  This paper is concerned with the problem of state estimation for
discrete-time linear systems in the presence of additional (equality or
inequality) constraints on the state (or estimate). By use of the minimum
variance duality, the estimation problem is converted into an optimal control
problem. Two algorithmic solutions are described: the full information
estimator (FIE) and the moving horizon estimator (MHE). The main result is to
show that the proposed estimator is stable in the sense of an observer. The
proposed algorithm is distinct from the standard algorithm for constrained
state estimation based upon the use of the minimum energy duality. The two are
compared numerically on the benchmark batch reactor process model.
