Abstract

To improve space target tracking precision and the stability of mobile optoelectronic tracking equipment, an error-space estimation method based on the Kalman filter is discussed, and a simplified algorithm is presented to reduce calculation cost. Based on an available measurement of a space target without sufficient validity and accuracy, the actual position related to the tracking equipment is decomposed to an earlier offline prediction of the kinetic model method and prediction errors. By regarding prediction errors as the motion of a weak maneuver target, the errors can be estimated more accurately in error space. By synthesizing estimation of the errors and offline prediction, the space target position is obtained with higher accuracy to improve tracking performance.

© 2010 Optical Society of America

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  1. T. Ichikawa, “An orbit estimation for the space-craft at closest approach phase to the planet,” in Proceedings of the SICE 2004 Annual Conference (IEEE, 2004), pp. 1768–1773.
  2. E. Burke and E. Rutkowski, “Vehicle based independent tracking system (VBITS): a small, modular, avionics suite for responsive launch vehicle and satellite applications,” in Proceedings of the 6th Responsive Space Conference (American Institute of Aeronautics and Astronautics, 2006), pp. 1–6.
  3. Z. Y. Wang and Z. Y. Xu, “Study on stable tracking target with single photoelectric theodolite,” Optoelectron. Eng. 30, 11–14(2003).
  4. N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
    [CrossRef]
  5. M. A. Zayan, “Resources minimization in the satellite navigation process,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2006), pp. 1–9.
  6. L. Liu, The Theory of Spacecraft Orbit (National Defense Industry Press, 2000).
  7. R. H. Battin, An Introduction to the Mathematics and Methods of Astrodynamics, revised ed. (American Institute of Aeronautics and Astronautics, 1999).
  8. D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).
  9. T. Ichikawa, “The orbit estimation for low thrust spacecraft,” in Proceedings of the SICE 2002 Annual Conference (IEEE, 2002), pp. 1839–1840.
    [CrossRef]
  10. Q. Li, F. C. Guo, and Y. Y. Zhou, “Observability of satellite to satellite passive tracking from angle measurements,” in Proceedings of the IEEE International Conference on Control and Automation (IEEE, 2007), pp. 1926–1931.
  11. R. Fabrizio and P. Giovanni, “Estimate problems for satellite clusters,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2008), pp. 1–18.
  12. O. Montenbruck and P. Ramos-Bosch, “Precision real-time navigation of LEO satellites using global positioning system measurements,” GPS Solutions 12, 187–198(2008).
    [CrossRef]
  13. G. R. Hu and J. K. Ou, “The theory of GPS-based geometric orbit determination for low-earth satellites,” Chin. J. Space Science 20, 32–39 (2000).
  14. M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).
  15. J. Duník and M. Šimandl, “Estimation of state and measurement noise covariance matrices by multi-step prediction,” in Proceedings of the 17th IFAC World Congress (International Federation of Automatic Control, 2008), pp. 3689–3694.
  16. S. L. Sun, “Optimal and self-tuning information fusion Kalman multi-step predictor,” IEEE Trans. Aerosp. Electron. Syst. 43, 418–427 (2007).
    [CrossRef]
  17. L. G. Taff, “On initial orbit determination,” Astron. J. 89, 1426–1428 (1984).
    [CrossRef]
  18. A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
    [CrossRef]
  19. D. Hobbs and P. Bohn, “Precise orbit determination for low Earth orbit satellites,” Ann. Marie Curie Fellowships 4, 1–7 (2006).
  20. S. Katagiri and Y. Yamamoto, “Technology of precise orbit determination,” Fujitsu Sci. Tech. J. 44, 401–409 (2008).
  21. U. Gebhardt, O. Loffeld, and M. Kalkuhl, “Orbit tracking and interpolation using a realistic gravitation model,” in Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing (IEEE, 2004), pp. 3767–3769.
  22. M. Cen, D. S. Luo, and X. F. Liu, “Comparison of two error-space estimate methods for space-earth optical communication,” in Proceedings of the International Symposium on Photonics and Optoelectronics (IEEE, 2009), pp. 1–5.
    [CrossRef]
  23. X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I: dynamic models,” IEEE Trans. Aerosp. Electron. Syst. 39, 1333–1364 (2003).
    [CrossRef]

