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Stochastic stability of the unscented Kalman filter with intermittent observations. (English) Zbl 1246.93121
Summary: In this paper, the stochastic stability of the discrete-time unscented Kalman filter for general nonlinear stochastic systems with intermittent observations is proposed. It is shown that the estimation error remains bounded if the system satisfies some assumptions. And the statistical convergence property of the estimation error covariance is studied, showing the existence of a critical value for the arrival rate of the observations. An upper bound on this expected state error covariance is given. A numerical example illustrates the effectiveness of the techniques developed.

MSC:
93E15 Stochastic stability in control theory
93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
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[1] Boutayeb, M.; Aubry, D., A strong tracking extended Kalman observer for nonlinear discrete-time systems, IEEE transactions on automatic control, 44, 8, 1550-1556, (1999) · Zbl 0957.93086
[2] Julier, S. 2002. The scaled unscented transformation. In Proceedings of the American control conference, Anchorage, AK (pp. 4555-4559).
[3] Julier, S., Uhlmann, J., & Durrant-Whyte, H. (1995). A new approach for filtering nonlinear system. In Proceedings of the American control conference. Washington, DC (pp. 1628-1632).
[4] Julier, S.; Uhlmann, J.; Durrant-Whyte, H.F., A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE transactions on automatic control, 45, 3, 477-482, (2000) · Zbl 0973.93053
[5] Kluge, S.; Reif, K.; Brokate, M., Stochastic stability of the extended Kalman filter with intermittent observations, IEEE transaction automatic control, 55, 2, 514-518, (2010) · Zbl 1368.93717
[6] Reif, K.; Gunther, S.; Yaz, E.; Unbehauen, R., Stochastic stability of the discrete-time extended Kalman filter, IEEE transactions on automatic control, 44, 4, 714-728, (1999) · Zbl 0967.93090
[7] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M.; Sastry, S., Kalman filtering with intermittent observations, IEEE transaction automatic control, 59, 9, 1453-1464, (2004) · Zbl 1365.93512
[8] Xia, Y.; Liu, G.P.; Fu, M.; Rees, D., Predictive control of networked systems with random delay and data dropout, IET control theory and applications, 3, 11, 1476-1486, (2008)
[9] Xiong, K. (2006). Nonlinear filter and its application in satellite attitude estimation. Doctor Thesis of Beihang University, Beijing, China.
[10] Xiong, K.; Zhang, H.; Chan, C., Performance evaluation of UKF based nonlinear filtering, Automatica, 42, 2, 261-270, (2006) · Zbl 1103.93045
[11] Xu, J., Dimirovski, G.M., Jing, Y., & Shen, C. (2008). Stochastic stability of the continuous-time unscented Kalman filter. In Proceedings of the 47th IEEE conference on decision and control. Cancun (pp. 5110-5115).
[12] Zhou, Y., Xu, J., Jing, Y., & Dimirovski, G. (2009). The unscented Kalman filtering in extended noise environments. In Proceedings of the 28th American control conference, St. Louis, MO, USA (pp. 1865-1870).
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