Convergence analysis of non-linear filtering based on cubature Kalman filter

Jafar Zarei; Ehsan Shokri

Convergence analysis of non-linear filtering based on cubature Kalman filter

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Author(s): Jafar Zarei ¹ and Ehsan Shokri ¹
- Affiliations: 1: Department of Control Engineering, School of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran
Source: Volume 9, Issue 3, May 2015, p. 294 – 305
DOI: 10.1049/iet-smt.2014.0056 , Print ISSN 1751-8822, Online ISSN 1751-8830

Received 02/03/2014, Accepted 01/07/2014, Revised 20/06/2014, Published 03/09/2014

This study analyses the stability of cubature Kalman filter (CKF) for non-linear systems with linear measurement. The certain conditions to ensure that the estimation error of the CKF remains bounded are proved. Then, the effect of process noise covariance is investigated and an adaptive process noise covariance is proposed to deal with large estimation error. Since adaptation law has a very important role in convergence, fuzzy logic is proposed to improve the versatility of the proposed adaptive noise covariance. Accordingly, a modified CKF (MCKF) is developed to enhance the stability and accuracy of state estimation. The performance of the modified CKF is compared to the CKF in two case studies. Simulation results demonstrate that the large estimation error may lead to instability of CKF, while the MCKF is successfully able to estimate the states. In addition, the superiority of MCKF that uses fuzzy adaptation rules is shown.

