Disclosed herein is a system for rapidly resolving position with centimeter-level accuracy for a mobile or stationary receiver . This is achieved by estimating a set of parameters that are related to the integer cycle ambiguities which arise in tracking the carrier phase of satellite downlinks [5,6]. In the preferred embodiment, the technique involves a navigation receiver  simultaneously tracking transmissions  from Low Earth Orbit Satellites (LEOS)  together with transmissions  from GPS navigation satellites . The rapid change in the line-of-sight vectors from the receiver  to the LEO signal sources , due to the orbital motion of the LEOS, enables the resolution with integrity of the integer cycle ambiguities of the GPS signals  as well as parameters related to the integer cycle ambiguity on the LEOS signals . These parameters, once identified, enable real-time centimeter-level positioning of the receiver . In order to achieve high-precision position estimates without the use of specialized electronics such as atomic clocks, the technique accounts for instabilities in the crystal oscillators driving the satellite transmitters, as well as those in the reference  and user  receivers. In addition, the algorithm accommodates as well as to LEOS that receive signals from ground-based transmitters, then re-transmit frequency-converted signals to the ground.