使用噪音观测到的定期固定递增序列的微型压压-硬质估计问题 (Minimax-robust estimation problems for sequences with periodically stationary increments observed with noise)

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are specified.

翻译：在对固定噪音序列进行观测的基础上,定期固定递增,根据随机序列的未观测值,对线性功能进行最佳估计。对于已知光谱密度的序列,我们考虑对线性功能进行最佳估计的问题。对于已知光谱密度的序列,我们获得了计算平均平方差值和最佳功能估计的光谱特性的公式。在具体指明某些可接受光谱密度的同时,还提出了确定最有利光谱密度和最佳功能线性估计的微麦克斯-气旋光谱特性的公式。