access icon free Cubature quadrature Kalman filter

© The Institution of Engineering and Technology
Received 11/03/2012, Accepted 18/04/2013, Revised 18/04/2013, Published

In this correspondence, the authors develop a novel method based on spherical radial cubature and Gauss–Laguerre quadrature rule for non-linear state estimation problems. The proposed filter, referred as cubature quadrature Kalman filter (CQKF) would be able to overcome inherent disadvantages associated with the earlier reported cubature Kalman filter (CKF). The theory and formulation of CQKF has been presented. Using two well-known non-linear examples, the superior performance of CQKF has been demonstrated. Owing to computational efficiency (compared to the particle and grid-based filter) and enhanced accuracy compared to the extended Kalman filter and the CKF, the developed algorithm may find place in on-board real life applications.

Inspec keywords: Kalman filters; stochastic processes

Other keywords: Gauss–Laguerre quadrature rule; nonlinear state estimation; spherical radial cubature; CQKF; cubature quadrature Kalman filter

Subjects: Other topics in statistics; Other topics in statistics; Filtering methods in signal processing; Signal processing theory

References

    1. 1)
      • 10. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman smoothers’, Automatica, 2011, 47, (10), pp. 2245–2250.
    2. 2)
      • 5. Carpenter, J., Clifford, P., Fearnhead, P.: ‘Improved particle filter for nonlinear problems’, IEE Proc. Radar Sonar Navig., 1999, 146, (1), pp. 2–7 (doi: 10.1049/ip-rsn:19990255).
    3. 3)
      • 19. Stewart, I.: ‘The Lorenz attractor exists’, Nature, 2000, 406, pp. 948–949 (doi: 10.1038/35023206).
    4. 4)
      • 4. Ito, K., Xiong, K.: ‘Gaussian filters for nonlinear filtering problems’, IEEE Trans. Autom. Control, 2000, 45, (5), pp. 910–927 (doi: 10.1109/9.855552).
    5. 5)
      • 16. Hildebrand, F.B.: ‘Introduction to numerical analysis’ (Dover Publication, New York, 2008, 2nd edn.).
    6. 6)
      • 9. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman filters’, IEEE Trans. Autom. Control, 1999, 54, (6), pp. 1254–1269 (doi: 10.1109/TAC.2009.2019800).
    7. 7)
      • 3. Jia, B., Xin, M., Cheng, Y.: ‘Sparse Gaussian–Hermite quadrature filter with application to spacecraft attitude estimation’, J. Guid. Control Dyn., 2011, 34, (2), pp. 367–379 (doi: 10.2514/1.52016).
    8. 8)
      • 2. Van der Merwe, R., Wan, E.A.: ‘The square-root unscented Kalman filter for state and parameter-estimation’. Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 2001, vol. 6, pp. 3461–3464.
    9. 9)
      • 11. Chalasani, G., Bhaumik, S.: ‘Bearing only tracking using Gauss-Hermite filter’. Proc. Seventh IEEE Conf. on Industrial Electronics and Applications, Singapore, 18–20 July 2012.
    10. 10)
      • 1. Julier, S., Uhlmann, J., Whyte, D.: ‘A new method for the nonlinear transformation of means and covariances in filters and estimators’, IEEE Trans. Autom. Control, 2000, 45, (3), pp. 477–482 (doi: 10.1109/9.847726).
    11. 11)
      • 8. Swati, , Bhaumik, S.: ‘Nonlinear estimation using cubature quadrature points’. Proc. Conf. on Energy, Automation, and Signal, India, 2011.
    12. 12)
      • 14. Genz, A.: ‘Numerical computation of multivariate normal probabilities’, J. Comput. Graph. Stat., 1992, 1, (2), pp. 141–149.
    13. 13)
      • 15. Krylov, V.I.: ‘Approximate calculation of integrals’ (Dover Publication, NC, Mineola, New York, 2005).
    14. 14)
      • 20. Tucker, W.: ‘The Lorentz attractor exists’, C.R.Acad. Sci. Paris Ser. I Math., 1999, 328, (12), pp. 1197–1202 (doi: 10.1016/S0764-4442(99)80439-X).
    15. 15)
      • 17. Anderson, B.D.O., Moore, J.B.: ‘Optimal filtering’ (Prentice-Hall, Eaglewood Cliffs, NJ, 1979).
    16. 16)
      • 7. Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: ‘A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking’, IEEE Trans. Signal Process., 2002, 50, (2), pp. 174–188 (doi: 10.1109/78.978374).
    17. 17)
      • 12. Song, T.L., Speyer, J.L.: ‘A stochastic analysis of a modified gain extended Kalman filter with applications to estimation with bearings-only measurements’, IEEE Trans. Autom. Control, 1985, AC-30, (10), pp. 940–949 (doi: 10.1109/TAC.1985.1103821).
    18. 18)
      • 13. Wu, Y., Hu, D., Wu, M., Hu, X.: ‘A numerical-integration perspective on Gaussian filters’, IEEE Trans. Signal Process., 2006, 54, (8), pp. 2910–2921 (doi: 10.1109/TSP.2006.875389).
    19. 19)
      • 6. Bhaumik, S., Srinivasan, M., Sadhu, S., Ghoshal, T.K.: ‘Adaptive grid risk-sensitive filter for non-linear problems’, IET Signal Process., 2011, 5, (2), pp. 235–241 (doi: 10.1049/iet-spr.2008.0224).
    20. 20)
      • 18. Terejanu, G., Singla, P., Singh, T., Scott, P.D.: ‘Adaptive Gaussian sum filter for nonlinear Baysian estimation’, IEEE Trans. Autom. Control, 2011, 56, (9), pp. 2151–2156 (doi: 10.1109/TAC.2011.2141550).
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