Abstract

The star tracker is one of the most promising attitude measurement devices widely used in spacecraft for its high accuracy. High dynamic performance is becoming its major restriction, and requires immediate focus and promotion. A star image restoration approach based on the motion degradation model of variable angular velocity is proposed in this paper. This method can overcome the problem of energy dispersion and signal to noise ratio (SNR) decrease resulting from the smearing of the star spot, thus preventing failed extraction and decreased star centroid accuracy. Simulations and laboratory experiments are conducted to verify the proposed methods. The restoration results demonstrate that the described method can recover the star spot from a long motion trail to the shape of Gaussian distribution under the conditions of variable angular velocity and long exposure time. The energy of the star spot can be concentrated to ensure high SNR and high position accuracy. These features are crucial to the subsequent star extraction and the whole performance of the star tracker.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. W. Zhang, W. Quan, L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  21. J. Gwanghyeok, Autonomous star sensing, pattern identification, and attitude determination for spacecraft: an analytical and experiment study Doctoral thesis, Texas A&M University, 2001.
  22. G. Rufino, D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
    [CrossRef]
  23. A. B. Katake, Modeling, image processing and attitude estimation of high speed star sensors Doctoral thesis, Texas A&M University, 2006.
  24. 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]

2013 (2)

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

T. Sun, F. Xing, Z. You, M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

2012 (2)

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

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

2011 (1)

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

2010 (1)

2006 (1)

F. Xing, Y. Dong, Z. You, “Laboratory calibration of star tracker with brightness independent star identification strategy,” Opt. Eng. 45(6), 063604 (2006).
[CrossRef]

2003 (1)

G. Rufino, 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, J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50(1), 113–123 (2002).

1995 (1)

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10(6), 10–16 (1995).
[CrossRef]

1986 (1)

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745 (1974).
[CrossRef]

1972 (1)

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62(1), 55–59 (1972).
[CrossRef]

1965 (1)

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

Accardo, D.

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

Chen, N.

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

Dong, Y.

F. Xing, Y. Dong, Z. You, “Laboratory calibration of star tracker with brightness independent star identification strategy,” Opt. Eng. 45(6), 063604 (2006).
[CrossRef]

Guo, L.

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

Junkins, J. L.

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

Liebe, C. C.

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

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10(6), 10–16 (1995).
[CrossRef]

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745 (1974).
[CrossRef]

Meinel, E. S.

Pollock, T. C.

M. A. Samaan, T. C. Pollock, 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, L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

Richardson, W. H.

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62(1), 55–59 (1972).
[CrossRef]

Rufino, G.

G. Rufino, 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, J. L. Junkins, “Predictive centroiding for star trackers with the effect of image smear,” J. Astronaut. Sci. 50(1), 113–123 (2002).

Shen, J.

Sun, T.

T. Sun, F. Xing, Z. You, M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

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

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

Wahba, G.

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

Wang, X.

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

Wei, M.

Wei, X.

Wu, X.

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

Xing, F.

T. Sun, F. Xing, Z. You, M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

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

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

F. Xing, Y. Dong, Z. You, “Laboratory calibration of star tracker with brightness independent star identification strategy,” Opt. Eng. 45(6), 063604 (2006).
[CrossRef]

You, Z.

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

T. Sun, F. Xing, Z. You, M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express 21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

F. Xing, Y. Dong, Z. You, “Laboratory calibration of star tracker with brightness independent star identification strategy,” Opt. Eng. 45(6), 063604 (2006).
[CrossRef]

Zhang, G.

Zhang, W.

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

Acta Astronaut. (2)

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

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

Astron. J. (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745 (1974).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (2)

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

C. C. Liebe, “Star trackers for attitude determination,” IEEE Trans. Aerosp. Electron. Syst. 10(6), 10–16 (1995).
[CrossRef]

J. Astronaut. Sci. (1)

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

J. Opt. Soc. Am. A (3)

Math. Probl. Eng. (1)

F. Xing, N. Chen, Z. You, T. Sun, “A novel approach based on MEMS-gyro's data deep coupling for determining the centroid of star spot,” Math. Probl. Eng. 2012, 403584 (2012).

Opt. Eng. (1)

F. Xing, Y. Dong, Z. You, “Laboratory calibration of star tracker with brightness independent star identification strategy,” Opt. Eng. 45(6), 063604 (2006).
[CrossRef]

Opt. Express (1)

Sensors (Basel) (2)

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

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

SIAM Rev. (1)

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

Other (9)

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, 2002).

M. Sonka, V. Hlavac, and R. Boyle, Image Processing, Analysis, and Machine Vision (Thomson, 2008).

B. Chanda and D. D. Majumder, Digital image processing and analysis, (PHI Learning Pvt. Ltd., 2004).

M. K. Singh, U. S. Tiwary and Y.H. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Sign. Process 2008 (2008).

J. Gwanghyeok, Autonomous star sensing, pattern identification, and attitude determination for spacecraft: an analytical and experiment study Doctoral thesis, Texas A&M University, 2001.

H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice Hall, 1977).

A. K. Katsaggelos, Digital Image Restoration (Springer, 2012).

A. B. Katake, Modeling, image processing and attitude estimation of high speed star sensors Doctoral thesis, Texas A&M University, 2006.

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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Figures (18)

Fig. 1
Fig. 1

Ideal imaging model of the star tracker.

