access icon free Robust measure of non-linearity-based cubature Kalman filter

In this study, a novel robust measure of non-linearity-based cubature Kalman filter (RMoNCKF) is proposed to obtain good performance with lower computational burden. The proposed filter inherits the virtues of high accuracy of the high-degree filter and computation efficiency of the low-degree one. When the measure of non-linearity (MoN) is evaluated and compared with the threshold in the dynamic system, the cubature rules nested in the RMoNCKF can be switched autonomously to decrease the computation complexity in the low non-linear condition. Furthermore, the robust estimation technology can help to improve the value of MoN for the non-Gaussian distributed case. Simulation results of target tracking and integrated navigation system demonstrate that the RMoNCKF can have a close performance to the fifth-degree CKF with less computation time. In the circumstances of the time-varying noise and contaminated Gaussian distributed noise, the RMoNCKF outperforms the UKF, the third-degree CKF and fifth-degree CKF.

Inspec keywords: Kalman filters; target tracking; estimation theory; Gaussian noise; navigation; computational complexity

Other keywords: nonlinearity-based cubature Kalman filter; UKF; computation complexity; nonGaussian distributed case; third-degree CKF; contaminated Gaussian distributed noise; time-varying noise; measure of nonlinearity evaluation; RMoNCKF; integrated navigation system; MoN evaluation; robust estimation technology; target tracking; fifth-degree CKF

Subjects: Signal processing and conditioning equipment and techniques; Filtering methods in signal processing; Other topics in statistics; Radionavigation and direction finding

