Consideration was given to the problem of robust stochastic filtering in a finite
horizon for the linear discrete time-varying system. A random disturbance with inaccurately
known probabilistic distribution is fed to the system input. Uncertainty of the input disturbance
is defined in the information-theoretical terms by the anisotropy functional of a random vector.
The sufficient condition for strict boundedness of the anisotropic norm of linear discrete timevarying
system assigned by the threshold value (lemma of real boundedness) was proved in
terms of the matrix inequalities. Sufficient conditions for boundedness of the anisotropic norm
of two limiting cases of the anisotropy levels of the input disturbance (a = 0 and a → ∞)
were established. A sufficient existence condition for the estimator guaranteeing boundedness
of the anisotropic norm of the estimation error operator by the given threshold value was
formulated and proved. Sufficient existence conditions for the estimators of two limiting cases
of the anisotropy levels of input disturbance were obtained. The estimation algorithm relies on
the recurrent solution of a system of matrix inequalities.