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An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking

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Abstract

Optimal and consistent estimation of the state of space objects is pivotal to surveillance and tracking applications. However, probabilistic estimation of space objects is made difficult by the non-Gaussianity and nonlinearity associated with orbital mechanics. In this paper, we present an unscented Kalman-particle hybrid filtering framework for recursive Bayesian estimation of space objects. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for estimation when measurements are available. When the target is outside the field of view (FOV) of the sensor, it updates the state probability density function (PDF) via a sequential Monte Carlo method. The hybrid filter addresses the problem of particle depletion through a suitably designed filter transition scheme. To assess the performance of the hybrid filtering approach, we consider two test cases of space objects that are assumed to undergo full three dimensional orbital motion under the effects of J 2 and atmospheric drag perturbations. It is demonstrated that the hybrid filters can furnish fast, accurate and consistent estimates outperforming standard UKF and particle filter (PF) implementations.

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References

  1. Alspach, D., Sorenson, H.: Nonlinear bayesian estimation using gaussian sum approximations. IEEE Trans. Autom. Control 17(4), 439–448 (1972)

    Article  MATH  Google Scholar 

  2. Arulampalam, S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking. IEEE Trans. Signal Process. 50(2), 174–188 (2001). doi:10.1109/78.978374

    Article  Google Scholar 

  3. Bailey, T., Nieto, J., Guivant, J., Stevens, M., Nebot, E.: Consistency of the Ekf-Slam Algorithm. In: Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3562–3568 (2006). doi:10.1109/IROS.2006.281644

  4. Bengtsson, T., Bickel, P., Li, B.: Curse-of-dimensionality revisited: collapse of particle filter in very large scale systems. In: Probability and Statistics: Essays in Honor of David A. Freedman, vol. 2, pp. 316–334 (2008)

  5. Burgers, G., Leeuwen, P.V., Evensen, G.: Analysis scheme in the ensemble kalman filter. Mon. Weather. Rev. 126(6), 1719–1724 (1998)

    Article  Google Scholar 

  6. Daum, F.: Nonlinear filters beyond the kalman filter. IEEE Aerosp. Electron. Syst. Mag. 20(8), 57–69 (2005). doi:10.1109/MAES.2005.1499276

    Article  MathSciNet  Google Scholar 

  7. Daum, F., Huang, J.: Curse of dimensionality and particle filters. In: Proceedings of IEEE Aerospace Conference, pp. 1979–1993 (2003). iSBN:0-7803-7651-X

  8. DeMars, K., Bishop, R., Jah, M.: Entropy-based approach for uncertainty propagation of nonlinear dynamical systems. J. Guid. Control. Dyn. 36(4), 1047–1056 (2013). doi:10.2514/1.58987

    Article  Google Scholar 

  9. Doucet, A.: On Sequential Monte Carlo Methods for Bayesian Filtering. Tech. Rep. CUED/F-INFENG/TR.310, Dept. Eng., Univ. Cambridge (1998)

  10. Evensen, G.: Sequential data assimilation with a nonlinear quasigeostrophic model using monte carlo methods to forecast error statistics. J. Geophys. Res. Oceans 99 (C5), 10 143–10 162 (1994)

    Article  Google Scholar 

  11. Gordon, N., Salmond, D., Smith, A.: A novel approach to nonlinear/non-gaussian bayesian state estimation. IEEE Proceedings F, Radar and Signal Processing 140(2), 107–113 (1993). doi:10.1049/ip-f-2.1993.0015

    Article  Google Scholar 

  12. Julier, S.J., Uhlmann, J.K.: Unscented filtering and nonlinear estimation. In: Proceedings of the IEEE, vol. 92, pp. 401–402 (2004). doi:10.1109/JPROC.2003.823141

  13. Julier, S.J., Uhlmann, J.K., Durrant-Whyte, H.: A new approach for filtering nonlinear systems. In: Proceedings of the American Control Conference, pp. 1628–1632 (1995). iSBN:0-7803-2445-5

  14. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82(1), 35–45 (1960). doi:10.1115/1.3662552

    Article  Google Scholar 

  15. Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. Trans. ASME J. Basic Eng. 83(1), 95–108 (1961). doi:10.1115/1.3658902

    Article  MathSciNet  Google Scholar 

  16. Kalnay, E., Li, H., Miyoshi, T., Ballabrera-Poy, J.: 4-D-var or ensemble kalman filter?. Tellus A 59(5), 758–773 (2007)

    Article  Google Scholar 

  17. Psiaki, M.L.: The blind tricyclist problem and a comparative study of nonlinear filters. IEEE Control. Syst. Mag. 33(3), 40–54 (2013)

    Article  MathSciNet  Google Scholar 

  18. Raihan, D., Chakravorty, S.: Particle gaussian mixture (Pgm) filters. In: Proceedings of the 2016 19Th International Conference on Information Fusion (FUSION), pp. 1369–1376 (2016). iSBN:978-0-9964-5274-8

  19. Ristic, B., Arulampalam, S., Gordon, N.: Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House, Boston, London (2004). iSBN:158053631X

    MATH  Google Scholar 

  20. Schaub, H., Junkins, J.: Analytical Mechanics of Space Systems. AIAA, Reston VA (2003). iSBN:1624102409

    Book  MATH  Google Scholar 

  21. Smith, G., Schmidt, S., McGee, L.: Application of statistical filter theory to the optimal estimation of position and velocity on board a circumlunar vehicle. Tech. Rep. NASA TR-135, NASA (1962)

  22. Sorenson, H., Alspach, D.: Recursive bayesian estimation using gaussian sums. Automatica 7(4), 465–479 (1971). doi:10.1016/0005-1098(71)90097-5

    Article  MathSciNet  MATH  Google Scholar 

  23. Terejanu, G., Singla, P., Singh, T., Scott, P.: Adaptive gaussian sum filter for nonlinear bayesian estimation. IEEE Trans. Autom. Control 56(9), 2151–2156 (2011). doi:10.1109/TAC.2011.2141550

    Article  MathSciNet  MATH  Google Scholar 

  24. Wan, E., van der Merwe, R.: The Unscented Kalman Filter. In: Haykin, S. (ed.) Kalman Filter and Neural Networks, pp. 221–280. Wiley, New York (2001). iSBN:9780471369981

  25. Whitaker, J., Hamill, T.: Ensemble data assimilation without perturbed observations. Mon. Weather. Rev. 130(7), 1913–1924 (2002)

    Article  Google Scholar 

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Authors and Affiliations

  1. Texas A&M University, College Station, TX, USA

    Dilshad Raihan A. V & Suman Chakravorty

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  1. Dilshad Raihan A. V
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  2. Suman Chakravorty
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Correspondence to Dilshad Raihan A. V.

Additional information

This work is funded by AFOSR grant number: FA9550-13-1-0074 under the Dynamic Data Driven Application Systems (DDDAS) program.

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Raihan A. V, D., Chakravorty, S. An Unscented Kalman-Particle Hybrid Filter for Space Object Tracking. J of Astronaut Sci 65, 111–134 (2018). https://doi.org/10.1007/s40295-017-0114-8

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  • DOI: https://doi.org/10.1007/s40295-017-0114-8

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