标题： 最小最大估计问题对于周期相关随机过程 显示英文标题

标题： Minimax Estimation Problem for Periodically Correlated Stochastic Processes

摘要： 考虑从具有加性噪声的过程观测中对依赖于周期相关随机过程未知值的线性泛函进行最优线性估计的问题。 在谱密度已知的情况下和在谱密度未知而给定允许谱密度类的情况下，提出了计算泛函最优线性估计的均方误差和谱特性的公式。 对于给定的允许谱密度类，提出了确定最不利谱密度和最小最大（鲁棒）谱特性的公式。 显示英文摘要

摘要： 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.