  We provide a rigorous derivation of the Ensemble Kalman-Bucy Filter as well
as the Ensemble Transform Kalman-Bucy Filter in case of nonlinear, unbounded
model and observation operators. We identify them as the continuous time limit
of the discrete-time Ensemble Kalman Filter and the Ensemble Square Root
Filters, respectively, together with concrete convergence rates in terms of the
discretization step size. Simultaneously, we establish well-posedness as well
as accuracy of both the continuous-time and the discrete-time filtering
algorithms.
