We consider the anisotropy-based filtering problem for a linear discrete time-varying multiplicative noise system on a finite time horizon. A random disturbance with an inaccurately known distribution is fed to the system input. The uncertainty in the description of this distribution is characterized by a constraint on the anisotropic functional. The output of the original system is estimated using the selected filter of a certain type according to the principle of minimizing the performance indicator in the form of the anisotropic norm of the filtering error system. Based on the lemma on the boundedness of the anisotropic norm of the filtering error system, relations for the unknown filter matrices are derived. As special cases, we consider anisotropy-based filtering problems for a system with measurement dropouts as well as a similar problem for a system with a filter of a special type. A numerical example where the method is used to synthesize an anisotropy-based filter is given.