Basel) 14(3), 4914–4931 (2014).
[Crossref] [PubMed]

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[Crossref] [PubMed]

T. Dzamba and J. Enright, “Ground testing strategies for verifying the slew rate tolerance of star trackers,” Sensors (Basel) 14(3), 3939–3964 (2014).
[Crossref] [PubMed]

Other (5)

E. Aretskin-Hariton and A. J. Swank, “Star Tracker Performance Estimate with IMU,” in AIAA Guidance, Navigation, and Control Conference (American Institute of Aeronautics and Astronautics, 2015), pp 0334.

B. R. Hancock, R. C. Stirbl, T. J. Cunningham, B. Pain, C. J. Wrigley, and P. G. Ringold, “CMOS active pixel sensor specific performance effects on star tracker/imager position accuracy”, in Symposium on Integrated Optics, (International Society for Optics and Photonics, 2001), pp. 43–53.
[Crossref]

S. Zhao, Y. Wang, H. Wang, and C. Ji, “Study on dynamic angle-measurement compensation for star sensor,” in Natural Computation (ICNC),2011Seventh International Conference on, (IEEE, 2011), 255–258.
[Crossref]

C. A. Nardell, J. Wertz, and P. B. Hays, “Image processing, simulation and performance predictions for the MicroMak star tracker,” in Optics & Photonics 2005, (International Society for Optics and Photonics, 2005), 59160U–59160U–59112.

T. Dzamba and J. Enright, “Optical trades for evolving a small arcsecond star tracker,” in Aerospace Conference,2013IEEE, (IEEE, 2013), pp. 1–9.
[Crossref]

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Figures (16)

Fig. 1
Fig. 1

Dynamic imaging process of a star spot.

Fig. 2
Fig. 2

Rotation transformation of the star streak.

Fig. 3
Fig. 3

Discrete star streak image.

Fig. 4
Fig. 4

Two types of rotation. (a) Rotation about boresight; (b) Rotation about cross-boresight axis.

Fig. 5
Fig. 5

Centroiding error of the non-linear moion. (a) Boresight rotation; (b) Cross-boresight rotation.

Fig. 6
Fig. 6

Centroiding error εxy vs. smear length.

Fig. 7
Fig. 7

σx,sys vs. Gaussian radius ρ and smear length L.

Fig. 8
Fig. 8

Total systematic error σsys vs. Gaussian radius ρ and smear length L.

Fig. 9
Fig. 9

Total random error vs. smear length under different Gaussian radii.

Fig. 10
Fig. 10

random error of centroiding vs. smear length.

Fig. 11
Fig. 11

Optimal exposure time vs. angular velocity under different stellar magnitudes.

Fig. 12
Fig. 12

Centroiding error vs. Gaussian radius.

Fig. 13
Fig. 13

Comparison of centroiding errors of different methods.

Fig. 14
Fig. 14

Centroiding error vs. smear length L.

Fig. 15
Fig. 15

Setup of the night sky experiment.

Fig. 16
Fig. 16

Centroiding error vs. smear length under different velocities in the night sky experiment.

Tables (1)

Tables Icon

Table 1 Parameters of the CMV4000 Image Sensor

Equations (53)

