A linear filtering problem using radon transform

Stochastics ◽  
1988 ◽  
Vol 25 (4) ◽  
pp. 183-193 ◽  
Author(s):  
SHIGEO Takenaka*
Keyword(s):  
Radon Transform ◽  
Linear Filtering ◽  
Filtering Problem

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Finite-dimensional models for hidden Markov chains

1995 ◽  
Vol 27 (01) ◽  
pp. 146-160
Author(s):  
Lakhdar Aggoun ◽  
Robert J. Elliott
Keyword(s):  
Markov Chains ◽  
Expectation Maximization ◽  
Continuous Time ◽  
Hidden Markov ◽  
Expectation Maximization Algorithm ◽  
Linear Filtering ◽  
Occupation Times ◽  
Finite Dimensional ◽  
Self Tuning ◽  
Filtering Problem

A continuous-time, non-linear filtering problem is considered in which both signal and observation processes are Markov chains. New finite-dimensional filters and smoothers are obtained for the state of the signal, for the number of jumps from one state to another, for the occupation time in any state of the signal, and for joint occupation times of the two processes. These estimates are then used in the expectation maximization algorithm to improve the parameters in the model. Consequently, our filters and model are adaptive, or self-tuning.

scholarly journals A linear filtering problem in complete correlated actions

1979 ◽  
Vol 9 (4) ◽  
pp. 599-613 ◽  
Author(s):  
Ion Suciu ◽  
Ilie Valuşescu
Keyword(s):  
Linear Filtering ◽  
Filtering Problem

scholarly journals Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals

2001 ◽  
Vol 14 (3) ◽  
pp. 215-226 ◽  
Author(s):  
M. L. Kleptsyna ◽  
A. Le Breton
Keyword(s):  
Gaussian Processes ◽  
Laplace Transforms ◽  
Quadratic Functional ◽  
Linear Filtering ◽  
Volterra Type ◽  
Conditional Mean ◽  
Optimal Linear ◽  
Filtering Problem ◽  
Optimal Linear Filtering ◽  
Optimal Filtering Problem

The optimal filtering problem for multidimensional continuous possibly non-Markovian, Gaussian processes, observed through a linear channel driven by a Brownian motion, is revisited. Explicit Volterra type filtering equations involving the covariance function of the filtered process are derived both for the conditional mean and for the covariance of the filtering error. The solution of the filtering problem is applied to obtain a Cameron-Martin type formula for Laplace transforms of a quadratic functional of the process. Particular cases for which the results can be further elaborated are investigated.

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