Continuous limits for constrained ensemble Kalman filter

The ensemble Kalman filter method can be used as an iterative particle numerical scheme for state dynamics estimation and control-to-observable identification problems. In applications it may be required to enforce the solution to satisfy equality constraints on the control space. In this work we deal with this problem from a constrained optimization point of view, deriving corresponding optimality conditions. Continuous limits, in time and in the number of particles, allows us to study properties of the method. We illustrate the performance of the method by using test inverse problems from the literature.