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Original Articles

A local linearization approach to nonlinear filtering

Pages 75-96 | Received 23 Feb 1991, Published online: 03 Apr 2007

REFERENCES

  • FROST , P. A. , and KAILATH , T. , 1971 , An innovation approach to least squares estimation. Part III Nonlinear estimation in white Gaussian noise . IEEE Transaction on Automatic Control , 16 , 217 – 226 .
  • HAZEWINKEL , M. , and WILLEMS , J. , 1981 , Stochastic systems the mathematics of filtering and identification and applications . Proceeding of the NATO Advanced Study Institute , Les Arcs , Savoie , France , 1980 (Dordrecht, The Netherlands D. Reidel) .
  • JAZWINSKI , A. H. , 1970 , Stochastic Processes and Filtering Theory ( New York Academic Press ).
  • KUSHNER , H. J. , 1962 , On the differential equations satisfied by conditional probability densities of Markov processes, with applications . SIAM Journal on Control, Series A , 2 , 106 – 119 ; 1967, Approximations to optimal nonlinear filters. IEEE Transaction on Automatic Control, v1, 546–556 .
  • LARSON , H. J. , and SHUBERT , B. O. , 1979 , Probabilistic Models in Engineering Sciences ,Vol II ( Wiley ).
  • LIANG , D. F. , 1983 , Comparisons of nonlinear recursive filters for systems with nonnegligible nonlinearities . Control and Dynamical Systems, Advances in Theory and Applications ,Vol 20 Nonlinear and Kalman Filtering Techniques, edited by C. T. Leondes , ( New York Academic Press ), pp. 341 – 401 .
  • MARKUS , S. I. , 1984 , Algebraic and geometric methods in nonlinear filtering . SIAM Journal on Control and Optimization , 22 , 817 – 844 .
  • MEDITCH , J. S. , 1967 , Orthogonal projection and discrete optimal linear smoothing . SIAM Journal on Control , 5 , 74 – 89 .
  • OZAKI , T. , 1985 , Nonlinear time series models and dynamical systems . Handbook of Statistics , Vol. 5 , Time Series in Time Domain, edited by E. J. Hannan, et al ., ( Amsterdam North-Holland ), pp. 25 – 83 ; 1986, Local Gaussian modelling of stochastic dynamical systems in the analysis of nonlinear random vibrations. Essays on Time Series and Allied Processes. Festschrift in honour of Professor E. J. Hannan (Applied Probability Trust), pp. 241-;255; 1989, Statistical identification of nonlinear random vibration systems. Journal of Applied Mechanics, 56, 186-191|pp; 1990 a, A bridge between nonlinear time series models and nonlinear stochastic dynamical systems a local Linearization approach. Submitted for publication; 1990b, Application of the local linearization filter method to the identification of stochastic dynamical systems. Research Memo No. 379, Institute of Statistical Mathematics, Tokyo; 1990 c, Identification of nonlinearities and non-Gaussianities in time series. Proceedings of 1990 Summer International Interdisciplinary Workshop on Time Series Analysis at the IMA, (Berlin Springer-Verlag), to be published .
  • OZAKI , T. , and OZAKI , V. H. , 1989 , Statistical identification of nonlinear dynamics in macroeconomics using nonlinear time series models . Statistical Analysis and Forecasting of Economic Structural Change , edited by P. Hackl ( Berlin Springer-Verlag ), pp. 345 – 365 .
  • SCHWARTZ , L. , and STEAR , E. B. , 1968 , A computational comparison of several nonlinear filters . IEEE Transactions on Automatic Control , 13 , 83 – 86 .
  • SMITH , J. M. , 1977 , Mathematical Modeling and Digital Simulation for Engineers and Scientists . ( Wiley ).
  • SORENSON , H. W. , 1966 , Kalman filtering technique. Advances in Control Systems , Theory and Applications , Vol. 3 , ( New York Academic Press ), pp. 219 – 292 .

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