Ambiguity resolution tends to fail when moving and base receivers are more than a few tens of kilometers apart, because of the poorly known effect of the ionosphere on the signals. This depends on time of day, season, latitude, and the sunspot cycle. Very large area mapping surveys with altimeters, SAR, InSAR, side-scanning sonar, etc., may depend on finding the precise location of the sensors with GPS over much longer distances (hundreds to thousands of kilometers). There is a way around, known as "floating" the ambiguities, that combines signals received at the two GPS frequencies to eliminate the effect of the ionosphere, but treats the phase ambiguities as mere real-valued error states. It is the preferred approach in very long baseline geodetic surveys, and also works quite well in navigation, but at a price. It can take quite long for the navigation Kalman filter to converge to the desired level of precision, particularly with the kinematic approach. This approach very wisely ignores the usually complex vehicle dynamics, and so it works with any vehicle. The speed of convergence matters both in real-time and in post-processing, and the trick is how to increase it without giving up the versatility of kinematic positioning. In this talk, the convergence problem and its possible solutions will be illustrated with results from actual tests.