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The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a waveletbiorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for ourfiltering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of theZakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than theclassical Galerkin method.