In this paper we solve asymptotically Kushner's equation for the conditional probability density function of a one dimensional diffusion process measured in a low noise channel. We obtain the Stratonovich version and solve asymptotically this equation. The asymptotic aolution agrees with the asymptotic solution of Zakai's equation. In the second part of this paper we solve asymptotically Kushner's equation for a model of feedback channel and construct a sub-optimal filter for this model.