Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems

References

• Bar–Shalom , Y . 1972 . Optimal Simultaneous State Estimation and Parameter Identification in Linear Discrete-time Systems . IEEE Transactions on Automatic Control , 17 : 308 – 319 .
   Web of Science ®Google Scholar
• Basin , MV , Calderon-Alvarez , D and Skliar , M . 2008 . Optimal Filtering for Incompletely Measured Polynomial States Over Linear Observations . International Journal of Adaptive Control and Signal Processing , 22 : 482 – 494 .
   Web of Science ®Google Scholar
• Basin , MV , Perez , J and Skliar , M . 2006 . Optimal Filtering for Polynomial System States with Polynomial Multiplicative Noise . International Journal of Robust and Nonlinear Control , 16 : 287 – 298 .
   Web of Science ®Google Scholar
• Becedas , J , Mamani , G and Fellu , V . 2010 . Algebraic Parameters Identification of DC Motors: Methodology and Analysis . International Journal of Systems Science , 41 : 1241 – 1255 .
   Web of Science ®Google Scholar
• Charalambous , CD and Logothetis , A . 2000 . Maximum Likelihood Parameter Estimation from Incomplete Data Via the Sensitivity Equations: The Continuous–time Case . IEEE Transactions on Automatic Control , 45 : 928 – 934 .
   Web of Science ®Google Scholar
• Coutinho , F and Cortesao , R . 2011 . Adaptive Stiffness Estimation for Compliant Robotic Manipulation Using Stochastic Disturbance Models . International Journal of Systems Science , 42 : 1241 – 1252 .
   Web of Science ®Google Scholar
• Duncan , TE , Mandl , P and Pasik–Duncan , B . 1999 . A Note on Sampling and Parameter Estimation in Linear Stochastic Systems . IEEE Transactions on Automatic Control , 44 : 2120 – 2125 .
   Web of Science ®Google Scholar
• Elliott , RJ and Krishnamurthy , V . 1997 . New Finite-dimensional Filters for Estimation of Continuous–time Linear Gaussian Systems . SIAM Journal of Control Optimization , 35 : 1908 – 1923 .
   Web of Science ®Google Scholar
• Elliott , RJ and Krishnamurthy , V . 1999 . New Finite-dimensional Filters for Parameter Estimation of Discrete–time Linear Gaussian Models . IEEE Transactions on Automatic Control , 44 : 938 – 951 .
   Web of Science ®Google Scholar
• Gao , H , Lam , J , Xie , L and Wang , C . 2005 . New Approach to Mixed H 2/H ∞ Filtering for Polytopic Discrete-time Systems . IEEE Transactions on Signal Processing , 53 : 3183 – 3192 .
   Web of Science ®Google Scholar
• Germani , A , Manes , P and Palumbo , P . 2002 . Linear Filtering for Bilinear Stochastic Differential Systems with Unknown Inputs . IEEE Transactions on Automatic Control , 47 : 1726 – 1730 .
   Web of Science ®Google Scholar
• Jeong , CS , Yaz , E , Bahakeem , A and Yaz , Y . 2006 . Nonlinear Observer Design with General Criteria . International Journal of Innovative Computing, Information and Control , 2 : 693 – 704 .
   Web of Science ®Google Scholar
• Liang , J and Lam , J . 2010 . Robust State Estimation for Stochastic Genetic Regulatory Networks . International Journal of Systems Science , 41 : 47 – 63 .
   Web of Science ®Google Scholar
• Lin , DC . 2012 . Adaptive Weighting Input Estimation for Nonlinear Systems . International Journal of Systems Science , 43 : 31 – 40 .
   Web of Science ®Google Scholar
• Mahmoud , M and Shi , P . 2003 . Robust Kalman Filtering for Continuous Time-lag Systems with Markovian Jump Parameters . IEEE Transactions on Circuits and Systems , 50 : 98 – 105 .
   Google Scholar
• Pugachev , VS . 1984 . Probability Theory and Mathematical Statistics for Engineers , London : Pergamon .
