This paper describes a method for constrained state estimation based on receding horizon optimization. The case studied here corresponds to an optimization horizon of size two and a constraint horizon of size one. It is shown that, in this case, a simple closed-form solution can be obtained. The resulting estimator is called a Rolling Horizon Estimator with Constraint Horizon One. It is shown that this estimator is analogous to a class of anti-windup control algorithms. Simulation results confirm the merits of using this scheme for state estimation in the presence of state constraints.