2008

O. Montenbruck and P. Ramos-Bosch, “Precision real-time navigation of LEO satellites using global positioning system measurements,” GPS Solutions 12, 187–198(2008).
[CrossRef]

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

S. Katagiri and Y. Yamamoto, “Technology of precise orbit determination,” Fujitsu Sci. Tech. J. 44, 401–409 (2008).

2007

D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

S. L. Sun, “Optimal and self-tuning information fusion Kalman multi-step predictor,” IEEE Trans. Aerosp. Electron. Syst. 43, 418–427 (2007).
[CrossRef]

2006

D. Hobbs and P. Bohn, “Precise orbit determination for low Earth orbit satellites,” Ann. Marie Curie Fellowships 4, 1–7 (2006).

2003

Z. Y. Wang and Z. Y. Xu, “Study on stable tracking target with single photoelectric theodolite,” Optoelectron. Eng. 30, 11–14(2003).

X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I: dynamic models,” IEEE Trans. Aerosp. Electron. Syst. 39, 1333–1364 (2003).
[CrossRef]

2002

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

2000

G. R. Hu and J. K. Ou, “The theory of GPS-based geometric orbit determination for low-earth satellites,” Chin. J. Space Science 20, 32–39 (2000).

1984

L. G. Taff, “On initial orbit determination,” Astron. J. 89, 1426–1428 (1984).
[CrossRef]

Abdalla, A. G. E.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Ali, B. M.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Battin, R. H.

R. H. Battin, An Introduction to the Mathematics and Methods of Astrodynamics, revised ed. (American Institute of Aeronautics and Astronautics, 1999).

Bohn, P.

D. Hobbs and P. Bohn, “Precise orbit determination for low Earth orbit satellites,” Ann. Marie Curie Fellowships 4, 1–7 (2006).

Burke, E.

E. Burke and E. Rutkowski, “Vehicle based independent tracking system (VBITS): a small, modular, avionics suite for responsive launch vehicle and satellite applications,” in Proceedings of the 6th Responsive Space Conference (American Institute of Aeronautics and Astronautics, 2006), pp. 1–6.

Cen, M.

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

M. Cen, D. S. Luo, and X. F. Liu, “Comparison of two error-space estimate methods for space-earth optical communication,” in Proceedings of the International Symposium on Photonics and Optoelectronics (IEEE, 2009), pp. 1–5.
[CrossRef]

Chen, K.

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

Denneau, L.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Duník, J.

J. Duník and M. Šimandl, “Estimation of state and measurement noise covariance matrices by multi-step prediction,” in Proceedings of the 17th IFAC World Congress (International Federation of Automatic Control, 2008), pp. 3689–3694.

Fabrizio, R.

R. Fabrizio and P. Giovanni, “Estimate problems for satellite clusters,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2008), pp. 1–18.

Farnocchia, D.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Fu, C. Y.

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

Gebhardt, U.

U. Gebhardt, O. Loffeld, and M. Kalkuhl, “Orbit tracking and interpolation using a realistic gravitation model,” in Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing (IEEE, 2004), pp. 3767–3769.

Giovanni, P.

R. Fabrizio and P. Giovanni, “Estimate problems for satellite clusters,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2008), pp. 1–18.

Gronchi, G. F.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Guo, F. C.

Q. Li, F. C. Guo, and Y. Y. Zhou, “Observability of satellite to satellite passive tracking from angle measurements,” in Proceedings of the IEEE International Conference on Control and Automation (IEEE, 2007), pp. 1926–1931.

Hobbs, D.

D. Hobbs and P. Bohn, “Precise orbit determination for low Earth orbit satellites,” Ann. Marie Curie Fellowships 4, 1–7 (2006).

Hu, G. R.

G. R. Hu and J. K. Ou, “The theory of GPS-based geometric orbit determination for low-earth satellites,” Chin. J. Space Science 20, 32–39 (2000).

Ichikawa, T.

