On Stochastic Lyapunov Functon Method in Optimal Linear Filtering Problem

1992 ◽  
Vol 25 (20) ◽  
pp. 231-235
Author(s):  
H.S. Hoang ◽  
O. Talagrand
Keyword(s):  
Linear Filtering ◽  
Optimal Linear ◽  
Filtering Problem ◽  
Optimal Linear Filtering

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.

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.

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