  Minimum variance duality based full information estimator and moving horizon
estimator (MHE) are presented for discrete time linear time invariant systems
in the presence of state constraints. The proposed estimators are equivalent to
the Kalman filter (KF) when uncertainties are assumed to be Gaussian and
constraints are absent. In the presence of constraints, the proposed estimator
is proved to be stable in the sense of an observer without making the standard
vanishing disturbance assumption. In order to approximate the arrival cost, we
need not to run KF in parallel. The standard MHE, which is based on minimum
energy duality, is compared with the proposed estimator by means of a numerical
experiment on the benchmark batch reactor process.
