THE SPECTRAL METHOD OF OPTIMAL FILTERING AND EXTRAPOLATION FOR JUMP-DIFFUSION MODELS
Abstract
The article deals with the optimal filtering and extrapolation problems for non-stationary stochastic differential systems with a Poisson component. To find an approximate density of the observed object’s state vector the spectral method based on the representation of robust Duncan-Mortensen-Zakai equation and Kolmogorov-Feller equation solutions in the form of orthogonal series is used.
References
1. Rybakov K.A. Solving robust Duncan-Mortensen-Zakai equation by spectral method. Information Processing Systems. 2013. No. 7 (114). Pp. 139–143. (in Russian).
2. Rybakov K.A. Solving robust Duncan-Mortensen-Zakai equation for nonstationary systems. Information and Communication Technologies. 2014. No. 22. Pp. 9–15. (in Russian).
3. Rybakov K.A. Solving robust Duncan-Mortensen-Zakai equation for jump-diffusion models by spectral method. Information Processing Systems. 2014. No. 7 (123). Pp. 143–147. (in Russian).
4. Rybakov K.A. The solution of the Duncan-Mortensen-Zakai equation for nonstationary jump-diffusion systems by spectral method. Proceedings of International Conference “Advanced Mathematics, Computations and Applications 2015”. Novosibirsk. 2015. Pp. 643–649. (in Russian).
5. Panteleev A.V., Rybakov K.A., Sotskova I.L. Spectral Method of Nonlinear Stochastic Control System Analysis. Moscow. 2015. (in Russian).
6. Solodovnikov V.V., Semenov V.V. Spectral Theory of Nonstationary Control Systems. Moscow. 1974. (in Russian).
7. Pugachev V.S., Sinitsyn I.N. Stochastic Systems: Theory and Applications, World Scientific. 2001.
8. Sinitsyn I.N. Kalman and Pugachev Filters. Moscow. 2007. (in Russian).
9. Lototsky S., Mikulevicius R., Rozovskii B.L. Nonlinear filtering revisited: A spectral approach. SIAM Journal on Control and Optimization. 1997. Vol. 35. No. 2. Pp. 435–461.
10. Luo X., Yau S.S.-T. Hermite spectral method to 1-D forward Kolmogorov equation and its application to nonlinear filtering problems. IEEE Transactions on Automatic Control. 2013. Vol. 58. No. 10. Pp. 2495–2507.
11. Rybakov K.A. Probability analysis of stochastic systems with Poisson component. Scientific Herald MSTUCA. 2013. No. 194. Pp. 55–62. (in Russian).
12. Rybakov K.A. Filtering for jump-diffusion models by statistical modeling method. Scientific Herald MSTUCA. 2015. No. 220. Pp. 73–81. (in Russian).
Review
For citations:
Rybakov K.A. THE SPECTRAL METHOD OF OPTIMAL FILTERING AND EXTRAPOLATION FOR JUMP-DIFFUSION MODELS. Civil Aviation High Technologies. 2016;(224):14-23. (In Russ.)
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