On nonlinear filtering problems for discrete time stochastic processes

 Okabe Yasunori OKABE Yasunori
 Department of Mathematical Informatics Graduate School of Information Science and Technology University of Tokyo

 Matsuura Masaya MATSUURA Masaya
 Department of Mathematical Informatics Graduate School of Information Science and Technology University of Tokyo
Access this Article
Search this Article
Author(s)

 Okabe Yasunori OKABE Yasunori
 Department of Mathematical Informatics Graduate School of Information Science and Technology University of Tokyo

 Matsuura Masaya MATSUURA Masaya
 Department of Mathematical Informatics Graduate School of Information Science and Technology University of Tokyo
Abstract
In this paper, we shall develop the linear causal analysis for the system consisting of two flows in a real inner product space and give an algorithm for calculating the nonlinear filter for a discrete stochastic system which is given by two discrete time stochastic processes, to be called a signal process and an observation process, based upon the theory of KM_2OLangevin equations.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 57(4), 10671076, 20051001
The Mathematical Society of Japan
References: 18

1
 A new approach to linear filtering and prediction problems

KALMAN R. E.
Trans. ASME J. Basic Eng., D 82, 3545, 1960
Cited by (1)

2
 New results in linear filtering and prediction theory

KALMAN R. E.
Trans. ASME J. Basic Eng., D 83, 95108, 1961
Cited by (1)

3
 Nonlinear prediction

MASANI P.
Probability and Statistics The Harald Cramer, 190212, 1959
Cited by (1)

4
 <no title>

NXRGAARD M. N. A.
Advances in derivativefree state estimation for nonlinear systems, 1998
Cited by (1)

5
 On a stochastic difference equation for the multidimensional weakly stationary process with discrete time

OKABE Y.
"Algebraic Analysis" in celebration of Professor M. Sato's sixtieth birthday, Prospect of Algebraic Analysis, 1988
Cited by (1)

6
 The theory of KM_2OLangevin equations and its applications to data analysis (I) : Stationary analysis

OKABE Y.
Hokkaido Math. J. 20, 4590, 1991
Cited by (1)

7
 Langevin equations and causal analysis

OKABE Y.
Amer. Math. Soc. Transl. 161, 1950, 1994
Cited by (1)

8
 On the theory of KM_2OLangevin equations for stationary flows (3) : extension theorem

OKABE Y.
Hokkaido Math. J. 29, 369382, 2000
Cited by (1)

9
 On a nonlinear prediction problem for multidimensional stochastic processes with its applications to data analysis

OKABE Y.
Hokkaido Math. J. 29, 601657, 2000
Cited by (1)

10
 <no title>

OKABE Y.
The FluctuationDissipation Principle in Time Series Analysis and Experimental Mathematics, 2002
Cited by (1)

11
 <no title>

SODERSTROM T.
Discretetime Stochastic Systems Estimation and Control, Adv. Textb. Control Signal Process., 2002
Cited by (1)

12
 Polynomial filtering for linear discrete time nonGaussian systems

CARRAVETTA F.
SIAM J. Control Optim. 34, 16661690, 1996
Cited by (1)

13
 On a nonlinear prediction problem for onedimensional stochastic processes

MATSUURA Masaya , OKABE Yasunori
Japanese journal of mathematics. New series 27(1), 51112, 20010601
JSTAGE References (37) Cited by (4)

14
 On the theory of KM_2OLangevin equations for nonstationary and degenerate flows

MATSUURA Masaya , OKABE Yasunori
Journal of the Mathematical Society of Japan 55(2), 523563, 20030401
JSTAGE References (21) Cited by (1)

15
 On the theory of KM_2OLagnevin equations for stationary flows (1):characterization theorem

OKABE Yasunori
Journal of the Mathematical Society of Japan 51(4), 817841, 19991001
JSTAGE References (12) Cited by (5)

16
 On the theory of KM_2OLangevin equations for stationary flows (2) : construction theorem

OKABE Y.
Acta Appl. Math. 63, 307322, 2000
DOI Cited by (4)

17
 The Theory of KM_2OLangevin equations and applications to data analysis (II) : causal analysis (1)

OKABE Y. , Inoue Akihiko
Nagoya Math. J. 134(1), 128, 1994
Cited by (2)

18
 The theory of KM_2OLangevin equations and its applications to data analysis (III) : deterministic analysis

OKABE Y. , Yamane Toshiyuki
Nagoya Math. J. 152, 175201, 1998
Cited by (3)