This paper describes a receding horizon discrete-time state observer using the deterministic least squares framework. The state estimation horizon, which determines the number of past measurement samples used to reconstruct the state vector, is introduced as a tuning parameter for the proposed state observer. A stability result concerning the choice of the state estimation horizon is established. It is also shown that the fixed memory receding horizon state observer can be related to the standard dynamic observer by using an appropriate end point state weighting on the estimator cost function.