  Ensemble Kalman methods constitute an increasingly important tool in both
state and parameter estimation problems. Their popularity stems from the
derivative-free nature of the methodology which may be readily applied when
computer code is available for the underlying state-space dynamics (for state
estimation) or for the parameter-to-observable map (for parameter estimation).
There are many applications in which it is desirable to enforce prior
information in the form of equality or inequality constraints on the state or
parameter. This paper establishes a general framework for doing so, describing
a widely applicable methodology, a theory which justifies the methodology, and
a set of numerical experiments exemplifying it.
