An explicit solution of the linear filtering problem for certain classes of nonrational spectral densities

1991 ◽  
Vol 53 (1) ◽  
pp. 87-94
Author(s):  
E. P. Fadeeva
Keyword(s):  
Explicit Solution ◽  
Linear Filtering ◽  
Spectral Densities ◽  
Filtering Problem

scholarly journals Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments

2021 ◽  
Vol 9 (4) ◽  
pp. 1010-1030
Author(s):  
Maksym Luz ◽  
Mikhail Moklyachuk
Keyword(s):  
Spectral Characteristics ◽  
Linear Filtering ◽  
Linear Functionals ◽  
Spectral Densities ◽  
Optimal Linear ◽  
The Mean ◽  
Noise Sequence ◽  
Mean Square Errors ◽  
Filtering Problem ◽  
Optimal Linear Filtering

We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence of this type based on observations of the sequence with a periodically stationary noise sequence. For sequences with known matrices of spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal filtering of the functionals. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal linear filtering of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

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.

Sign in / Sign up

Export Citation Format

Share Document