   Google Scholar
• Pugachev , VS and Sinitsyn , IN . 2001 . Stochastic Systems: Theory and Applications , Singapore : World Scientific .
   Google Scholar
• Rao , CR . 1973 . Linear Statistical Inference and Its Applications , New York : Wiley-Interscience .
   Google Scholar
• Shen , B , Wang , Z , Shu , H and Wei , G . 2008 . On Nonlinear H ∞ Filtering for Discrete-time Stochastic Systems with Missing Measurements . IEEE Transactions on Automatic Control , 53 : 2170 – 2180 .
   Web of Science ®Google Scholar
• Sheng , J . 2005 . Optimal Filtering for Multirate Systems Based on Lifted Models . Proceedings of American Control Conference . 2005 . pp. 3459 – 3461 . Portland, OR , , USA
   Google Scholar
• Sheng , J , Chen , T and Shah , SL . 2005 . Optimal Filtering for Multirate Systems . IEEE Transactions on Circuits and Systems , 52 : 228 – 232 .
   Google Scholar
• Shi , P . 1998 . Filtering on Sampled-data Systems with Parametric Uncertainty . IEEE Transactions on Automatic Control , 43 : 1022 – 1027 .
   Web of Science ®Google Scholar
• Shi , P , Boukas , E and Agarwal , RK . 1999 . Control of Markovian Jump Discrete-time Systems with Norm-bounded Uncertainty and Unknown Delay . IEEE Transactions on Automatic Control , 44 : 2139 – 2144 .
   Web of Science ®Google Scholar
• Shin , DR and Verriest , E . 1994 . Optimal Access Control of Simple Integrated Networks with Incomplete Observations . Proceedings of American Control Conference . 1994 . pp. 3487 – 3488 . Baltimore, MD , , USA
   Google Scholar
• Tucker , HG . 1967 . A Graduate Course in Probability , New York : Academic Press .
   Google Scholar
• Wang , Z . 2003 . Filtering on Nonlinear Time-delay Stochastic Systems . Automatica , 39 : 101 – 109 .
   Web of Science ®Google Scholar
• Wang , Z , Liu , Y and Liu , Y . 2008 . H ∞ Filtering for Uncertain Stochastic Time-delay Systems with Sector-bounded Nonlinearities . Automatica , 44 : 1268 – 1277 .
   Web of Science ®Google Scholar
• Wu , FX , Mu , L and Shi , ZK . 2010 . Estimation of Parameters in Rational Reaction Rates of Molecular Biological Systems Via Weighted Least Squares . International Journal of Systems Science , 44 : 73 – 80 .
   Web of Science ®Google Scholar
• Xia , Y , Amann , A and Liu , B . 2010 . Detection of Abrupt Changes in Electrocardiogram with GLR Algorithm . IET Signal Processing , 4 : 650 – 657 .
   Web of Science ®Google Scholar
• Xia , Y , Li , L , Mahmoud , MS and Yang , H . 2012 . H ∞ Filtering for Nonlinear Singular Markovian Jumping Systems with Interval Time-varying Delays . International Journal of Systems Science , 43 : 272 – 284 .
   Web of Science ®Google Scholar
• Xu , S and van Dooren , PV . 2002 . Robust H ∞-Filtering for a Class of Nonlinear Systems with State Delay and Parameter Uncertainty . International Journal of Control , 75 : 766 – 774 .
   Web of Science ®Google Scholar
• Yang , F , Wang , W and Hung , YS . 2002 . Robust Kalman Filtering for Discrete Time-varying Uncertain Systems with Multiplicative Noises . IEEE Transactions on Automatic Control , 47 : 1179 – 1183 .
   Web of Science ®Google Scholar
• Zhang , WH , Chen , BS and Tseng , CS . 2005 . Robust H ∞ Filtering for Nonlinear Stochastic Systems . IEEE Transactions on Signal Processing , 53 : 589 – 598 .
   Web of Science ®Google Scholar
• Zheng , WX . 2003 . On Unbiased Parameter Estimation of Linear Systems Using Noisy Measurements . Cybernetics and Systems , 34 : 59 – 70 .
   Web of Science ®Google Scholar