Precise Point Positioning (PPP) provides accurate absolute position information without the direct need of measurements from a reference station at the user. The current challenge of GPS L1/L2-based PPP is its long convergence time of more than 20 minutes being caused by the need to estimate atmospheric parameters, and the relatively large code noise and multipath errors. There are two options to reduce the convergence time of PPP: First, the Galileo wideband signals on E5 and E6 have a much lower code noise than current GPS L1 and L2 pseudoranges. Second, the satellite positions and satellite-related biases can be determined much faster and more accurately with optical inter-satellite links supporting ranging, time-transfer and intra-system communication. In this paper, we consider both options. A joint estimation of the receiver position, receiver clock offset, tropospheric zenith delay, ionospheric slant delays and carrier phase ambiguities is performed with a Kalman filter. Orbital errors and pseudo range multipath are also taken into account. The float carrier phase ambiguity estimates are mapped to integers using the famous Least-Squares Ambiguity Decorrelation Adjustment (LAMBDA) method. The simulation results show that an ambiguity fixing and, thereby, a highly-accurate PPP solution, can be achieved consistently within a few epochs. This is a quite substantial benefit and could make PPP attractive for numerous applications.