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Stochastic stability of extended filtering for non-linear systems with measurement packet losses

Stochastic stability of extended filtering for non-linear systems with measurement packet losses

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This study is concerned with stochastic stability of a new extended filtering for non-linear systems subject to measurement packet losses. The measurements sensored are transmitted to the estimator through a packet-dropping network. By introducing a time-stamped packet arrival indicator sequence, the measurement loss process is modelled as an independent, identically distributed (i.i.d.) and therefore a Bernoulli process. The boundedness of estimation error covariance matrices is proved by showing the existence of a critical threshold for measurement packet arrival probability. It is also shown that, under appropriate assumptions, the estimation error remains bounded as long as the noise covariance matrices and the initial estimation error can be ensured small enough. Finally, simulation results validating the effectiveness of this proposed filtering framework are also presented.

References

    1. 1)
      • 1. Hespanha, J., Naghshtabrizi, P., Xu, Y.: ‘A survey of recent results in networked control systems’, Proc. IEEE, 2007, 95, (1), pp. 138162 (doi: 10.1109/JPROC.2006.887288).
    2. 2)
      • 2. Che, W., Wang, J., Yang, G.: ‘Quantised H filtering for networked systems with random sensor packet losses’, IET Control Theory Appl., 2010, 4, (8), pp. 13391352 (doi: 10.1049/iet-cta.2009.0120).
    3. 3)
      • 3. Hu, J., Wang, Z., Gao, H., Stergioulas, L. K.: ‘Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements’, Automatica, 2012, 48, (9), pp. 20072015 (doi: 10.1016/j.automatica.2012.03.027).
    4. 4)
      • 4. Wang, Z., Shen, B., Liu, X.: ‘H filtering with randomly occurring sensor saturations and missing measurements’, Automatica, 2012, 48, (3), pp. 556562 (doi: 10.1016/j.automatica.2012.01.008).
    5. 5)
      • 5. You, K., Xie, L.: ‘Linear quadratic Gaussian control with quantised innovations Kalman filter over a symmetric channel’, IET Control Theory Appl., 2011, 5, (3), pp. 437446 (doi: 10.1049/iet-cta.2009.0488).
    6. 6)
      • 6. Shen, B., Wang, Z., Shu, H., Wei, G.: ‘Robust H finite-horizon filtering with randomly occurred nonlinearities and quantisation effects’, Automatica, 46, (11), pp. 17431751 (doi: 10.1016/j.automatica.2010.06.041).
    7. 7)
      • 7. Sun, S., Xie, L., Xiao, W., Soh, Y.: ‘Optimal linear estimation for systems with multiple packet dropouts’, Automatica, 2008, 44, (5), pp. 13331342 (doi: 10.1016/j.automatica.2007.09.023).
    8. 8)
      • 8. Shen, B., Ding, S., Wang, Z.: ‘Finite-horizon H fault estimation for linear discrete time-varying systems with delayed measurements’, Automatica, 2012, 49, (1), pp. 293296 (doi: 10.1016/j.automatica.2012.09.003).
    9. 9)
      • 9. Nahi, N.: ‘Optimal recursive estimation with uncertain observation’, IEEE Trans. Inf. Theory, 1969, 15, (4), pp. 457462 (doi: 10.1109/TIT.1969.1054329).
    10. 10)
      • 10. Hadidi, M., Schwartz, S.: ‘Linear recursive state estimators under uncertain observations’, IEEE Trans. Autom. Control, 1979, 24, (6), pp. 944948 (doi: 10.1109/TAC.1979.1102171).
    11. 11)
      • 11. Tugnait, J.: ‘Stability of optimum linear estimators of stochastic signals in white multiplicative noise’, IEEE Trans. Autom. Control, 1981, 26, (3), pp. 757761 (doi: 10.1109/TAC.1981.1102688).
