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Original Articles

Global convergence conditions in maximum likelihood estimation

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Pages 475-490 | Received 20 Oct 2011, Accepted 12 Jan 2012, Published online: 07 Feb 2012

References

  • Åström , KJ . (1968), ‘Lectures on the Identification Problem-the Least Squares Method’, Technical Report 6806, Lund Institute of Technology, Division of Automatic Control
  • Åström , KJ . 1980 . Maximum Likelihood and Prediction Error Methods . Automatica , 16 : 551 – 574 .
  • Åström , KJ . and Bohlin, T. (1965), ‘Numerical Identification of Linear Dynamic Systems from Normal Operating Records’, in Proceeding of 2nd IFAC Symposium on Self-adaptive Systems, Teddington, UK, 14–17 September 1965
  • Åström , KJ and Söderström , T . 1974 . Uniqueness of Maximum Likelihood Estimates of the Parameters of an ARMA Model . IEEE Transactions on Automatic Control , 19 : 769 – 773 .
  • Box , GEP and Jenkins , GM . 1970 . Time Series Analysis, Forecasting and Control , San Francisco : Holden-Day .
  • Chen , J , Zhang , Y and Ding , R . 2010 . Auxiliary Model-Based Multi-innovation Algorithms for Multivariable Nonlinear Systems . Mathematical and Computer Modelling , 52 : 1428 – 1434 .
  • Clarke , DW . (1967), ‘Generalized Least Squares Estimation of Parameters of a Dynamic Model’, in Proceeding of IFAC Symposium on Identification in Automatic Control Systems, Prague, Czechoslovakia
  • Cramér , H . 1946 . Mathematical Methods of Statistics , Princeton : Princeton University Press . 1946
  • Ding , F . 2010 . Several Multi-innovation Identification Methods . Digital Signal Processing , 20 : 1027 – 1039 .
  • Ding , F and Chen , T . 2007 . Performance Analysis of Multi-innovation Gradient Type Identification Methods . Automatica , 43 : 1 – 14 .
  • Ding , F , Liu , G and Liu , PX . 2010a . Partially Coupled Stochastic Gradient Identification Methods for Non-uniformly Sampled Systems . IEEE Transactions on Automatic Control , 55 : 1976 – 1981 .
  • Ding , F , Liu , PX and Liu , G . 2009 . Auxiliary Model-Based Multi-innovation Extended Stochastic Gradient Parameter Estimation with Colored Measurement Noises . Signal Processing , 89 : 1883 – 1890 .
  • Ding , F , Liu , PX and Liu , G . 2010b . Gradient-based and Least-squares-based Iterative Identification Methods for OE and OEMA Systems . Digital Signal Processing , 20 : 664 – 677 .
  • Ding , F , Liu , PX and Liu , G . 2010c . Multiinnovation Least-squares Identification for System Modeling . IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics , 40 : 767 – 778 .
  • Dugard , L and Landau , ID . 1980 . Recursive Output Error Identification Algorithms . Automatica , 16 : 443 – 462 .
  • Fisher , RA . 1912 . On an Absolute Criterion for Fitting Frequency Curves . Messenger of Mathematics , 41 : 155 – 160 .
  • Fisher , RA . 1921 . On the Mathematical Foundations of Theoretical Statistics . Philosophical Transactions of the Royal Society of London. Series A , 222 : 309 – 368 .
  • Forssell , U and Ljung , L . 1999 . Closed-loop Identification Revisited . Automatica , 35 : 1215 – 1241 .
  • Goodwin , GC . Carlos, J.A., and Skelton, R.E. (2001), ‘Conditions for Local Convergence of Maximum Likelihood Estimation for ARMAX Models’, in Proceeding of 13th IFAC Symposium on System Identification, Rotterdam, The Netherland
  • Ljung , L . 1999 . System Idenfication: Theory for the User, , 2nd , New Jersey : Prentice Hall .
  • Ljung , L and Söderström , T . 1983 . Theory and Practice of Recursive Identification , Cambridge : The MIT Press .
  • Ogata , K . 1996 . Modern Control Engineering, , 3rd , New Jersey : Prentice Hall .
  • Pintelon , R and Schoukens , J . 2001 . System Identification: A Frequency Domain Approach , New York : IEEE Press .
  • Söderström , T . 1974 . Convergence Properties of the Generalised Least Squares Identification Method . Automatica , 10 : 617 – 626 .
  • Söderström , T . 1975 . On the Uniqueness of Maximum Likelihood Identification . Automatica , 11 : 193 – 197 .
  • Söderström , T and Stoica , P . 1982 . Some Properties of the Output Error Method . Automatica , 18 : 93 – 99 .
  • Söderström , T and Stoica , P . 1989 . System Identification , London : Prentice Hall .
  • Stoica , P , Hoist , J and Söderström , T . 1982 . Eigenvalue Location of Certain Matrices Arising in Convergence Analysis Problems . Automatica , 18 : 487 – 491 .
  • van Overschee , P and DeMoor , B . 1996 . Subspace Identification for Linear Systems: Theory, Implementation, Applications , Dordrecht : Kluwer Academic Publishers .
  • Wald , A . 1949 . Note on the Consistency of the Maximum Likelihood Estimate . The Annals of Mathematical Statistics , 20 : 595 – 601 .
  • Wang , D , Chu , Y and Ding , F . 2010a . Auxiliary Model-based RELS and MI-ELS Algorithm for Hammerstein OEMA Systems . Computers and Mathematics with Applications , 59 : 3092 – 3098 .
  • Wang , D , Chu , Y , Yang , G and Ding , F . 2010b . Auxiliary Model Based Recursive Generalized Least Squares Parameter Estimation for Hammerstein OEAR Systems . Mathematical and Computer Modelling , 52 : 309 – 317 .
  • Wang , D and Ding , F . 2008 . Extended Stochastic Gradient Identification Algorithms for Hammerstein-wIener ARMAX Systems . Computers and Mathematics with Applications , 56 : 3157 – 3164 .
  • Wang , D and Ding , F . 2010a . Input–Output Data Filtering Based Recursive Least Squares Identification for CARARMA Systems . Digital Signal Processing , 20 : 991 – 999 .
  • Wang , D and Ding , F . 2010b . Performance Analysis of the Auxiliary Models Based Multi-innovation Stochastic Gradient Estimation Algorithm for Output Error Systems . Digital Signal Processing , 20 : 750 – 762 .
  • Young , PC . (1968), ‘The Use of Linear Regression and Related Procedures for the Identification of Dynamic Processes’, in Proceedings of 7th IEEE Symposium on Adaptive Processes, San Antonio, TX
  • Zhang , J , Ding , F and Shi , Y . 2009 . Self-tuning Control Based on Multi-innovation Stochastic Gradient Parameter Estimation . Systems and Control Letters , 58 : 69 – 75 .
  • Zou , Y . (2009), ‘Attainment of Global Convergence in Maximum Likelihood Estimation’, Ph.D. Thesis, University of Manchester, School of Electronic and Electrical Engineering

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