T. Ichikawa, “The orbit estimation for low thrust spacecraft,” in Proceedings of the SICE 2002 Annual Conference (IEEE, 2002), pp. 1839–1840.
[CrossRef]

T. Ichikawa, “An orbit estimation for the space-craft at closest approach phase to the planet,” in Proceedings of the SICE 2004 Annual Conference (IEEE, 2004), pp. 1768–1773.

Jedicke, R.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Jilkov, V. P.

X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I: dynamic models,” IEEE Trans. Aerosp. Electron. Syst. 39, 1333–1364 (2003).
[CrossRef]

Kalkuhl, M.

U. Gebhardt, O. Loffeld, and M. Kalkuhl, “Orbit tracking and interpolation using a realistic gravitation model,” in Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing (IEEE, 2004), pp. 3767–3769.

Katagiri, S.

S. Katagiri and Y. Yamamoto, “Technology of precise orbit determination,” Fujitsu Sci. Tech. J. 44, 401–409 (2008).

Khatun, S.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Kneževic, Z.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Kyun, N. C.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Li, Q.

Q. Li, F. C. Guo, and Y. Y. Zhou, “Observability of satellite to satellite passive tracking from angle measurements,” in Proceedings of the IEEE International Conference on Control and Automation (IEEE, 2007), pp. 1926–1931.

Li, X. R.

X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I: dynamic models,” IEEE Trans. Aerosp. Electron. Syst. 39, 1333–1364 (2003).
[CrossRef]

Li, Z. G.

D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).

Liu, L.

L. Liu, The Theory of Spacecraft Orbit (National Defense Industry Press, 2000).

Liu, X. F.

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

M. Cen, D. S. Luo, and X. F. Liu, “Comparison of two error-space estimate methods for space-earth optical communication,” in Proceedings of the International Symposium on Photonics and Optoelectronics (IEEE, 2009), pp. 1–5.
[CrossRef]

Loffeld, O.

U. Gebhardt, O. Loffeld, and M. Kalkuhl, “Orbit tracking and interpolation using a realistic gravitation model,” in Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing (IEEE, 2004), pp. 3767–3769.

Luo, D. S.

M. Cen, D. S. Luo, and X. F. Liu, “Comparison of two error-space estimate methods for space-earth optical communication,” in Proceedings of the International Symposium on Photonics and Optoelectronics (IEEE, 2009), pp. 1–5.
[CrossRef]

Milani, A.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Montenbruck, O.

O. Montenbruck and P. Ramos-Bosch, “Precision real-time navigation of LEO satellites using global positioning system measurements,” GPS Solutions 12, 187–198(2008).
[CrossRef]

Noordin, N. K.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Ou, J. K.

G. R. Hu and J. K. Ou, “The theory of GPS-based geometric orbit determination for low-earth satellites,” Chin. J. Space Science 20, 32–39 (2000).

Pierfederici, F.

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

Ramos-Bosch, P.

O. Montenbruck and P. Ramos-Bosch, “Precision real-time navigation of LEO satellites using global positioning system measurements,” GPS Solutions 12, 187–198(2008).
[CrossRef]

Rutkowski, E.

E. Burke and E. Rutkowski, “Vehicle based independent tracking system (VBITS): a small, modular, avionics suite for responsive launch vehicle and satellite applications,” in Proceedings of the 6th Responsive Space Conference (American Institute of Aeronautics and Astronautics, 2006), pp. 1–6.

Sahbuddin, R. K. Z.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Šimandl, M.

J. Duník and M. Šimandl, “Estimation of state and measurement noise covariance matrices by multi-step prediction,” in Proceedings of the 17th IFAC World Congress (International Federation of Automatic Control, 2008), pp. 3689–3694.

Sun, S. L.

S. L. Sun, “Optimal and self-tuning information fusion Kalman multi-step predictor,” IEEE Trans. Aerosp. Electron. Syst. 43, 418–427 (2007).
[CrossRef]

Taff, L. G.

L. G. Taff, “On initial orbit determination,” Astron. J. 89, 1426–1428 (1984).
[CrossRef]

Wang, Z. Y.

Z. Y. Wang and Z. Y. Xu, “Study on stable tracking target with single photoelectric theodolite,” Optoelectron. Eng. 30, 11–14(2003).

Xu, Z. Y.