    12. 12)
      • 12. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: ‘Kalman filtering with intermittent observations’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 14531464 (doi: 10.1109/TAC.2004.834121).
    13. 13)
      • 13. Huang, M., Dey, S.: ‘Stability of Kalman filtering with Markovian packet losses’, Automatica, 2007, 43, (4), pp. 598607 (doi: 10.1016/j.automatica.2006.10.023).
    14. 14)
      • 14. You, K., Fu, M., Xie, L.: ‘Mean square stability for Kalman filtering with Markovian packet losses’, Automatica, 2011, 47, (12), pp. 26472657 (doi: 10.1016/j.automatica.2011.09.015).
    15. 15)
      • 15. Zhang, H., Song, X., Shi, L.: ‘Convergence and mean square stability of suboptimal estimator for systems with measurement packet dropping’, IEEE Trans. Autom. Control, 2012, 57, (5), pp. 12481253 (doi: 10.1109/TAC.2012.2191857).
    16. 16)
      • 16. Liu, Y., Xu, B.: ‘Filter designing with finite packet losses and its application for stochastic systems’, IET Control Theory Appl., 2011, 5, (6), pp. 775784 (doi: 10.1049/iet-cta.2010.0178).
    17. 17)
      • 17. Dong, H., Wang, Z., Lam, J., Gao, H.: ‘Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts’, IEEE Trans. Syst. Man Cybern. B, 2012, 42, (2), pp. 365376 (doi: 10.1109/TSMCB.2011.2163797).
    18. 18)
      • 18. Hu, J., Wang, Z., Shen, B., Gao, H.: ‘Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays’, IEEE Trans. Signal Process., 2013, 61, (5), pp. 12301238 (doi: 10.1109/TSP.2012.2232660).
    19. 19)
      • 19. Hu, J., Wang, Z., Shen, B., Gao, H.: ‘Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements’, Int. J. Control, 2013, 86, (4), pp. 650663 (doi: 10.1080/00207179.2012.756149).
    20. 20)
      • 20. Dong, H., Wang, Z., Lam, J., Gao, H.: ‘Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts’, Int. J. Robust Nonlin. Control, 2013, doi: 10.1002/rnc.2960.
    21. 21)
      • 21. Probst, A., Maganña, M., Sawodny, O.: ‘Using a Kalman filter and a Pade approximation to estimate random time delays in a networked feedback control system’, IET Control Theory Appl., 2010, 4, (11), pp. 22632272 (doi: 10.1049/iet-cta.2009.0339).
    22. 22)
      • 22. 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 (doi: 10.1109/TAC.2009.2037467).
    23. 23)
      • 23. Li, L., Xia, Y.: ‘Stochastic stability of the unscented Kalman filter with intermittent observations’, Automatica, 2012, 48, (5), pp. 978981 (doi: 10.1016/j.automatica.2012.02.014).
    24. 24)
      • 24. Reif, K., Gunther, S., Yaz, E., Unbehauen, R.: ‘Stochastic stability of the discrete-time extended Kalman filter’, IEEE Trans. Autom. Control, 1999, 44, (4), pp. 714728 (doi: 10.1109/9.754809).
    25. 25)
      • 25. Joseph, J.: ‘A comparison of unscented and extended Kalman filtering for estimating quaternion motion’. American Control Conf., 2003, pp. 24352440.
    26. 26)
      • 26. Anderson, B., Moore, J.: ‘Detectability and stabilisability of time-varying discrete-time linear systems’, SIAM J. Control Optim., 1981, 19, (1), pp. 2032 (doi: 10.1137/0319002).
    27. 27)
      • 27. Horn, R., Johnson, C.: ‘Matrix analysis’ (Cambridge University Press, 1990).
    28. 28)
      • 28. Lu, L., Pearce, C.: ‘Some new bounds for singular values and eigenvalues of matrix products’, Ann. Oper. Res., 2000, 98, (1), pp. 141148 (doi: 10.1023/A:1019200322441).
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