Autonomous subpixel satellite track end point determination for space-based images

Lance M. Simms

doi:10.1364/AO.50.0000D1

Abstract

An algorithm for determining satellite track end points with subpixel resolution in spaced-based images is presented. The algorithm allows for significant curvature in the imaged track due to rotation of the spacecraft capturing the image. The motivation behind the subpixel end point determination is first presented, followed by a description of the methodology used. Results from running the algorithm on real ground-based and simulated spaced-based images are shown to highlight its effectiveness.

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References

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H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]
A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]
M. A. Earl, “Determining the range of an artificial satellite using its observed trigonometric parallax,” J. R. Astron. Soc. Can. 99, 50–55 (2005).
M. Levesque, “Automatic reacquisition of satellite positions by detecting their expected streaks in astronomical images,” presented at the Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, 1–4 Sept. 2009.
L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).
Note that a simplification has been made by approximating the path of the target as a straight line during the exposure, which it is not.
This information will be available from calibration data taken before the observation.
AMS Collaboration, “Protons in near earth orbit,” Phys. Lett. B 472, 215–226 (2000).
[Crossref]
D. Shaw and P. Hodge, “Cosmic ray rejection in STIS CCD images,” Instrument Science Rep. STIS 98-22 (Space Telescope Science Institute, 1998).
While the STARE pathfinder satellites will suffer from this problem, the future STARE constellation CubeSats will carry high quality sensors that will not.

2010 (1)

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

2006 (1)

H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]

2005 (1)

M. A. Earl, “Determining the range of an artificial satellite using its observed trigonometric parallax,” J. R. Astron. Soc. Can. 99, 50–55 (2005).

2004 (1)

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

2000 (1)

AMS Collaboration, “Protons in near earth orbit,” Phys. Lett. B 472, 215–226 (2000).
[Crossref]

1998 (1)

D. Shaw and P. Hodge, “Cosmic ray rejection in STIS CCD images,” Instrument Science Rep. STIS 98-22 (Space Telescope Science Institute, 1998).

Ali, H.

H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]

Bauman, B.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Breuel, T.

H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]

De Vries, W.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Earl, M. A.

M. A. Earl, “Determining the range of an artificial satellite using its observed trigonometric parallax,” J. R. Astron. Soc. Can. 99, 50–55 (2005).

Hambly, N. C.

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

Hodge, P.

D. Shaw and P. Hodge, “Cosmic ray rejection in STIS CCD images,” Instrument Science Rep. STIS 98-22 (Space Telescope Science Institute, 1998).

Lampert, C.

H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]

Levesque, M.

M. Levesque, “Automatic reacquisition of satellite positions by detecting their expected streaks in astronomical images,” presented at the Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, 1–4 Sept. 2009.

Mann, R. G.

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

Nikolaev, S.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Olivier, S.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Pertica, A.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Phillion, D.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Riot, V.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Shaw, D.

D. Shaw and P. Hodge, “Cosmic ray rejection in STIS CCD images,” Instrument Science Rep. STIS 98-22 (Space Telescope Science Institute, 1998).

Simms, L.

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Storkey, A. J.

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

Williams, C. K. I.

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

J. R. Astron. Soc. Can. (1)

M. A. Earl, “Determining the range of an artificial satellite using its observed trigonometric parallax,” J. R. Astron. Soc. Can. 99, 50–55 (2005).

Mon. Not. R. Astron. Soc. (1)

A. J. Storkey, N. C. Hambly, C. K. I. Williams, and R. G. Mann, “Cleaning sky survey data bases using hough transform and renewal string approaches,” Mon. Not. R. Astron. Soc. 347, 36–51 (2004).
[Crossref]

Phys. Lett. B (1)

AMS Collaboration, “Protons in near earth orbit,” Phys. Lett. B 472, 215–226 (2000).
[Crossref]

Proc. SPIE (1)

L. Simms, V. Riot, W. De Vries, S. Olivier, A. Pertica, B. Bauman, D. Phillion, and S. Nikolaev, “Optical payload for the STARE mission,” Proc. SPIE 8044-5, 804406 (2010).

Other (6)

Note that a simplification has been made by approximating the path of the target as a straight line during the exposure, which it is not.

This information will be available from calibration data taken before the observation.

D. Shaw and P. Hodge, “Cosmic ray rejection in STIS CCD images,” Instrument Science Rep. STIS 98-22 (Space Telescope Science Institute, 1998).

While the STARE pathfinder satellites will suffer from this problem, the future STARE constellation CubeSats will carry high quality sensors that will not.

H. Ali, C. Lampert, and T. Breuel, “Satellite tracks removal in astronomical images,” in Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science (Springer, 2006), Vol. 4225, pp. 892–901.
[Crossref]

M. Levesque, “Automatic reacquisition of satellite positions by detecting their expected streaks in astronomical images,” presented at the Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, Hawaii, 1–4 Sept. 2009.

