This paper addresses the problem of autonomous navigation of a quadrotor helicopter using state estimators when the GPS signal is not available. The main objective is to estimate the translational position and velocity of the flying machine. The observer proposed uses a double integral approximation of the acceleration defined in the mathematical model in order to estimate the states previously mentioned. To apply this approach, a recursive least squares algorithm is programmed to get better estimations. Real-time experiments have been conducted in order to verify the validity and effectiveness of the proposed estimation approach, and the obtained results are presented and discussed.