For satellite orbit determination, the most accurate observable available today is microwave radio phase, which can be differenced between observing stations and between satellites to cancel both transmitter- and receiver-related errors. For maximum accurace, the integer cycle ambiguities of the doubly differenced observations must be resolved. To perform this ambiguity resolution, we propose a bootstrapping strategy. This strategy requires the tracking stations to have a wide ranging progression of spacings. By conventional ''integrated Doppler'' processing of the observations from the most widely spaced stations, the orbits are determined well enough to permit resolution of the ambiguities for the most closely spaced stations. The resolution of these ambiguities reduced the uncertainty of the orbit determination enough to enable ambiguity resolution for more widely spaced stations, which further reduces the orbital uncertainty. In a test of this strategy with six tracking stations, both the formal and the true errors of determining Global Positioning System satellite orbits were reduced by a factor of 2. ¿ American Geophysical Union 1989