A position domain Hatch filter is proposed as an efficient carrier-smoothed-code processing algorithm for real-time kinematic differential global satellite navigation systems. The well-known range domain Hatch filter is newly interpreted with a stochastical point of view. The interpretation result is extended to derive the position domain Hatch filter. By a covariance simulation, it is shown that Hatch gain is, in general, more efficient than Kalman-type gain in carrier-smoothed-code processing and the proposed position domain Hatch filter is more advantageous than the conventional range domain Hatch filter if the visible satellite constellation changes during the positioning task.???