Robust filtering of stochastic

Mikhail Moklyachuk ; Aleksandr Masyutka

Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 166-181

Résumé

The considered problem is estimation of the unknown value of the functional $A\vec{\xi}=\int^\infty_0\vec{a}(t)\vec{\xi}(-t)dt$ which depends on the unknown values of a multidimensional stationary stochastic process $\vec{\xi}(t)$ based on observations of the process $\vec{\xi}(t)+ vec{\eta}(t)$ for $t\leq0.$ Formulas are obtained for calculation the mean square error and the spectral characteristic of the optimal estimate of the functional under the condition that the spectral density matrix $F(\lambda)$ of the signal process $\vec{\xi}(t)$ and the spectral density matrix $G(\lambda)$ of the noise process $\vec{\eta}(t)$ are known. The least favorable spectral densities and the minimax-robust spectral characteristic of the optimal estimate of the functional $A\vec{\xi}$ are found for concrete classes $D = D_F\times D_G$ of spectral densities under the condition that spectral density matrices $F(\lambda)$ and $G(\lambda)$ are not known, but classes $D = D_F\times D_G$ of admissible spectral densities are given.

Détail

Keywords: Stationary stochastic process, filtering, robust estimate, observations with noise, mean square error, least favorable spectral densities, minimax-robust spectral characteristic.