Compared to ambiguity-float precise point positioning (PPP), ambiguity-fixed PPP needs a short convergence time and has better positioning accuracy. However, when there are only a few GPS satellites without an optimal geometrical distribution, ambiguity-fixed PPP requires time to achieve a first fixed solution. The objective of our research was to reduce the time to first fixed solution (TFFS) for GPS-only PPP by adding GLONASS satellites. An observation model for GPS/GLONASS ambiguity-fixed PPP using the integer phase clock method was developed and tested. Forty kinematic tests using static data show that the average TFFS is 50.2 min for GPS ambiguity-fixed PPP while only 25.7 min for GPS/GLONASS ambiguity-fixed PPP; reduced by 48.8% after adding GLONASS observations. A vehicular test demonstrates that GPS-only PPP cannot get its first fixed solution due to a less than ideal observation environment while GPS/GLONASS PPP can realize ambiguity fixing.