Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements. (English) Zbl 1278.93269

Summary: This article is concerned with the recursive finite-horizon filtering problem for a class of nonlinear time-varying systems subject to multiplicative noises, missing measurements and quantisation effects. The missing measurements are modelled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. The quantisation phenomenon is described by using the logarithmic function and the multiplicative noises are considered to account for the stochastic disturbances on the system states. Attention is focused on the design of a recursive filter such that, for all multiplicative noises, missing measurements as well as quantisation effects, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimised by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form suitable for online applications. Finally, two simulation examples are exploited to demonstrate the effectiveness and applicability of the proposed filter design scheme.


93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
93E10 Estimation and detection in stochastic control theory
Full Text: DOI


[1] DOI: 10.1080/00207720903045825 · Zbl 1301.93157
[2] DOI: 10.1109/9.867021 · Zbl 0988.93069
[3] DOI: 10.1016/j.dsp.2009.06.011
[4] DOI: 10.1109/TSMCA.2005.843383
[5] Carli R, in Proceedings of the 17th IFAC World Congress pp 8062– (2008)
[6] DOI: 10.1016/j.automatica.2008.01.027 · Zbl 1153.93492
[7] DOI: 10.1109/TAC.2010.2040497 · Zbl 1368.93357
[8] DOI: 10.1109/9.948466 · Zbl 1059.93521
[9] DOI: 10.1016/j.automatica.2009.09.033 · Zbl 1192.93115
[10] DOI: 10.1109/TAC.2005.858689 · Zbl 1365.81064
[11] DOI: 10.1017/CBO9780511840371
[12] DOI: 10.1016/j.automatica.2006.12.025 · Zbl 1123.93085
[13] DOI: 10.1016/j.automatica.2012.03.027 · Zbl 1257.93099
[14] DOI: 10.1016/j.sysconle.2012.01.005 · Zbl 1250.93121
[15] DOI: 10.1109/TAC.2008.2010962 · Zbl 1367.93648
[16] Kallapur AG, in 18th IFAC World Congress pp 1– (2011)
[17] DOI: 10.1109/3477.558841
[18] DOI: 10.1109/TAC.2009.2037467 · Zbl 1368.93717
[19] DOI: 10.1109/TAES.2011.5705658
[20] DOI: 10.1109/TSP.2008.920470 · Zbl 1390.93793
[21] DOI: 10.1109/TSP.2009.2037853 · Zbl 1391.93252
[22] DOI: 10.1016/j.sysconle.2008.01.011 · Zbl 1153.93034
[23] DOI: 10.1109/TSP.2008.923196 · Zbl 1390.94428
[24] DOI: 10.1109/78.485915
[25] DOI: 10.1016/j.automatica.2012.01.008 · Zbl 1244.93162
[26] DOI: 10.1109/TAC.2011.2176362 · Zbl 1369.93583
[27] DOI: 10.1109/9.293203 · Zbl 0812.93069
[28] DOI: 10.1109/TSP.2006.871880 · Zbl 1373.94736
[29] DOI: 10.1002/oca.928 · Zbl 1213.93192
[30] DOI: 10.1109/TSMCA.2009.2037018
[31] DOI: 10.1109/TSP.2011.2141666 · Zbl 1392.94544
[32] DOI: 10.1109/TSP.2006.870585 · Zbl 1373.94749
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.