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Cubature Information Filters Using High-Degree and Embedded Cubature Rules

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Abstract

The information form of the Kalman filter (KF) is preferred over standard covariance filters in multiple sensor fusion problems. Aiming at this issue, two types of cubature information filters (CIF) for nonlinear systems are presented in this article. The two approaches, which we have named the embedded cubature information filter (ECIF) and the fifth-degree cubature information filter (FCIF), are developed from a fifth-degree cubature Kalman filter and a newly proposed embedded cubature KF. Theoretical analysis shows that the proposed filters can achieve higher level estimation accuracy than conventional information filters, such as the CIF and the extended information filter (EIF). Performance comparisons of the proposed information filters with the conventional CIF are demonstrated via two independent multisensor tracking problems. The experimental results, presented herein, demonstrate that the proposed algorithms are more reliable and accurate than the CIF.

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References

  1. I. Arasaratnam, Sensor fusion with square-root cubature information filter. Intell. Control Autom. 4, 11–17 (2013)

    Article  Google Scholar 

  2. I. Arasaratnam, S. Haykin, Cubature Kalman filters. IEEE Trans. Autom. Control 54, 1254–1269 (2009)

    Article  MathSciNet  Google Scholar 

  3. I. Arasaratnam, S. Haykin, T.R. Hurd, Cubature Kalman filtering for continuous-discrete systems: theory and simulations. IEEE Trans. Signal Process. 58, 4977–4993 (2010)

    Article  MathSciNet  Google Scholar 

  4. R.S. Bucy, K.D. Senne, Digital synthesis of non-linear filters. Automatica 7, 287–298 (1971)

    Article  MATH  Google Scholar 

  5. F.R. Castella, An adaptive two-dimensional Kalman tracking filter. IEEE Trans. Aerosp. Electron. Syst. AES 16, 822–829 (1980)

    Article  Google Scholar 

  6. K.P.B. Chandra, D.W. Gu, I. Postlethwaite, Cubature information filter and its applications, in 2011 American Control Conference (2011), pp. 3609–3614

  7. K.P.B. Chandra, D.W. Gu, I. Postlethwaite, Square root cubature information filter. IEEE Sens. J. 13, 750–758 (2013)

    Article  Google Scholar 

  8. R. Cools, Advanced in multidimensional integration. J. Comput. Appl. Math. 149, 1–12 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Cools, Extrapolation and adaptive in software for automatic numerical integration on a cube. Numer. Algorithms 34, 259–269 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Cools, E. Novak, Spherical product algorithms and the integration of smooth functions with one singular point. SIAM J. Numer. Anal. 39, 1132–1145 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. N.J. Gordon, D.J. Salmond, A.F.M. Smith, Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc. F 140, 107–113 (1993)

    Google Scholar 

  12. K. Ito, K. Xiong, Gaussian filters for nonlinear filtering problems. IEEE Trans. Autom. Control 45, 910–927 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. S.R.K. Iyengar, R.K. Jain, Numerical Methods (New Age International Publisher, New Delhi, 2009)

    Google Scholar 

  14. S.J. Julier, J.K. Uhlmann, A new extension of the Kalman filter to nonlinear systems, in Proceedings of the Society of Photo-optical Instrumentation Engineers (SPIE) (1997), pp. 182–193

  15. S.J. Julier, J.K. Uhlmann, Unscented filtering and nonlinear estimation. Proc. IEEE 92, 401–422 (2004)

    Article  Google Scholar 

  16. B. Jia, M. Xin, Y. Cheng, Multiple sensor estimation using the sparse Gauss-Hermite quadrature information filter. in 2012 American Control Conference (2012), pp. 5544-5549

  17. B. Jia, M. Xin, K. Pham, E. Blasch, G. Chen, Multiple sensor estimation using a high-degree cubature information filter, in Proceedings of the Society of Photo-optical Instrumentation Engineers (SPIE) (2013), pp. 87390T–1–87390T-13

  18. R.E. Kalman, A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82, 35–45 (1960)

    Article  Google Scholar 

  19. J.H. Kotecha, P.A. Djuric, Gaussian particle filtering. IEEE Trans. Signal Process. 51, 2592–2601 (2003)

    Article  MathSciNet  Google Scholar 

  20. D.J. Lee, Nonlinear estimation and multiple sensor fusion using unscented information filtering. IEEE Signal Process. Lett. 15, 861–864 (2008)

    Article  Google Scholar 

  21. X. Lu, W. Wang, Robust Kalman filtering for discrete-time systems with multiple time-delayed measurements. Circ. Syst. Signal Process. 26, 551–571 (2007)

    Article  MATH  Google Scholar 

  22. J.N. Lyness, U. Rude, Cubature of integrands containing derivatives. Numer. Math. 78, 439–461 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  23. A.G.O. Mutambara, Decentralized Estimation and Control for Multisensory Systems (CRC Press, Boca Raton, 1998)

    Google Scholar 

  24. J.R. Raol, G. Girija, Sensor data fusion algorithms using square root information filtering. IEE Proc. F 49, 89–96 (2002)

    Google Scholar 

  25. I. Strid, K. Walentin, Block Kalman filtering for large-scale DSGE models. Comput. Econ. 33, 277–304 (2009)

    Article  MATH  Google Scholar 

  26. Y. Sunahara, K. Yamashita, An approximate method of state estimation for non-linear dynamical systems with state-dependent noise. Int. J. Control 11, 957–972 (1970)

    Article  MATH  Google Scholar 

  27. Y.B. Shalom, X.R. Li, T. Kirubarajan, Estimation with Applications to Tracking and Navigation (Wiley, New York, 2001)

    Book  Google Scholar 

  28. D. Zhou, New Guidance Laws for Homing Missiles (National Defense Industry Press, Beijing, 2002)

    Google Scholar 

  29. X.C. Zhang, C.J. Guo, Square-root embedded cubature Kalman filtering. Control Theory A 30, 1116–1121 (2013)

    Google Scholar 

  30. X.C. Zhang, C.J. Guo, Cubature Kalman filters: derivation and extension. Chin. Phys. B 22, 128401–1–128401–6 (2013)

    Google Scholar 

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Authors and Affiliations

  1. University of Electronic Science and Technology of China, No. 2006, Xiyuan Ave., West High-Tech Zone, Chengdu , 611731, Sichuan, China

    Xin-Chun Zhang

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Zhang, XC. Cubature Information Filters Using High-Degree and Embedded Cubature Rules. Circuits Syst Signal Process 33, 1799–1818 (2014). https://doi.org/10.1007/s00034-013-9730-0

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  • DOI: https://doi.org/10.1007/s00034-013-9730-0

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