SCIENCE CHINA Information Sciences, Volume 60, Issue 1: 012202(2017) https://doi.org/10.1007/s11432-015-0327-x

Robust state estimation for uncertain linear systems with random parametric uncertainties

Huabo LIU1,2,*, Tong ZHOU1,3
More info
  • ReceivedMar 1, 2016
  • AcceptedJun 28, 2016
  • PublishedNov 22, 2016


In this paper, we investigate state estimations of a dynamical system with random parametric uncertainties which may arbitrarily affect a plant state-space model. A robust estimator is derived based on expectation minimization of estimation errors. An analytic solution similar to that of the well-known Kalman filter is derived for this new robust estimator which can be realized recursively with a comparable computational complexity. Under some weak assumptions, it is proved that this estimator converges to a stable system, the covariance matrix of estimation errors is bounded, and the estimation is asymptotically unbiased. Numerical simulations show that the obtained robust filter has an estimation accuracy comparable to other robust estimators and can be applied in a wider range.

Funded by

National Natural Science Foundation of China(61174122)

Specialized Research Fund for the Doctoral Program of Higher Education China(20110002110045)

National Natural Science Foundation of China(51361135705)



This work was supported by National Natural Science Foundation of China (Grant Nos. 61174122, 51361135705) and Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20110002110045).


[1] Kailath T, Sayed A H, Hassibi B. Linear Estimation. Upper Saddle River: Prentice Hall, 2000. Google Scholar

[2] Sayed A H. A framework for state-space estimation with uncertain models. IEEE Trans Automat Control, 2001, 46: 998-1013 CrossRef Google Scholar

[3] Zhou T. Sensitivity penalization based robust state estimation for uncertain linear systems. IEEE Trans Automat Control, 2010, 55: 1018-1024 CrossRef Google Scholar

[4] Simon D. Optimal State Estimation: Kalman, $H_\infty$ and Nonlinear Approaches. Hoboken: John Wiley & Sons, 2006. Google Scholar

[5] Nagpal K M, Khargonekar P P. Filtering and smoothing in an $H_\infty$-setting. IEEE Trans Automat Control, 1991, 36: 151-166 Google Scholar

[6] Ba{\c{s}}ar T, Bernhard P. $H_\infty$-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Boston: Birkhäuser, 2009. Google Scholar

[7] Fu M Y, de Souza C E, Xie L H. $H_\infty$ estimation for uncertain systems. Int J Robust Nonlinear Contr, 1992, 2: 87-105 CrossRef Google Scholar

[8] Xie L H, de Souza C E, Fu M Y. $H_\infty$ estimation discrete-time linear uncertain systems. Int J Robbust Nonlinear Contr, 1991, 1: 111-123 CrossRef Google Scholar

[9] Zhang W H, Chen B S, Tseng C S. Robust $H_\infty$ filtering for nonlinear stochastic systems. IEEE Trans Signal Process, 2005, 53: 589-598 CrossRef Google Scholar

[10] Garulli A, Vicino A, Zappa G. Conditional central algorithms for worst case set-membership identificaion and filtering. IEEE Trans Automat Control, 2000, 45: 14-23 CrossRef Google Scholar

[11] Jain B N. Guaranteed error estimation in uncertain systems. IEEE Trans Automat Control, 1975, 20: 230-232 CrossRef Google Scholar

[12] Huang Y, Chen Z J, Wei C. Least trace extended set-membership filter. Sci China Inf Sci, 2010, 53: 258-270 CrossRef Google Scholar

[13] Bolzern P, Colaneri P, De Nicolao G. Optimal design of robust predictors for linear discrete-time systems. Syst Control Lett, 1995, 26: 25-31 CrossRef Google Scholar

[14] Mahmoud M S, Shi P. Optimal guaranteed cost filtering for Markovian jump discrete-time systems. Math Probl Eng, 2004, 2004: 33-48 CrossRef Google Scholar

[15] Tadmor G, Mirkin L. $H_\infty$ control and estimation with preview---Part I: matrix ARE solutions in continuous time. IEEE Trans Automat Control, 2005, 50: 19-28 CrossRef Google Scholar

[16] Xu H, Mannor S. A Kalman filter design based on the performance/robustness tradeoff. IEEE Trans Automat Control, 2009, 54: 1171-1175 CrossRef Google Scholar

[17] Ishihara J Y, Terra M H, Cerri J P. Optimal robust filtering for systems subject to uncertainties. Automatica, 2015, 52: 111-117 CrossRef Google Scholar

[18] Neveux P, Blanco E, Thomas G. Robust filtering for linear time invariant continuous systems. IEEE Trans Signal Process, 2007, 55: 4752-4757 CrossRef Google Scholar

[19] Zhou T. Robust state estimation using error sensitivity penalizing. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, 2008. 2563--2568. Google Scholar

[20] Rubinstein R Y, Kroese D P. Simulation and the Monte Carlo Method. New York: John Wiley & Sons, 2011. Google Scholar

[21] Zhou T, Liang H Y. On asymptotic behaviors of a sensitivity penalization based robust state estimator. Syst Control Lett, 2011, 60: 174-180 CrossRef Google Scholar

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1       京公网安备11010102003388号