We consider the robust anisotropic filtering problem for a linear discrete nonstationary system on a finite time interval. We assume that external disturbances acting on the object have anisotropy bounded from above and additionally satisfy two constraints on the moments. Our solution of the filtering problem is based on the boundedness criterion for the anisotropic norm in reverse time and reduces to finding a solution for a convex optimization problem. We illustrate the operation of a suboptimal anisotropic estimator with a numerical example.