References

    1. 1)
      • 6. Wang, X.X., Liang, Y., Pan, Q., et al: ‘A Gaussian approximation recursive filter for nonlinear systems with correlated noises’, Automatica, 2012, 48, (9), pp. 22902297.
    2. 2)
      • 14. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman filters’, IEEE Trans. Autom. Control, 2009, 54, (6), pp. 12541269.
    3. 3)
      • 12. Chandra, K.P.B., Gu, D.W., Postlethwaite, I.: ‘Square root cubature information filter’, IEEE Sens. J., 2013, 13, (2), pp. 750758.
    4. 4)
      • 7. Alonge, F., Cangemi, T., D'Ippolito, F., et al: ‘Convergence analysis of extended Kalman filter for sensorless control of induction motor’, IEEE Trans. Ind. Electron., 2015, 62, (4), pp. 23412352.
    5. 5)
      • 8. Farahanifar, M., Assadian, N.: ‘Integrated magnetometer-horizon sensor low-earth orbit determination using UKF’, Acta Astronaut.., 2014, 106, pp. 1223.
    6. 6)
      • 28. Li, L., Xia, Y.Q., Chang, G.B.: ‘Stochastic stability of the unscented Kalman filter with intermittent observations’, Automatica, 2012, 48, (5), pp. 978981.
    7. 7)
      • 24. Chang, L.B., Hu, B.Q., Chang, G.B., et al: ‘Huber-based novel robust unscented Kalman filter’, IET Sci. Meas. Technol., 2012, 6, (6), pp. 502509.
    8. 8)
      • 23. Wu, Y.X., Hu, D.W., Wu, M.P.: ‘A numerical integration perspective on Gaussian filters’, IEEE Trans. Signal Process., 2006, 54, (8), pp. 29102921.
    9. 9)
      • 21. Straka, O., Dunik, J., Simandl, M.: ‘Unscented Kalman filter with controlled adaptation’. Proc. of IFAC Symp. on System Identification, July 2012, pp. 906911.
    10. 10)
      • 10. Tang, X.J., Yan, J., Zhong, D.D.: ‘Square-root sigma-point Kalman filtering for spacecraft relative navigation’, Acta Astronaut.., 2010, 66, (6), pp. 704713.
    11. 11)
      • 17. Jia, B., Xin, M., Cheng, Y.: ‘High-degree cubature Kalman filter’, Automatica, 2013, 49, (2), pp. 510518.
    12. 12)
      • 9. Wang, X.X., Pan, Q., Liang, Y., et al: ‘Gaussian smoothers for nonlinear systems with one-step randomly delayed measurements’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 18281835.
    13. 13)
      • 18. Sun, T., Xin, M., Jia, B.: ‘Nonlinearity-based adaptive sparse-grid quadrature filter’. Proc. of American Control Conf., July 2015, pp. 24992504.
    14. 14)
      • 1. Gaspar, T., Oliveira, P.: ‘Model-based H2 adaptive filter for 3D positioning and tracking systems’, Automatica, 2014, 50, (1), pp. 225232.
    15. 15)
      • 15. Zhang, X., Teng, Y.: ‘A new derivation of the cubature Kalman filters’, Asian J. Control, 2015, 16, (5), pp. 15011510.
    16. 16)
      • 5. Huang, Y.L., Zhang, Y.G., Wang, X.X., et al: ‘Gaussian filter for nonlinear systems with correlated noises at the same epoch’, Automatica, 2015, 60, (10), pp. 122126.
    17. 17)
      • 26. Huang, Y., Wu, L.H., Sun, F.: ‘Robust cubature Kalman filter based on the Huber M estimator’, Control Decis., 2014, 29, (3), pp. 572576.
    18. 18)
      • 16. Jia, B., Xin, M., Cheng, Y.: ‘Sparse-grid quadrature nonlinear filtering’, Automatica, 2012, 48, (2), pp. 327341.
    19. 19)
      • 29. Kluge, S., Reif, K., Brokate, M.: ‘Stochastic stability of the extended Kalman filter with intermittent observations’, IEEE Trans. Autom. Control, 2010, 55, (2), pp. 514518.
    20. 20)
      • 22. Dunłk, J., Straka, O., Simandl, M.: ‘Nonlinearity and non-Gaussianity measures for stochastic dynamic systems’. Proc. of IEEE Int. Conf. on Information Fusion, July 2013, pp. 204211.
    21. 21)
      • 4. Hu, G.G., Gao, S.S., Zhong, Y.M.: ‘A derivative UKF for tightly coupled INS/GPS integrated navigation’, ISA Trans., 2015, 56, pp. 135144.
    22. 22)
      • 2. Zhang, L., Yang, C., Chen, Q.W., et al: ‘Robust H-infinity CKF/KF hybrid filtering method for SINS alignment’, IET Sci. Meas. Technol., 2016, 10, (8), pp. 916925.
    23. 23)
      • 19. Li, K.L., Chang, L.B., Hu, B.Q.: ‘A variational Bayesian based unscented Kalman filter with both adaptivity and robustness’, IEEE Sens. J., 2016, 16, (18), pp. 69666976.
    24. 24)
      • 25. Chang, L.B., Hu, B.Q., Chang, G.B., et al: ‘Robust derivative-free Kalman filter based on Huber's M-estimation methodology’, J. Process Control, 2013, 23, (10), pp. 15551561.
    25. 25)
      • 11. Chang, G.B.: ‘Marginal unscented Kalman filter for cross-correlated process and observation noise at the same epoch’, IET Radar Sonar Nav., 2014, 8, (1), pp. 5464.
    26. 26)
      • 31. Zhao, Y.W.: ‘Cubature + extended hybrid Kalman filtering method and its application in PPP/IMU tightly coupled navigation systems’, IEEE Sens. J., 2015, 15, (12), pp. 69736985.
    27. 27)
      • 20. Jia, B., Xin, M.: ‘Multiple sensor estimation using a new fifth-degree cubature information filter’, Trans. Inst. Meas. Control, 2014, 37, (1), pp. 1524.
    28. 28)
      • 30. Xiong, K., Zhang, H.Y., Chan, C.W.: ‘Performance evaluation of UKF based nonlinear filtering’, Automatica, 2006, 42, (2), pp. 261270.
    29. 29)
      • 3. Chang, L.B., Hu, B.Q., Li, A., et al: ‘Strapdown inertial navigation system alignment based on marginalised unscented Kalman filter’, IET. Sci. Meas. Technol., 2013, 7, (8), pp. 128138.
    30. 30)
      • 27. Zhang, W.J., Wang, S.Y., Feng, Y.L., et al: ‘Huber-based high-degree cubature Kalman tracking algorithm’, Acta Phys. Sin., 2013, 65, (8), p. 088401.
    31. 31)
      • 13. Singer, H.: ‘Conditional Gauss-Hermite filtering with application to volatility estimation’, IEEE Trans. Autom. Control, 2015, 60, (9), pp. 24762481.
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