The filtering problem for discrete Volterra equations is a nontrivial task due to an increasing dimension of the equivalent single-step process model. A difference equation of a moderate dimension is chosen as an approximate model for the original system. Then the reduced Kalman filter can be used as an approximate but efficient estimator. Using the duality theory of convex variational problems, a level of nonoptimality for the chosen filter is obtained. This level can be efficiently computed without exact solving the full filtering problem.