Unbiased information filtering for systems with missing measurement based on disturbance estimation.

*(English)*Zbl 1395.93533Summary: This paper designs the information filters for a class of linear discrete-time systems with unknown disturbance. A recursive three-step information filter (RTSIF) is presented at first, which is used to estimate the unknown disturbance and state separately. In the presence of measurement dropout, a recursive three-step information filter with missing measurement (RTSIFMM) is also developed, in which the missing measurement is modelled as Bernoulli process with a binary variable. Two types of stochastic stability are introduced to give the boundedness of proposed filter. It is shown that the estimation error will be bounded, if some assumptions are satisfied. The relationships between the designed filter in this paper and some existing results are given. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed filter.

##### MSC:

93E11 | Filtering in stochastic control theory |

93E10 | Estimation and detection in stochastic control theory |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C55 | Discrete-time control/observation systems |

93E15 | Stochastic stability in control theory |

93C05 | Linear systems in control theory |

##### Keywords:

unbiased information filtering; missing measurement systems; disturbance estimation; linear discrete-time systems; stochastic stability
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\textit{T. Du} and \textit{L. Guo}, J. Franklin Inst. 353, No. 4, 936--954 (2016; Zbl 1395.93533)

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##### References:

[1] | Kitanidis, Peter K., Unbiased minimum-variance linear state estimation, Automatica, 23, 6, 775-778, (1987) · Zbl 0627.93065 |

[2] | Jie Chen, Ron J. Patton, Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances, IEE Proc.—Control Theory Appl. 143(1) (1996) 31-36. · Zbl 0850.93748 |

[3] | Dong, Hongli; Wang, Zidong; Ding, Steven X.; Gao, Huijun, Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems, Automatica, 50, 12, 3182-3189, (2014) · Zbl 1309.93155 |

[4] | Guo, Lei; Cao, Songyin; Qi, Chuntang; Gao, Xiaoying, Initial alignment for nonlinear inertial navigation systems with multiple disturbances based on enhanced anti-disturbance filtering, Int. J. Control, 85, 5, 491-501, (2012) · Zbl 1256.93106 |

[5] | Cao, Songyin; Guo, Lei, Multi-objective robust initial alignment algorithm for inertial navigation system with multiple disturbances, Aerosp. Sci. Technol., 21, 1, 1-6, (2012) |

[6] | Darouach, Mohamed; Zasadzinski, Michel, Unbiased minimum variance estimation for systems with unknown exogenous inputs, Automatica, 33, 4, 717-719, (1997) · Zbl 0874.93086 |

[7] | Darouach, Mohamed; Zasadzinski, Michel; Boutayeb, Mohamed, Extension of minimum variance estimation for systems with unknown inputs, Automatica, 39, 5, 867-876, (2003) · Zbl 1036.93058 |

[8] | Gillijns, Steven; De Moor, Bart, Unbiased minimum-variance input and state estimation for linear discrete-time systems, Automatica, 43, 1, 111-116, (2007) · Zbl 1140.93480 |

[9] | Hsieh, Chien-Shu, Robust two-stage Kalman filters for systems with unknown inputs, IEEE Trans. Autom. Control, 45, 12, 2374-2378, (2000) · Zbl 0990.93130 |

[10] | Simon, Dan, Optimal state estimation: Kalman, H infinity, and nonlinear approaches, (2006), John Wiley & Sons New York |

[11] | Mutambara, Arthur G. O., Decentralized estimation and control for multisensor systems, (1998), CRC Press Boca Raton, Florida · Zbl 0966.93007 |

[12] | Wang, Shiyuan; Feng, Jiuchao; Tse, Chi K., A class of stable square-root nonlinear information filters, IEEE Trans. Autom. Control, 59, 7, 1893-1898, (2014) · Zbl 1360.93716 |

[13] | Xia, Yuanqing; Liu, G.-P.; Fu, M.; Rees, David, Predictive control of networked systems with random delay and data dropout, IET Control Theory Appl., 3, 11, 1476-1486, (2009) |