Z. Y. Wang and Z. Y. Xu, “Study on stable tracking target with single photoelectric theodolite,” Optoelectron. Eng. 30, 11–14(2003).

Yamamoto, Y.

S. Katagiri and Y. Yamamoto, “Technology of precise orbit determination,” Fujitsu Sci. Tech. J. 44, 401–409 (2008).

Yin, D. M.

D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).

Zayan, M. A.

M. A. Zayan, “Resources minimization in the satellite navigation process,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2006), pp. 1–9.

Zhao, Y.

D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).

Zhou, Y. Y.

Q. Li, F. C. Guo, and Y. Y. Zhou, “Observability of satellite to satellite passive tracking from angle measurements,” in Proceedings of the IEEE International Conference on Control and Automation (IEEE, 2007), pp. 1926–1931.

Acta Astron. Sin.

D. M. Yin, Y. Zhao, and Z. G. Li, “Determination orbit of synchronous satellite with short segmental arc,” Acta Astron. Sin. 48, 248–255 (2007).

Ann. Marie Curie Fellowships

D. Hobbs and P. Bohn, “Precise orbit determination for low Earth orbit satellites,” Ann. Marie Curie Fellowships 4, 1–7 (2006).

Astron. J.

L. G. Taff, “On initial orbit determination,” Astron. J. 89, 1426–1428 (1984).
[CrossRef]

Chin. J. Space Science

G. R. Hu and J. K. Ou, “The theory of GPS-based geometric orbit determination for low-earth satellites,” Chin. J. Space Science 20, 32–39 (2000).

Fujitsu Sci. Tech. J.

S. Katagiri and Y. Yamamoto, “Technology of precise orbit determination,” Fujitsu Sci. Tech. J. 44, 401–409 (2008).

GPS Solutions

O. Montenbruck and P. Ramos-Bosch, “Precision real-time navigation of LEO satellites using global positioning system measurements,” GPS Solutions 12, 187–198(2008).
[CrossRef]

Icarus

A. Milani, G. F. Gronchi, D. Farnocchia, Z. Knežević, R. Jedicke, L. Denneau, and F. Pierfederici, “Topocentric orbit determination: algorithms for the next generation surveys,” Icarus 195, 474–492 (2008).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

S. L. Sun, “Optimal and self-tuning information fusion Kalman multi-step predictor,” IEEE Trans. Aerosp. Electron. Syst. 43, 418–427 (2007).
[CrossRef]

X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part I: dynamic models,” IEEE Trans. Aerosp. Electron. Syst. 39, 1333–1364 (2003).
[CrossRef]

J. Univ. Electron. Sci. Technol. Chin.

M. Cen, C. Y. Fu, K. Chen, and X. F. Liu, “Error-space estimate method for synergic target tracking,” J. Univ. Electron. Sci. Technol. Chin. 36, 217–219 (2007).

Lect. Notes Comput. Sci.

N. C. Kyun, A. G. E. Abdalla, N. K. Noordin, S. KhatunB. M. Ali, and R. K. Z. Sahbuddin,, “Modeling and simulation of phased array antenna for LEO satellite tracking,” Lect. Notes Comput. Sci. 2344, 359–371 (2002).
[CrossRef]

Optoelectron. Eng.

Z. Y. Wang and Z. Y. Xu, “Study on stable tracking target with single photoelectric theodolite,” Optoelectron. Eng. 30, 11–14(2003).

Other

T. Ichikawa, “An orbit estimation for the space-craft at closest approach phase to the planet,” in Proceedings of the SICE 2004 Annual Conference (IEEE, 2004), pp. 1768–1773.

E. Burke and E. Rutkowski, “Vehicle based independent tracking system (VBITS): a small, modular, avionics suite for responsive launch vehicle and satellite applications,” in Proceedings of the 6th Responsive Space Conference (American Institute of Aeronautics and Astronautics, 2006), pp. 1–6.

J. Duník and M. Šimandl, “Estimation of state and measurement noise covariance matrices by multi-step prediction,” in Proceedings of the 17th IFAC World Congress (International Federation of Automatic Control, 2008), pp. 3689–3694.

M. A. Zayan, “Resources minimization in the satellite navigation process,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2006), pp. 1–9.

