This paper focuses on the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence. Estimates are based on observations of the sequence with an additive stationary noise sequence. The aim of the paper is to develop methods of finding the optimal estimates of the functionals in the case of missing observations. The problem is investigated in the case of spectral certainty where the spectral densities of the sequences are exactly known. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived under the condition of spectral certainty. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities of the sequences are not known exactly while sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special sets of admissible densities.

翻译：本文聚焦于对依赖于多维平稳随机序列未知值的线性泛函进行均方最优估计的问题。估计基于对带有加性平稳噪声序列的观测值进行。本文旨在开发在观测值缺失情况下寻找泛函最优估计的方法。该问题在谱确定性条件下进行研究，即序列的谱密度精确已知。在谱确定性条件下，推导了计算最优线性泛函估计的均方误差及谱特征的公式。在谱不确定性情况下，即序列的谱密度未精确已知但给定了容许谱密度集合时，应用了极小极大（稳健）估计方法。针对某些特殊容许密度集合，提出了确定最优泛函估计的最不利谱密度及极小极大谱特征的公式。