Linear filtering with Ornstein-Ulhenbeck process as noise
We consider a linear filtering model (with feedback) when the observation noise is an Ornstein-Ulhenbeck (OU) process with parameter β. The coefficients appearing in the model are all assumed to be bounded. In addition, the coefficients appearing in the observation equation are also assumed to be differentiable. We consider the general case when the OU noise is also correlated with the signal. Under these conditions, we derive the filtering equations for the optimal filter.