Abstract:
An algorithm for solving the optimal nonlinear filtering problem by statistical modeling is proposed. It is based on reducing the filtration problem to the analysis of stochastic systems with terminating and branching paths, using a structure similarity of the Duncan–Mortensen–Zakai equations and the generalized Fokker–Planck–Kolmogorov equation. The solution of such problem of analysis can be approximately found by using numerical methods for solving stochastic differential equations and methods for modeling inhomogeneous Poisson flows.
Key words:
branching processes, conditional density, the Duncan–Mortensen–Zakai equation, Monte Carlo method, optimal filtering problem, stochastic system.
Citation:
K. A. Rybakov, “An approximate solution of the optimal nonlinear filtering problem for stochastic differential systems by statistical modeling”, Sib. Zh. Vychisl. Mat., 16:4 (2013), 377–391; Num. Anal. Appl., 6:4 (2013), 324–336
\Bibitem{Ryb13}
\by K.~A.~Rybakov
\paper An approximate solution of the optimal nonlinear filtering problem for stochastic differential systems by statistical modeling
\jour Sib. Zh. Vychisl. Mat.
\yr 2013
\vol 16
\issue 4
\pages 377--391
\mathnet{http://mi.mathnet.ru/sjvm525}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3380136}
\elib{https://elibrary.ru/item.asp?id=21896873}
\transl
\jour Num. Anal. Appl.
\yr 2013
\vol 6
\issue 4
\pages 324--336
\crossref{https://doi.org/10.1134/S1995423913040071}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888996714}
Linking options:
https://www.mathnet.ru/eng/sjvm525
https://www.mathnet.ru/eng/sjvm/v16/i4/p377
This publication is cited in the following 12 articles:
T. A. Averina, K. A. Rybakov, “Metody tipa Rozenbroka dlya resheniya stokhasticheskikh differentsialnykh uravnenii”, Sib. zhurn. vychisl. matem., 27:2 (2024), 123–145
T. A. Averina, K. A. Rybakov, “Rosenbrock-Type Methods for Solving Stochastic Differential Equations”, Numer. Analys. Appl., 17:2 (2024), 99
Konstantin A. Rybakov, Smart Innovation, Systems and Technologies, 217, Applied Mathematics and Computational Mechanics for Smart Applications, 2021, 287
T Averina, K Rybakov, “Statistical filtering algorithms based on the maximum cross section method for stochastic systems with regime switching”, J. Phys.: Conf. Ser., 1715:1 (2021), 012060
K Rybakov, “Modified spectral method for optimal estimation in linear continuous-time stochastic systems”, J. Phys.: Conf. Ser., 1864:1 (2021), 012025
Konstantin N. Chugai, Ivan M. Kosachev, Konstantin A. Rybakov, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 351
K. Rybakov, 2020 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), 2020, 1
F Mesa, D M Devia, R Ospina, “Estimation of the parameters of the particular solution of a partial differential equation through Cramer Rao”, J. Phys.: Conf. Ser., 1671:1 (2020), 012014
K Rybakov, “Application of Walsh series to represent iterated Stratonovich stochastic integrals”, IOP Conf. Ser.: Mater. Sci. Eng., 927:1 (2020), 012080
T. A. Averina, K. A. Rybakov, “An approximate solution of the prediction problem for stochastic jump-diffusion systems”, Num. Anal. Appl., 10:1 (2017), 1–10
K. Rybakov, “Robust Duncan–Mortensen–Zakai equation for non-stationary stochastic systems”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 151–154
E. A. Rudenko, “Optimal structure of continuous nonlinear reduced-order Pugachev filter”, J. Comput. Syst. Sci. Int., 52:6 (2013), 866–892
Citation in format AMSBIB
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