The decomposition synthetic approach is considered for solving the problem of optimal nonlinear filtering of dynamic processes. Decomposition structures are applied as filters with growing memory based on artificial neural networks, fuzzy logic systems, wavelets, and combinations thereof. The solution of the nonlinear problem of estimation shows that using synthetic systems of decomposition aids to achieve high estimation accuracy wherein the learning speed of these systems is much higher than that of initial decomposition-free ones.The regularities of speed increase while using decomposition are obtained.