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f PSF (x)= 1 2π ρ exp( x 2 2 ρ 2 ),
f LSSF ( x )= 1 L xL x f PSF ( u )du = 1 2L [ erf( x 2 ρ )erf( xL 2 ρ ) ],
E sta (x,y)= ΦT 2π ρ 2 exp[ (x x c ) 2 + (y y c ) 2 2 ρ 2 ] =ΦT f PSF (x x c ) f PSF (y y c ),
E dyn (x,y)= 0 T Φ 2π ρ 2 exp { [x x c (t)] 2 + [y y c (t)] 2 2 ρ 2 }dt =Φ 0 T f PSF ( x x c (t) ) f PSF ( y y c (t) )dt.
E dyn (x,y)=Φ 0 T f PSF ( x x 0 vt ) f PSF ( y y 0 )dt = Φ 2v [ erf( x x 0 2 ρ )erf( x x 0 vT 2 ρ ) ] f PSF ( y y 0 ) =ΦT f LSSF ( x x 0 ) f PSF ( y y 0 ).
E dyn (x,y)=Φ 0 T f PSF ( x x 0 vtcosθ ) f PSF ( y y 0 vtsinθ ) dt = Φ 2v [ erf( u 2 ρ )erf( uvT 2 ρ ) ] 1 2π ρ exp( v 2 2 ρ 2 ) =ΦT f LSSF ( u ) f PSF ( v ),
{ x=XcosθYsinθ y=Xsinθ+Ycosθ .
E dyn (X,Y)=ΦT f LSSF ( X X 0 ) f PSF ( Y Y 0 ).
E max (X,Y)=ΦT f LSSF ( vT /2 ) f PSF ( y 0 )= Φ 2π ρv erf( vT 2 2 ρ ).
E lim = lim T Φ 2π ρv erf( vT 2 2 ρ )= Φ 2π ρv .
I ij = y j 0.5 y j +0.5 x i 0.5 x i +0.5 η QE K E dyn (x,y)dx dy =ΦT η QE K x i 0.5 x i +0.5 f LSSF ( x x 0 )dx y j 0.5 y j +0.5 f PSF ( y y 0 )dy , =ΦT η QE K F LSSF ( x i x 0 ) F PSF ( y j y 0 )
F LSSF ( x i )= x i 0.5 x i +0.5 f LSSF ( x )dx = 1 2L { ( x i +0.5 )erf[ ( x i +0.5 ) / ( 2 ρ) ]+2 ρ 2 f PSF ( x i +0.5 ) ( x i 0.5 )erf[ ( x i 0.5 ) / ( 2 ρ) ]2 ρ 2 f PSF ( x i 0.5 ) ( x i +0.5L )erf[ ( x i +0.5L ) / ( 2 ρ) ]2 ρ 2 f PSF ( x i +0.5L ) ( x i 0.5L )erf[ ( x i 0.5L ) / ( 2 ρ) ]+2 ρ 2 f PSF ( x i 0.5L ) }.
I i = j I ij =ΦT η QE K F LSSF ( x i x 0 ).
I total = i j I ij = i I i =ΦT η QE K.
L z (t)=ftanθΔ θ z =ftanθ ω z t= v z t,
L xy (t)=f[tan(θ+Δ θ xy )tanθ]=f[tan(θ+ ω xy t)tanθ].
v xy (t)= d L xy (t) dt =f ω xy [1+ tan 2 (θ+ ω xy t)]f ω xy .
ε z =| P'P |=| OP || OP' |=r(1cos ω z t 2 ).
ε z =r(1cos ω z t 2 ) h 2 (1cos ω z t 2 )=4.76× 10 6 h.
ε z 4.76× 10 6 h/d =0.0097pixels,
| AP |= 1 T 0 T L xy (t)dt = f ω xy T ln cosθ cos(θ+ ω xy T) ftanθ,
| AP' |= v xy (0) T 2 =f ω xy [1+ tan 2 (θ)] T 2 .
ε xy =| AP || AP' | = f ω xy T ln cosθ cos(θ+ ω xy T) ftanθf ω xy [1+ tan 2 (θ)] T 2 f ω xy T ln cos( θ FOV /2) cos( θ FOV /2+ ω xy T) ftan θ FOV 2 f ω xy [1+ tan 2 θ FOV 2 ] T 2
x ¯ = x E dyn (x,y)dxdy E dyn (x,y)dxdy , y ¯ = y E dyn (x,y)dxdy E dyn (x,y)dxdy .
