The problem of the mean-square optimal linear estimation of the functional $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values of stochastic stationary process $\xi(t)$ from observations of the process $\xi(t)+\eta(t)$ at points $t\in\mathbb{R} ^{-} \backslash S $, $S=\bigcup\limits_{l=1}^{s}[-M_{l}-N_{l}, \, \ldots, \, -M_{l} ],$ $R^s=[0,\infty) \backslash S^{+},$ $S^{+}=\bigcup\limits_{l=1}^{s}[ M_{l}, \, \ldots, \, M_{l}+N_{l}]$ is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functional are proposed under the condition of spectral certainty, where spectral densities of the processes $\xi(t)$ and $\eta(t)$ are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly, but sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed for some special sets of admissible spectral densities.

翻译：本文研究了基于过程 $\xi(t)+\eta(t)$ 在点 $t\in\mathbb{R} ^{-} \backslash S $, $S=\bigcup\limits_{l=1}^{s}[-M_{l}-N_{l}, \, \ldots, \, -M_{l} ]$, $R^s=[0,\infty) \backslash S^{+}$, $S^{+}=\bigcup\limits_{l=1}^{s}[ M_{l}, \, \ldots, \, M_{l}+N_{l}]$ 上的观测，对依赖于随机平稳过程 $\xi(t)$ 未知值的泛函 $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt$ 进行均方最优线性估计的问题。在谱确定性条件下，即过程 $\xi(t)$ 和 $\eta(t)$ 的谱密度精确已知时，提出了用于计算最优线性估计的均方误差及谱特征的公式。在谱密度并非精确已知，但给定了容许谱密度集合的情况下，采用了极小化极大（稳健）估计方法。针对某些特殊的容许谱密度集合，提出了确定最不利谱密度和极小化极大谱特征的公式。