Skip to main content
Top

2015 | OriginalPaper | Chapter

2. Recursive Filtering with Missing Measurements and Quantized Effects

Authors : Jun Hu, Zidong Wang, Huijun Gao

Published in: Nonlinear Stochastic Systems with Network-Induced Phenomena

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In Chap. 2, the recursive filtering problems are investigated for non-linear systems with missing measurements over a finite horizon. Firstly, the EKF problem with multiple missing measurements is studied. Both deterministic and stochastic non-linearities are included in the system model. The phenomenon of measurement missing occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0, 1]. The aim of the addressed filtering problem was to design a filter such that, in the presence of both the stochastic non-linearities and multiple missing measurements, an upper bound is obtained for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. Secondly, the proposed recursive filtering strategy is extended to deal with the filtering problem for systems with missing measurements, quantization effects, and multiplicative noises. A set of parallel results is obtained by using the similar techniques.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference NaNacara W, Yaz EE (1997) Recursive estimators for linear and nonlinear systems with uncertain observations. Signal Process 62(2):215–228CrossRefMATH NaNacara W, Yaz EE (1997) Recursive estimators for linear and nonlinear systems with uncertain observations. Signal Process 62(2):215–228CrossRefMATH
2.
go back to reference Mao X (2007) Stochastic differential equations and applications, 2nd edn. Horwood Publishing, ChichesterMATH Mao X (2007) Stochastic differential equations and applications, 2nd edn. Horwood Publishing, ChichesterMATH
3.
go back to reference Wei G, Wang Z, Shu H (2009) Robust filtering with stochastic nonlinearities and multiple missing measurements. Automatica 45(3):836–841CrossRefMATHMathSciNet Wei G, Wang Z, Shu H (2009) Robust filtering with stochastic nonlinearities and multiple missing measurements. Automatica 45(3):836–841CrossRefMATHMathSciNet
4.
go back to reference Horn RA, Johnson CR (1991) Topic in matrix analysis. Cambridge University Press, New YorkCrossRef Horn RA, Johnson CR (1991) Topic in matrix analysis. Cambridge University Press, New YorkCrossRef
5.
go back to reference Xie L, Soh YC, de Souza CE (1994) Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans Autom Control 39(6):1310–1314CrossRefMATH Xie L, Soh YC, de Souza CE (1994) Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans Autom Control 39(6):1310–1314CrossRefMATH
6.
go back to reference Theodor Y, Shaked U (1996) Robust discrete-time minimum-variance filtering. IEEE Trans Signal Process 44(2):181–189CrossRefMathSciNet Theodor Y, Shaked U (1996) Robust discrete-time minimum-variance filtering. IEEE Trans Signal Process 44(2):181–189CrossRefMathSciNet
7.
go back to reference Calafiore G (2005) Reliable localization using set-valued nonlinear filters. IEEE Trans Syst, Man, Cybernt A: Syst Hum 35(2):189–197CrossRefMathSciNet Calafiore G (2005) Reliable localization using set-valued nonlinear filters. IEEE Trans Syst, Man, Cybernt A: Syst Hum 35(2):189–197CrossRefMathSciNet
8.
go back to reference Xiong K, Wei C, Liu L (2010) Robust extended Kalman filtering for nonlinear systems with stochastic uncertainties. IEEE Trans Syst, Man, Cybern A: Syst Hum 40(2):399–405CrossRef Xiong K, Wei C, Liu L (2010) Robust extended Kalman filtering for nonlinear systems with stochastic uncertainties. IEEE Trans Syst, Man, Cybern A: Syst Hum 40(2):399–405CrossRef
9.
go back to reference Xiong K, Liu L, Liu Y (2011) Robust extended Kalman filtering for nonlinear systems with multiplicative noises. Optimal Control Appl Methods 32(1):47–63CrossRefMATHMathSciNet Xiong K, Liu L, Liu Y (2011) Robust extended Kalman filtering for nonlinear systems with multiplicative noises. Optimal Control Appl Methods 32(1):47–63CrossRefMATHMathSciNet
10.
go back to reference Kluge S, Reif K, Brokate M (2010) Stochastic stability of the extended Kalman filter with intermittent observations. IEEE Trans Autom Control 55(2):514–518CrossRefMathSciNet Kluge S, Reif K, Brokate M (2010) Stochastic stability of the extended Kalman filter with intermittent observations. IEEE Trans Autom Control 55(2):514–518CrossRefMathSciNet
11.
12.
go back to reference Fu M, Xie L (2005) The sector bound approach to quantized feedback control. IEEE Trans Autom Control 50(11):1698–1711CrossRefMathSciNet Fu M, Xie L (2005) The sector bound approach to quantized feedback control. IEEE Trans Autom Control 50(11):1698–1711CrossRefMathSciNet
13.
go back to reference Hounkpevi FO, Yaz EE (2007) Robust minimum variance linear state estimators for multiple sensors with different failure rates. Automatica 43(7):1274–1280CrossRefMATHMathSciNet Hounkpevi FO, Yaz EE (2007) Robust minimum variance linear state estimators for multiple sensors with different failure rates. Automatica 43(7):1274–1280CrossRefMATHMathSciNet
14.
go back to reference Wang Z, Ho DWC, Liu X (2003) Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Trans Autom Control 48(7):1254–1258CrossRefMathSciNet Wang Z, Ho DWC, Liu X (2003) Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Trans Autom Control 48(7):1254–1258CrossRefMathSciNet
15.
go back to reference Lei M, van Wyk BJ, Qi Y (2011) Online estimation of the approximate posterior cramer-rao lower bound for discrete-time nonlinear filtering. IEEE Trans Aerosp Electron Syst 47(1):37–57CrossRef Lei M, van Wyk BJ, Qi Y (2011) Online estimation of the approximate posterior cramer-rao lower bound for discrete-time nonlinear filtering. IEEE Trans Aerosp Electron Syst 47(1):37–57CrossRef
Metadata
Title
Recursive Filtering with Missing Measurements and Quantized Effects
Authors
Jun Hu
Zidong Wang
Huijun Gao
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-08711-5_2