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Fig. 1 Flow diagram for the various steps used in the STARE end point detection algorithm. Each of the circled numbers corresponds to one of the Subsections in this Section.

Download Full Size | PPT Slide | PDF

Fig. 2 Example of the local fitting at each end point. The left image shows the track fit in red when all pixels were used, the middle when the left 200 pixels were used, and the right when 170 pixels were used.

Download Full Size | PPT Slide | PDF

Fig. 3 Illustration of the matched filter process. (a) Shows an ROI taken from a corrected raw image. (b) Shows a simulated ROI, where a line segment of length

L_{1}

has been convolved with a match filter to attempt to reproduce the real track in (a). In (c) the length has been extended to

L_{2}

as part of the iterative process. And in (d), the entire simulated ROI has been spanned to produce a residual at all

R \cdot r

grid points. The first and last 10 points appear flat because the edges of the ROI are ignored due to convolution edge effects. The real track length

L_{real}

is evident at the minimum of the residual curve.

Download Full Size | PPT Slide | PDF

Fig. 4 End point determination for satellite track detected in three separate Oceanit images. While precise end point coordinates are not available for comparison, as they are in the simulated images, the reported end points match up well with what we expect based on the PSF of the system.

Download Full Size | PPT Slide | PDF

Fig. 5 Plot showing the total end point error from a run of 400 tracks of random lengths, orientation, and brightness. The y axis shows the total end point error and the x axis shows photons per micrometer, both of which are described in the text. At 250 photons per micrometer, the SNR ranges from 2–4. At 600 photons per micrometer, the SNR ranges roughly from 6–12. These values depend on the orientation of the track relative to pixel boundaries.

Download Full Size | PPT Slide | PDF

Equations (5)

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

x = x_{o} + v_{x} t, y = y_{o} + v_{y} t, z = z_{o} + v_{z} t,

x^{'} = (x_{o}^{'} + v_{x}^{'} t) \cos (\dot{θ} t) + (y_{o}^{'} + v_{y}^{'} t) \sin (\dot{θ} t), y^{'} = - (x_{o}^{'} + v_{x}^{'} t) \sin (\dot{θ} t) + (y_{o}^{'} + v_{y}^{'} t) \cos (\dot{θ} t),

\frac{d^{2} y^{'}}{d x^{' 2}} = \frac{2 \dot{θ} (- v_{x}^{'} \sin (\dot{θ} t) + v_{y}^{'} \cos (\dot{θ} t)) - {\dot{θ}}^{2} ((x_{o}^{'} + v_{x}^{'} t) \cos (\dot{θ} t) + (y_{o}^{'} + v_{y}^{'} t) \sin (\dot{θ} t))}{2 \dot{θ} (- v_{x}^{'} \cos (\dot{θ} t) - v_{y}^{'} \sin (\dot{θ} t)) - {\dot{θ}}^{2} ((x_{o}^{'} + v_{x}^{'} t) \sin (\dot{θ} t) + (y_{o}^{'} + v_{y}^{'} t) \cos (\dot{θ} t))},

m = \frac{\sum_{i = 0}^{N_{pix}} x^{' 2} \sum_{i = 0}^{N_{pix}} I y^{'} - \sum_{i = 0}^{N_{pix}} I x^{'} \sum_{i = 0}^{N_{pix}} I x^{'} y^{'}}{N_{pix} \sum_{i = 0}^{N_{pix}} I x^{' 2} - (\sum_{i = 0}^{N_{pix}} I x^{'})^{2}}, b = \frac{N_{pix} \sum_{i = 0}^{N_{pix}} I x^{'} y^{'} - \sum_{i = 0}^{N_{pix}} I x^{'} \sum_{i = 0}^{N_{pix}} I y^{'}}{N_{pix} \sum_{i = 0}^{N_{pix}} I x^{' 2} - (\sum_{i = 0}^{N_{pix}} I x^{'})^{2}},

D = \frac{I (m x^{'} - y^{'} + b)}{I_{max} \sqrt{m^{2} + 1^{2}}},

Abstract

References

2010 (1)

2006 (1)

2005 (1)

2004 (1)

2000 (1)

1998 (1)

Ali, H.

Bauman, B.

Breuel, T.

De Vries, W.

Earl, M. A.

Hambly, N. C.

Hodge, P.

Lampert, C.

Levesque, M.

Mann, R. G.

Nikolaev, S.

Olivier, S.

Pertica, A.

Phillion, D.

Riot, V.

Shaw, D.

Simms, L.

Storkey, A. J.

Williams, C. K. I.

J. R. Astron. Soc. Can. (1)

Mon. Not. R. Astron. Soc. (1)

Phys. Lett. B (1)

Proc. SPIE (1)

Other (6)

Cited By

Figures (5)

Equations (5)

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