[14] | Li, Wenling; Jia, Yingmin; Du, Junping; Zhang, Jun, Robust state estimation for jump Markov linear systems with missing measurements, J. Frankl. Inst., 350, 6, 1476-1487, (2013) · Zbl 1293.93717 |

[15] | Sinopoli, Bruno; Schenato, Luca; Franceschetti, Massimo; Poolla, Kameshwar; Jordan, Michael I.; Sastry, Shankar S., Kalman filtering with intermittent observations, IEEE Trans. Autom. Control, 49, 9, 1453-1464, (2004) · Zbl 1365.93512 |

[16] | Wang, Zidong; Yang, Fuwen; Ho, Daniel W. C.; Liu, Xiaohui, Robust h infinity control for stochastic time-delay systems with missing measurements, IEEE Trans. Signal Process., 54, 7, 2579-2587, (2006) · Zbl 1373.94729 |

[17] | Shen, Bo; Wang, Zidong; Shu, Huisheng; Wei, Guoliang, On nonlinear filtering for discrete-time stochastic systems with missing measurements, IEEE Trans. Autom. Control, 53, 9, 2170-2180, (2008) · Zbl 1367.93659 |

[18] | Dong, Hongli; Wang, Zidong; Gao, Huijun, Distributed filtering for a class of time-varying systems over sensor networks with quantization errors and successive packet dropouts, IEEE Trans. Signal Process., 60, 6, 3164-3173, (2012) · Zbl 1391.93232 |

[19] | Wang, Zidong; Dong, Hongli; Shen, Bo; Gao, Huijun, Finite-horizon h-infinity filtering with missing measurements and quantization effects, IEEE Trans. Autom. Control, 58, 7, 1707-1718, (2013) · Zbl 1369.93660 |

[20] | Wang, Zidong; Ho, Daniel W. C.; Liu, Xiaohui, Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE Trans. Autom. Control, 48, 7, 1254-1258, (2003) · Zbl 1364.93814 |

[21] | Kluge, Sebastian; Reif, Konrad; Brokate, Martin, Stochastic stability of the extended Kalman filter with intermittent observations, IEEE Trans. Autom. Control, 55, 2, 514-518, (2010) · Zbl 1368.93717 |

[22] | Hu, Jun; Wang, Zidong; Gao, Huijun; Stergioulas, Lampros K., Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements, Automatica, 48, 9, 2007-2015, (2012) · Zbl 1257.93099 |

[23] | Li, Li; Xia, Yuanqing, Stochastic stability of the unscented Kalman filter with intermittent observations, Automatica, 48, 5, 978-981, (2012) · Zbl 1246.93121 |

[24] | Jinya Su, Baibing Li, Wenhua Chen, Bayesian recursive filtering with partially observed inputs and missing measurements, in: 2013 19th International Conference on Automation and Computing (ICAC), IEEE, London, 2013, pp. 1-6. |

[25] | Kailath, Thomas; Sayed, Ali H.; Hassibi, Babak, Linear Estimation, vol. 1, (2000), Prentice Hall Upper Saddle River, NJ · Zbl 0980.93077 |

[26] | Reif, Konrad; Günther, Stefan; Yaz, Engin; Unbehauen, Rolf, Stochastic stability of the discrete-time extended Kalman filter, IEEE Trans. Autom. Control, 44, 4, 714-728, (1999) · Zbl 0967.93090 |

[27] | Keller, J. Y.; Summerer, L.; Boutayeb, M.; Darouach, M., Generalized likelihood ratio approach for fault detection in linear dynamic stochastic systems with unknown inputs, Int. J. Syst. Sci., 27, 12, 1231-1241, (1996) · Zbl 0869.93045 |

[28] | Cheng, Yue; Ye, Hao; Wang, Yongqiang; Zhou, Donghua, Unbiased minimum-variance state estimation for linear systems with unknown input, Automatica, 45, 2, 485-491, (2009) · Zbl 1158.93415 |

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