x ¯ = x f LSSF ( x x 0 )dx = x 0 + vT /2 = x c . y ¯ = y f PSF ( y y 0 )dy = y 0 = y c
x ¯ = i j x i I ij i j I ij ,
x ¯ = i x i I i i I i .
δ x = x ¯ x c = i x i I i i I i ( x 0 + L 2 ).
δ x = i x i ΦT η QE K F LSSF ( x i x 0 ) ΦT η QE K ( x 0 + L 2 ) = 1 2L i x i x i 0.5 x i +0.5 [ erf( x x 0 2 ρ )erf( x x 0 L 2 ρ ) ]dx ( x 0 + L 2 ).
σ x,sys ( σ,L )= [ 0.5 0.5 δ x 2 ( ρ,L, x 0 )d x 0 ] 1/2 .
l=2× 3ρ0.5 +1+ L , w=2× 3ρ0.5 +1 ,
σ y,sys ( ρ )= lim L0 σ x,sys ( ρ,L ).
σ sys = σ x,sys 2 + σ y,sys 2 .
σ x,ran 2 = i ( x ¯ x i ) 2 n x,i 2 + i ( x ¯ I i ) 2 n I,i 2 = i ( I i I toltal ) 2 n x,i 2 + i ( x i x ¯ I toltal ) 2 n I,i 2 ,
σ x,ran 2 = i ( x i x ¯ I toltal ) 2 n I,i 2 .
n add 2 = n dc 2 + n read 2 + n ADC 2 = I dark T+ n read 2 +1/ (12 K 2 ) .
n I,ij 2 = K 2 ( n ij,shot 2 + n add 2 )=K I ij + K 2 n add 2 .
n I,i 2 = j n I,ij 2 =K I i +w K 2 n add 2 .
σ x,ran 2 = K I toltal 2 i ( x i x ¯ ) 2 I i + w K 2 n add 2 I toltal 2 i ( x i x ¯ ) 2 = 1 ΦT η QE 3ρ+ x 0 x 0 +L+3ρ ( x i x 0 L/2 ) 2 f LSSF ( x i )d x i + w n add 2 (ΦT η QE ) 2 3ρ+ x 0 x 0 +L+3ρ ( x i x 0 L/2 ) 2 d x i .
σ x,shot 2 = 1 ΦT η QE 3ρ+ x 0 x 0 +L+3ρ ( x i x 0 L/2 ) 2 f LSSF ( x i )d x i 1 ΦT η QE ( x i L/2 ) 2 f LSSF ( x i )d x i = v Φ η QE L ( 1 12 L 2 + ρ 2 ).
σ x,add 2 = w n add 2 ( ΦT η QE ) 2 3ρ+ x 0 x 0 +L+3ρ ( x i x 0 L/2 ) 2 d x i = 6ρ v 2 n add 2 Φ 2 η QE 2 L 2 1 12 ( L+6ρ ) 3 .
σ y,shot 2 = K I toltal 2 j ( y j y ¯ ) 2 I j = v ρ 2 Φ η QE L .
σ y,add 2 = K 2 n add 2 l I toltal 2 j ( y j y ¯ ) 2 = 18 v 2 n add 2 ( L+6ρ ) ρ 3 ( Φ η QE L ) 2 .
σ ran 2 =( σ x,shot 2 + σ y,shot 2 )+( σ x,add 2 + σ y,add 2 ) = v Φ η QE L ( 1 12 L 2 +2 ρ 2 )+ v 2 n add 2 ρ( L+6ρ ) 2 ( Φ η QE L ) 2 ( L 2 +12Lρ+72 ρ 2 ).
σ c 2 = σ sys 2 + σ ran 2 .
Φ=τ E 0 /ε 2.512 m π D 2 /4 ,
vfω= h/2 dtan( θ FOV / 2) ω= N pix /2 tan( θ FOV / 2) ω,
σ shot 2 = σ x,shot 2 + σ y,shot 2 = v Φ η QE L ( 1 12 L 2 +2 ρ 2 ).
L 1 =2 6 ρ4.899ρ,
σ add 2 = σ x,add 2 + σ y,add 2 = 18 v 2 n add 2 ρ( L+6ρ ) ( Φ η QE L ) 2 ( L 2 +12Lρ+72 ρ 2 ).
L 2 =2ρ[ ( 54+6 33 ) 1/3 +12 ( 54+6 33 ) 1/3 ]14.289ρ.
L o = arg L { min[ σ ran 2 (L)] },L[ L 1 , L 2 ].
ρ o = arg ρ { min[ σ c 2 (ρ)] }= arg ρ { min[ σ sys 2 (ρ)+ σ ran 2 (ρ)] }.

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