We study a problem of singular perturbations for a special class of nonlinear filtering problems in which the dimension of the signal process is 2 and only one of the two components of this process is observed. We propose an approximate filter of finite dimension for the observed part. Using this filter, we construct an approximate filter of infinite dimension for the nonobserved part. This filter solves a Zakai-type equation whose spatial variable dimension is 1 even though the spatial variable dimension of the Zakai equation solved by the exact filter is 2. The method used gives the order of the approximation error.