This article considers moving horizon strategies for constrained linear state estimation. Additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states, noise, and other variables. Formulating a linear state estimation problem with inequality constraints, however, prevents recursive solutions such as Kalman filtering, and, consequently, the estimation problem grows with time as more measurements become available. To bound the problem size, we explore moving horizon strategies for constrained linear state estimation. In this work we discuss some practical and theoretical properties of moving horizon estimation. We derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate. We also discuss smoothing strategies for moving horizon estimation. Our framework is solely deterministic. (C) 2001 Elsevier Science Ltd. All rights reserved.