Fig. 2
Fig. 2

Position analysis and motion model of star spot.

Fig. 3
Fig. 3

Degradation and restoration process model.

Fig. 4
Fig. 4

Flow chart of restoration method.

Fig. 5
Fig. 5

Static and dynamic simulated star images and their partial detailed views. (a) Static simulated star image. (b) Dynamic simulated star image with rotation of two axes ( ω x = 2 ° / s , ω y = 1 ° / s , ω z = 0 ° / s ). (c) Partial detailed view of one star spot of (a). (d) Partial detailed view of one spot of (b).

Fig. 6
Fig. 6

Curve of angular velocity and time.

Fig. 7
Fig. 7

Comparison between original star image and restored star image. (a), (b) and (c) are gray images, contour lines, and histograms of the original star image. (d), (e) and (f) are gray images, contour lines, and histograms of the restored star image.

Fig. 8
Fig. 8

Energy distribution of the star spot. (a) is sectional shape of original star image. (b) is sectional shape of restored star image.

Fig. 9
Fig. 9

Curve of angular velocity and time.

Fig. 10
Fig. 10

Comparison between original star image and restored star image. (a), (b) and (c) are gray images, contour lines, and histograms of the original star image. (d), (e) and (f) are gray images, contour lines, and histograms of the restored star image.

Fig. 11
Fig. 11

Energy distribution of the star spot. (a) is sectional shape of original star image. (b) is sectional shape of restored star image.

Fig. 12
Fig. 12

Comparison between original star image and restored star image. (a), (b) and (c) are comparison of gray star images. (d), (e) and (f) are comparison of histograms.

Fig. 13
Fig. 13

Position accuracy curves of original star spots and restored star spots in continuous imaging mode.

Fig. 14
Fig. 14

Position accuracy curves of original star spots and restored star spots in continuous imaging mode.

Fig. 15
Fig. 15

Position accuracy curves of original star spots and restored star spots in continuous imaging mode.

Fig. 16
Fig. 16

Laboratory experiment system.

Fig. 17
Fig. 17

Comparison of original star spot and restored star spot in the case of angular velocity of 2.201°/s and angular acceleration of 2.881°/s2. (a) and (b) are gray image and sectional shape of original star image. (c) and (d) are gray image and sectional shape of restored star image.

Fig. 18
Fig. 18

Position accuracy curves of the star spots in the laboratory experiment.

Equations (22)

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

w i = 1 ( x i x 0 ) 2 + ( y i y 0 ) 2 + L f 2 [ ( x i x 0 ) ( y i y 0 ) - L f ] .
w i = A v i .
{ O C P = w i t = A t v i O C p = w i t + Δ t = A t t + Δ t A t v t .
w i t + Δ t = A t t + Δ t w i t .
A t t + Δ t = I ω ˜ t Δ t = I [ 0 ω z t ω y t ω z t 0 ω x t ω y t ω x t 0 ] Δ t = [ 1 ω z t Δ t ω y t Δ t ω z t Δ t 1 ω x t Δ t ω y t Δ t ω x t Δ t 1 ] .
{ x i t + Δ t = x i t + y i t ω z t Δ t + L f ω y t Δ t ( x i t ω y t Δ t + y i t ω x t Δ t ) / L f + 1 y i t + Δ t = y i t x i t ω z t Δ t L f ω x t Δ t ( x i t ω y t Δ t + y i t ω x t Δ t ) / L f + 1 .
{ x i t + Δ t = x i t + ( y i t ω z t + L f ω y t ) Δ t y i t + Δ t = y i t ( x i t ω z t + L f ω x t ) Δ t .
g ( x , y ) = h ( x , y ) * c ( x , y ) + η ( x , y ) .
G ( u , v ) = H ( u , v ) C ( u , v ) + N ( u , v ) .
g = H c + η .
g ( x , y ) = 0 Δ t f ( x x C , y y C ) d t = 0 Δ t ( E s u m M v 2 π σ P S F 2 exp [ ( x x C ) 2 2 σ P S F 2 ] exp [ ( y y C ) 2 2 σ P S F 2 ] ) d t .
g ( x , y ) = 0 Δ t f ( x x C ( t ) , y y C ( t ) ) d t .
G ( u , v ) = [ 0 Δ t f ( x x C ( t ) , y y C ( t ) ) d t ] e j 2 π ( u x + v y ) d x d y = F ( u , v ) 0 Δ t e j 2 π [ u x C ( t ) + v y C ( t ) ] d t .
H ( u , v ) = 0 Δ t e j 2 π [ u x C ( t ) + v y C ( t ) ] d t .
P ( X = k ) = λ k e λ k ! , 0 k < .
g ( n ) = i h ( n i ) c ( i ) + ξ ( n ) .
a ( n ) = i h ( n i ) c ( i ) .
P ( g | c ) = n a ( n ) g ( n ) e a ( n ) g ( n ) ! .
L = ln P ( g | c ) .
c ( k ) ln P ( g | c ) = n ( h ( n k ) g ( n ) a ( n ) h ( n k ) ) = 0 ,
n h ( n k ) ( g ( n ) a ( n ) 1 ) = 0 , k = 0 , 1 , ... , N 1.
c ( k ) j + 1 = c ( k ) j ( n h ( n k ) g ( n ) i h ( n i ) c ( i ) j ) m , k = 0 , 1 , ... , N 1.

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