Position holding, also called hovering, is a key specification of rotor based aircraft. Its control problem for small quadrotor UAVs (unmanned aerial vehicles) is addressed in this paper. Given the flight dynamics of quadrotors, the P+D+DD based position holding control laws are presented. For the resultant two loop overall configuration, the outer loop controls the throttle magnitude required to reach the target position and generates the reference attitude command for the inner loop, while the inner attitude loop ensures that aircraft's thrust is orientated to the target. The control algorithm is validated via a serial of field tests on a platform developed, including position holding and point to point navigation, showing the effectiveness of the approaches. Some implementation issues, such as translation velocity estimation, its Kalman filter design and multiple sensor data fusion are also addressed.