Finite horizon anisotropy-based multicriteria ¯ltering problem for the linear varying discrete time system has been solved. Multidimensional input disturbance consists of groups of signals, each group is characterized by its inaccurately given information theory properties. For that mathematical model, the bounded real lemma for an anisotropic norm has been proved. If the subsystem norms are limited to speci¯c values, a su±cient condition for multicriteria estimator existence has been obtained. An estimation algorithm is based on recursion solving of linear di®erence matrix inequalities simultaneously with the inequality of a special type.