Derivation of ensemble Kalman-Bucy filters with unbounded nonlinear coefficients

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 discretisation step size. Simultaneously, we establish well-posedness as well as accuracy of both the continuous-time and the discrete-time filtering algorithms.

Automated summary

This paper provides a rigorous derivation of the ensemble Kalman-Bucy filter and the ensemble transform Kalman-Bucy filter in the case of nonlinear, unbounded model and observation operators. It also establishes convergence rates in terms of the discretisation step size. The paper simultaneously establishes the well-posedness and accuracy of both the continuous-time and the discrete-time filtering algorithms.