We study stochastic sequences $\xi(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence $\xi(k)$ based on observations with the periodically stationary noise sequence. For sequences with known matrices of 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 minimax (robust) spectral characteristics of the optimal linear estimates of the functionals are proposed in the case where spectral densities of sequences are not exactly known while some sets of admissible spectral densities are given.

翻译：我们研究的是固定的分序增量,这些分序结合了循环静止、多季节、综合和分集集的形态。我们根据对定期固定噪音序列的观测结果,解决了从未观测到的分序值中构建的线性功能过滤问题。对于光谱密度的已知矩阵序列,我们获得了计算平均平方差值和功能最佳估计光谱特性的公式。在给出某些可接受光谱密度的同时,对光谱频谱密度不完全已知的情况下,提出了确定功能最佳线性估计的最优光谱密度和微量光谱特征的公式。