The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the mean square error and the spectral characteristic of the optimal linear estimate of the functionals are proposed in the case where spectral densities are exactly known and in the case where the spectral densities are unknown while a class of admissible spectral densities is given. Formulas that determine the least favorable spectral densities and the minimax (robust) spectral characteristics are proposed for a given class of admissible spectral densities.

翻译：本文研究了基于带加性噪声观测的周期相关随机过程，对其未知值的线性泛函进行最优线性估计的问题。在谱密度精确已知的情况下，以及在谱密度未知但给定容许谱密度类的情况下，提出了计算最优线性估计的均方误差和谱特征的公式。针对给定的容许谱密度类，提出了确定最不利谱密度和最小最大（稳健）谱特征的公式。