  This paper provides a unifying mean field based framework for the derivation
and analysis of ensemble Kalman methods. Both state estimation and parameter
estimation problems are considered, and formulations in both discrete and
continuous time are employed. For state estimation problems both the control
and filtering approaches are studied; analogously, for parameter estimation
(inverse) problems the optimization and Bayesian perspectives are both studied.
The approach taken unifies a wide-ranging literature in the field, provides a
framework for analysis of ensemble Kalman methods, and suggests open problems.
