Approximate finite-dimensional filtering for polynomial states over polynomial observations

References

• Alcorta , MA , Basin , M , Maldonado , JJ and Anguiano , SG . 2008 . Sub-optimal Risk-sensitive Filtering for Third Degree Polynomial Stochastic Systems . ICIC Express Letters , 2 : 371 – 377 .
   Google Scholar
• Basin , MV . 2008 . New Trends in Optimal Filtering and Control for Polynomial and Time-delay Systems , Berlin : Springer .
   Google Scholar
• Basin , MV and Calderon-Alvarez , D . 2008 . Alternative Optimal Filter for Linear Systems with Multiple State and Observation Delays . International Journal of Innovative Computing, Information and Control , 4 : 2889 – 2898 .
   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 , M , Perez , J and Calderon-Alvarez , D . 2008 . Optimal Filtering for Linear Systems Over Polynomial Observations . International Journal of Innovative Computing, Information and Control , 4 : 313 – 320 .
   Web of Science ®Google Scholar
• Basin , MV , Shi , P and Calderon-Alvarez , D . 2009 . Optimal Filtering for Incompletely Measured Polynomial Systems with Multiplicative Noises . Circuits, Systems and Signal Processing , 28 : 223 – 239 .
   Web of Science ®Google Scholar
• Benes , VE . 1981 . Exact Finite-dimensional Filters for Certain Diffusions with Nonlinear Drift . Stochastics , 5 : 65 – 92 .
   Google Scholar
• Fleming , WH and McEneaney , WM . 2001 . Robust Limits of Risk Sensitive Nonlinear Filters . Mathematics of Control, Signals and Systems , 14 : 109 – 142 .
   Web of Science ®Google Scholar
• Fridman , E and Shaked , U . 1997 . On Regional Nonlinear H ∞ Filtering . Systems and Control Letters , 29 : 233 – 240 .
   Web of Science ®Google Scholar
• Gao , H and Chen , T . 2007 . H ∞ Estimation for Uncertain Systems with Limited Communication Capacity . IEEE Transactions on Automatic Control , 52 : 2070 – 2084 .
   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
• Gao , H and Wang , C . 2004 . A Delay-dependent Approach to Robust H ∞ Filtering for Uncertain Discrete-time State-delayed Systems . IEEE Transactions on Signal Processing , 52 : 1631 – 1640 .
   Web of Science ®Google Scholar
• Hazewinkel , M , Marcus , SI and Sussmann , HJ . 1983 . Nonexistence of Exact Finite-dimensional Filters for Conditional Statistics of the Cubic Sensor Problem . Systems and Control Letters , 5 : 331 – 340 .
   Web of Science ®Google Scholar
• Jazwinski , AH . 1970 . Stochastic Processes and Filtering Theory , New York : Academic Press .
   Google Scholar
• Kalman , RE and Bucy , RS . 1961 . New Results in Linear Filtering and Prediction Theory . ASME Transactions, Part D: Journal of Basic Engineering , 83 : 95 – 108 .
   Google Scholar
• Kushner , HJ . 1964 . On Differential Equations Satisfied by Conditional Probability Densities of Markov Processes . SIAM Journal of Control , 12 : 106 – 119 .
   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
• Nguang , SK and Fu , MY . 1996 . Robust Nonlinear H ∞ Filtering . Automatica , 32 : 1195 – 1199 .
   Web of Science ®Google Scholar
• Oksendal , B . 2006 . Stochastic Differential Equations , Berlin : Springer .
   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
• Shi , P . 1998 . Filtering on Sampled-data Systems with Parametric Uncertainty . IEEE Transactions on Automatic Control , 43 : 1022 – 1027 .
   Web of Science ®Google Scholar
• Shen , B , Wang , Z , Shu , H and Wei , G . 2009 . H ∞ Infinity Filtering for Nonlinear Discrete-time Stochastic Systems with Randomly Varying Sensor Delays . Automatica , 45 : 1032 – 1037 .
   Web of Science ®Google Scholar
• Tucker , HG . 1967 . A Graduate Course in Probability , New York : Academic Press .
   Google Scholar
• Wang , Z , Ho , DWC , Liu , Y and Liu , X . 2009 . Robust H ∞ Infinity Control for a Class of Nonlinear Discrete Time-delay Stochastic Systems with Missing Measurements . Automatica , 45 : 684 – 691 .
   Web of Science ®Google Scholar
• Wang , Z , Lam , J and Liu , X . 2003 . Nonlinear Filtering for State Delayed Systems with Markovian Switching . IEEE Transactions on Signal Processing , 51 : 2321 – 2328 .
   Web of Science ®Google Scholar
• Wang , Z , Liu , Y and Liu , X . 2008 . H ∞ Infinity Filtering for Uncertain Stochastic Time-delay Systems with Sector-bounded Nonlinearities . Automatica , 44 : 1268 – 1277 .
   Web of Science ®Google Scholar
• Wei , G , Wang , Z and Shu , H . 2009 . Robust Filtering with Stochastic Nonlinearities and Multiple Missing Measurements . Automatica , 45 : 836 – 841 .
   Web of Science ®Google Scholar
• Wonham , WM . 1965 . Some Applications of Stochastic Differential Equations to Nonlinear Filtering . SIAM Journal of Control , 2 : 347 – 369 .
   Google Scholar
• Xie , LH , De Souza , CE and Wang , YY . 1996 . Robust Filtering for a Class of Discrete-time Uncertain Nonlinear Systems . International Journal of Robust and Nonlinear Control , 6 : 297 – 312 .
   Web of Science ®Google Scholar
• Xu , SY and Chen , TW . 2003 . Robust H ∞ Filtering for Uncertain Impulsive Stochastic Systems Under Sampled Measurements . Automatica , 39 : 509 – 516 .
   Web of Science ®Google Scholar
• Xu , SY , Lam , J , Gao , HJ and Zhou , Y . 2005 . Robust H ∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays . Circuits, Systems and Signal Processing , 24 : 753 – 770 .
   Web of Science ®Google Scholar
• Xu , SY 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
• Yau , SS-T . 1994 . Finite-dimensional Filters with Nonlinear Drift I: A Class of Filters Including Both Kalman–bucy and Benes Filters . Journal of Mathematical Systems, Estimation, and Control , 4 : 181 – 203 .
   Google Scholar
• Yaz , E and Yaz , Y . 2001 . State Estimation of Uncertain Nonlinear Systems with General Criteria . Applied Mathematics Letters , 14 : 605 – 610 .
   Web of Science ®Google Scholar
• Zhang , H , Basin , MV and Skliar , M . 2007 . Ito-Volterra Optimal State Estimation with Continuous, Multirate, Randomly Sampled, and Delayed Measurements . IEEE Transactions on Automatic Control , 52 : 401 – 416 .
   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