References

1. 1)
  - 27. Song, Y., Grizzle, J.W.: ‘The extended Kalman filter as a local asymptotic observer for discrete-time nonlinear systems’, J. Math. Syst. Estimation Control, 1995, 5, (1), pp. 59–78.
2. 2)
  - 29. Sasiadek, J., Wang, Q., Zeremba, M.: ‘Fuzzy adaptive Kalman filtering for Ins/Gps data fusion’. Proc. of the IEEE Int. Symp. on Intelligent Control, 2000, pp. 181–186.
3. 3)
  - M. Boutayeb , H. Rafaralahy , M. Darouach . Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems. IEEE Trans. Autom. Control , 4 , 581 - 586
4. 4)
  - 3. Bittanti, S., Savaresi, S.M.: ‘On the parametrization and design of an extended Kalman filter frequency tracker’, IEEE Trans. Autom. Control, 2000, 45, (9), pp. 1718–1724 (doi: 10.1109/9.880631).
5. 5)
  - 46. Ho, Y.C., Lee, R.C.K.: ‘A Bayesian approach to problems in stochastic estimation and control’, IEEE Trans. Autom. Control, 1964, 9, pp. 333–339 (doi: 10.1109/TAC.1964.1105763).
6. 6)
  - 5. Bogosyan, S., Barut, M., Gokasan, M.: ‘Braided extended Kalman filters for sensorless estimation in induction motors at high-low/zero speed’, IET Control Theory Appl., 2007, 1, (4), pp. 987–998 (doi: 10.1049/iet-cta:20060329).
7. 7)
  - 20. Zarei, J., Shokri, E.: ‘Robust sensor fault detection based on nonlinear unknown input observer’, Measurement, 2014, 48, pp. 355–367 (doi: 10.1016/j.measurement.2013.11.015).
8. 8)
  - 17. Pakki, K., Chandra, B., Gu, D.W., et al: ‘A square root Cubature information filter’, IEEE Sensors J., 2013, 13, (2), pp. 750–758 (doi: 10.1109/JSEN.2012.2226441).
9. 9)
  - K. Reif , S. Gunther , E. Yaz . Stochastic stability of the discrete-time extende Kalman filter. IEEE Trans. Autom. Control , 4 , 714 - 728
10. 10)
  - 2. Hall, D.L., Llinas, J.: ‘Multisensor data fusion’ (CRC press, 2001).
11. 11)
  - S. Julier , J.K. Uhlmann , H.F. Durrant-Whyte . A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Autom. Control , 3 , 477 - 482
12. 12)
  - 8. Vaccarella, A., De Momi, E., Enquobahrie, A., Ferrigno, G.: ‘Unscented Kalman filter based sensor fusion for robust optical and electromagnetic tracking in surgical navigation’, IEEE Trans. Instrum. Meas., 2013, 62, (7), pp. 2067–2081 (doi: 10.1109/TIM.2013.2248304).
13. 13)
  - 18. Jia, B., Xin, M., Cheng, Y.: ‘High-degree cubature Kalman filter’, Automatica, 2013, 49, (2), pp. 510–518 (doi: 10.1016/j.automatica.2012.11.014).
14. 14)
  - M. Boutayeb , D. Aubry . A strong tracking extended Kalman observer for nonlinear discrete-time systems. IEEE Trans. Autom. Control , 1550 - 1556
15. 15)
  - 10. Xiong, K., Chan, C., Zhang, H.: ‘Detection of satellite attitude sensor faults using the Ukf’, IEEE Trans. Aerosp. Electron. Syst., 2007, 43, (2), pp. 480–491 (doi: 10.1109/TAES.2007.4285348).
16. 16)
  - 31. Busse, F.D., How, J., Simpson, M., Center, N.: ‘Demonstration of adaptive extended Kalman filter for low earth orbit formation estimation using CDGPS’, Journal of the Institute of Navigation, 2003, 50, pp. 79–94 (doi: 10.1002/j.2161-4296.2003.tb00320.x).
17. 17)
  - 21. Bhaumik, S., Swati, : ‘Square-root cubature-quadrature Kalman filter’, Asian J. Control, 2013, 16, (2), pp. 617–622 (doi: 10.1002/asjc.704).
18. 18)
  - K. Xiong , H.Y. Zhang , C.W. Chan . Performance evaluation of UKF-based nonlinear filtering. Automatica , 261 - 270
19. 19)
  - 28. Rahbari, R., Leach, B.W., Dillon, J., de Silva, C.W.: ‘Adaptive tuning of a Kalman filter using the fuzzy integral for an intelligent navigation system’. Proc. of the IEEE Int. Symp. on Intelligent Control, 2002, pp. 252–257.
20. 20)
  - Y.X. Wu , D.W. Hu , M.P. Wu , X.P. Hu . A numerical-integration perspective on Gaussian filters. IEEE Trans. Signal Process. , 8 , 2910 - 2921
21. 21)
  - 14. Xiong, K., Wei, C.L., Liu, L.D.: ‘Robust unscented Kalman filtering for nonlinear uncertain systems’, Asian J. Control, 2010, 12, (3), pp. 426–433 (doi: 10.1002/asjc.190).
22. 22)
  - 12. Zarei, J., Poshtan, J.: ‘Design of nonlinear unknown input observer for process fault detection’, Ind. Eng. Chem. Res., 2010, 49, (22), pp. 11443–11452 (doi: 10.1021/ie100477m).
23. 23)
  - 12. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman filters’, IEEE Trans. Autom. Control, 2009, 54, (6), pp. 1254–1269 (doi: 10.1109/TAC.2009.2019800).
24. 24)
  - 1. Del Gobbo, D., Napolitano, M., Famouri, P., Innocenti, M.: ‘Experimental application of extended Kalman filtering for sensor validation’, IEEE Trans. Control Syst. Technol., 2001, 9, (2), pp. 376–380 (doi: 10.1109/87.911389).
25. 25)
  - P.K. Dash , R.K. Jena , G. Panda , A. Routray . An extended complex Kalman filter for frequency measurement of distorted signals. IEEE Trans. Instrum. Meas. , 4 , 746 - 753
26. 26)
  - 10. Han, Y., Oh, S., Choi, B.-K., Kwak, D., Kim, H.-C.J., Kim, Y.: ‘Fault detection and identification of aircraft control surface using adaptive observer and input bias estimator’, IET Control Theory Applic., 2012, 6, (10), pp. 1367–1387 (doi: 10.1049/iet-cta.2010.0724).
27. 27)
  - 6. Ali, J.: ‘Strapdown inertial navigation system/astronavigation system data synthesis using innovation-based fuzzy adaptive Kalman filtering’, IET Sci. Meas. Technol., 2010, 4, (5), pp. 246–255 (doi: 10.1049/iet-smt.2009.0065).
28. 28)
  - 11. Li, W., Jia, Y.: ‘Consensus-based distributed multiple model Ukf for jump Markov nonlinear systems’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 227–233 (doi: 10.1109/TAC.2011.2161838).
29. 29)
  - 16. Arasaratnam, I., Haykin, S.: ‘Cubature Kalman smoothers’, Automatica, 2011, 47, (10), pp. 2245–2250.
30. 30)
  - 30. Tang, X., Wei, J., Chen, K.: ‘Square-root adaptive cubature Kalman filter with application to spacecraft attitude estimation’. 2012 15th Int. Conf. on Information Fusion (FUSION), 2012, pp. 1406–1412.
31. 31)
  - 19. Zarei, J., Shokri, E.: ‘Nonlinear and constrained state estimation based on the cubature Kalman filter’, Ind. Eng. Chem. Res., 2014, 53, (10), pp. 3938–3949 (doi: 10.1021/ie4020843).

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Convergence analysis of non-linear filtering based on cubature Kalman filter

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