A real-time kinematic (RTK) filter (48) uses the backup data to estimate a relative position vector between the mobile receiver (20) at the first measurement time and the mobile receiver (20) at the second measurement time and to provide recovery data associated with a satellite-differenced double-difference estimation for the mobile receiver (20) between the first measurement time and the second measurement time. A navigation positioning estimator (50) can apply the relative position vector, the backup data, the recovery data from the RTK filter (48), and received correction data with precise clock and orbit information on the satellite signals, as inputs, constraints, or both for convergence or resolution of wide-lane and narrow-lane ambiguities, and determination of a precise position, in accordance with a precise positioning algorithm.