Minimax Filtering of Sequences with Periodically Stationary Increments

The authors consider the problem of optimal filtering of functionals that depend on unknown values of the stochastic sequence with periodically stationary increments based on observations of the sequence with a stationary noise. For sequences with known spectral densities, formulas are obtained for the root-mean-square errors and 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 functionals are proposed in the case where spectral densities of the sequence are not known exactly while some sets of feasible spectral densities are given.