Nonlinear state prediction by separation approach for continuous-discrete stochastic systems
Jaroslav Švácha; Miroslav Šimandl
Kybernetika (2008)
- Volume: 44, Issue: 1, page 61-74
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topReferences
top- Daum F. E., New exact nonlinear filters, In: Bayesian Analysis of Time Series and Dynamic Models (J. C. Spall, ed.), Marcel Dekker, New York 1988, pp. 199–226 (1988)
- Higham D. J., Kloeden P. E., Maple and Matlab for Stochastic Differential Equations in Finance, Technical Report. University of Strathclyde 2001
- Chang J. S., Cooper G., A practical difference scheme for Fokker–Planck equations, J. Comput. Phys. 6 (1970), 1–16 (1970) Zbl0221.65153
- Moral P. del, Jacod J., Interacting particle filtering with discrete observations, In: Sequential Monte Carlo Methods in Practice (A. Doucet, N. de Freitas, and N. Gordon, eds.), Springer-Verlag, New York 2001, pp. 43–75 MR1847786
- Jazwinski A. H., Stochastic Processes and Filtering Theory, Academic Press, New York 1970 Zbl0203.50101
- Kalman R. E., Bucy R. S., New results in linear filtering and prediction theory, J. Basic Engrg. 83 (1961), 95–108 (1961) MR0234760
- Kouritzin M. A., On exact filters for continuous signals with discrete observations, IEEE Trans. Automat. Control 43 (1998), 709–715 (1998) Zbl0908.93064MR1618075
- Kushner H. J., Budhijara A. S., A nonlinear filtering algorithm based on an approximation of the conditional distribution, IEEE Trans. Automat. Control 45 (2000), 580–585 MR1762882
- LeVeque R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, New York 2002 Zbl1010.65040MR1925043
- Lototsky S. V., Rozovskii B. L., Recursive nonlinear filter for a continuous-discrete time model: Separation of parameters and observations, IEEE Trans. Automat. Control 43 (1998), 1154–1158 (1998) Zbl0957.93085MR1636479
- Mirkovic D., -dimensional Finite Element Package, Technical Report. Department of Mathematics, Iowa State University 1996
- Park B. T., Petrosian V., Fokker–Planck equations of stochastic acceleration: A study of numerical methods, Astrophys. J., Suppl. Ser. 103 (1996), 255–267 (1996)
- Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W. T., Numerical Recipes, Cambridge University Press, New York 1986 Zbl1132.65001MR0833288
- Risken H., The Fokker–Planck Equation, Springer–Verlag, Berlin 1984 Zbl0866.60071MR0749386
- Schmidt G. C., Designing nonlinear filters based on Daum’s theory, J. Guidance, Control and Dynamics 16 (1993), 371–376 (1993) Zbl0775.93283
- Sorenson H. W., Alspach D. L., Recursive Bayesian estimation using Gaussian sums, Automatica 7 (1971), 465–479 (1971) Zbl0219.93020MR0321581
- Spencer B. F., Bergman L. A., On the numerical solution of the Fokker–Planck equation for nonlinear stochastic systems, Nonlinear Dynamics 4 (1993), 357–372 (1993)
- Spencer B. F., Wojtkiewicz S. F., Bergman L. A., Some experiments with massively parallel computation for Monte Carlo simulation of stochastic dynamical systems, In: Proc. Second Internat. Conference on Computational Stochastic Mechanics, Athens 1994
- Šimandl M., Švácha J., Nonlinear filters for continuous-time processes, In: Proc. 5th Internat. Conference on Process Control, Kouty nad Desnou 2002
- Šimandl M., Královec J., Filtering, prediction and smoothing with Gaussian sum Rrpresentation, In: Proc. Symposium on System Identification. Santa Barbara 2000
- Šimandl M., Královec, J., Söderström T., Anticipative grid design in point-mass approach to nonlinear state estimation, IEEE Trans. Automat. Control 47 (2002), 699–702 MR1893533
- Šimandl M., Královec, J., Söderström T., Advanced point–mass method for nonlinear state estimation, Automatica 42 (2006), 1133–1145 Zbl1118.93052
- Šimandl M., Švácha J., Separation approach for numerical solution of the Fokker–Planck equation in estimation problem, In: Preprints of 16th IFAC World Congress. Prague 2005
- Zhang D. S., Wei G. W., Kouri D. J., Hoffman D. K., Numerical method for the nonlinear Fokker–Planck equation, Amer. Physical Society 56 (1997), 1197–1206 (1997)
- Zorzano M. P., Mais, H., Vazquez L., Numerical solution for Fokker–Planck equations in accelerators, Phys. D: Nonlinear Phenomena 113 (1998), 379–381 (1998) Zbl0962.82055