We consider the nonlinear filtering model with Ornstein-Uhlenbeck
  process as noise and obtain an analogue of the Bayes' formula for
  the filter. For this we need to consider a modified model, where the
  instaneteneous effect $h(X_t)$ of the signal in the usual model is
  replaced by $\xi_t^{\alpha} = \alpha \int _{(t- \frac{1}{\alpha})
    \vee 0}^t h (X_u) \,du$, (where $\alpha$ is a large parameter).
  This means that there is a lingering effect of the signal for a time
  period $ \frac{1}{\alpha} $.
  
  Further, we also show the filter with Ornstein-Uhlenbeck converges
  to the usual filter in probability.