The problem of multicriteria anisotropy-based robust filtering on finite horizon for a discrete linear time-varying system with observed and estimated outputs is solved. A multidimensional input disturbance with an inexactly known probability distribution consists of groups of input signals with different statistical characteristics. These statistical characteristics are different levels of anisotropy (chrominance) of a random signal. For this mathematical model, a sufficient condition for the anisotropic norm of a linear discrete time-varying system to be bounded by a predetermined threshold value is presented. A sufficient condition for the existence of a multicriteria estimator is obtained assuming that the anisotropic norms of the subsystems are bounded by predetermined thresholds. The estimation algorithm is based on the recursive solution of a system of matrix inequalities.