L. Liu, The Theory of Spacecraft Orbit (National Defense Industry Press, 2000).

R. H. Battin, An Introduction to the Mathematics and Methods of Astrodynamics, revised ed. (American Institute of Aeronautics and Astronautics, 1999).

T. Ichikawa, “The orbit estimation for low thrust spacecraft,” in Proceedings of the SICE 2002 Annual Conference (IEEE, 2002), pp. 1839–1840.
[CrossRef]

Q. Li, F. C. Guo, and Y. Y. Zhou, “Observability of satellite to satellite passive tracking from angle measurements,” in Proceedings of the IEEE International Conference on Control and Automation (IEEE, 2007), pp. 1926–1931.

R. Fabrizio and P. Giovanni, “Estimate problems for satellite clusters,” in Proceedings of the IEEE Aerospace Conference (IEEE, 2008), pp. 1–18.

U. Gebhardt, O. Loffeld, and M. Kalkuhl, “Orbit tracking and interpolation using a realistic gravitation model,” in Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing (IEEE, 2004), pp. 3767–3769.

M. Cen, D. S. Luo, and X. F. Liu, “Comparison of two error-space estimate methods for space-earth optical communication,” in Proceedings of the International Symposium on Photonics and Optoelectronics (IEEE, 2009), pp. 1–5.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Composition and principle of a vehicular optoelectronic tracking system.

Fig. 2
Fig. 2

Principle of the error-space estimation method.

Fig. 3
Fig. 3

Comparison of satellite azimuth prediction errors of four methods.

Fig. 4
Fig. 4

Comparison of satellite elevation prediction errors of four methods.

Fig. 5
Fig. 5

Calculation costs of two error-space estimation methods.

Fig. 6
Fig. 6

Comparison of azimuth error in error space with different memory lengths.

Fig. 7
Fig. 7

Comparison of elevation error in error space with different memory lengths.

Equations (24)

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

X ( k ) = Φ ( k 1 ) X ( k 1 ) + Γ ( k 1 ) W ( k 1 ) ,
Z ( k ) = H ( k ) X ( k ) + V ( k ) ,
X ^ ( k + p , k ) = Φ p X ^ ( k ) ,
P ( k + p , k ) = Φ p P ( k , k ) ( Φ T ) p + n = 0 p 1 Φ n Q ( Φ T ) n .
X ε ( k ) = X ( k ) X p ( k ) ,
X ε ( k ) = Φ ε ( k 1 ) X ε ( k 1 ) + Γ ε ( k 1 ) W ε ( k 1 ) ,
Z ε ( k ) = H ε ( k 1 ) X ε ( k ) + V ε ( k ) ,
Q > Q ε .
P ε ( k + p , k ) = Φ ε p P ε ( k , k ) ( Φ ε T ) p + n = 0 p 1 Φ ε n Q ε ( Φ ε T ) n ,
P ( k + p , k ) > P ε ( k + p , k ) .
Z p ( k ) = H p ( k ) X p ( k ) ,
Z ε ( k ) = Z ( k ) Z p ( k ) .
X ^ ε ( k + p , k ) = Φ ε p ( k ) X ^ ε ( k ) .
X ^ ( k + p , k ) = X p ( k + p ) + X ^ ε ( k + p , k ) .
Z ε T ( k ) = h T ( k ) θ ( k ) ,
θ ( k ) = [ a m a 1 a 0 e m e 1 e 0 ] T .
G = ( H T H ) 1 H T ,
θ ^ ( k ) = G Z ε ,
Z ε = [ Z ε T ( 1 ) Z ε T ( 2 ) Z ε T ( n ) ] T ,
H = [ h T ( 1 ) h T ( 2 ) h T ( n ) ] T .
Z ^ ε T ( k , k + p ) = h T ( k + p ) θ ^ ( k ) .
Z ^ ( k , k + p ) = Z p ( k + p ) + Z ^ ε ( k + p ) .
θ ^ ( k ) = [ a m a 1 a 0 e m e 1 e 0 ] T .
θ ^ ( k ) = [ a m a 1 a 0 + a c e m e 1 e 0 + e c ] T .

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