Accuracy increases with observation time. The height of the receiver may have an influence on the visibility of satellites, especially in mountain regions and in cities, and accurary increases with the number of visible satellites. I recommend the Springer Handbook of Global Navigation Satellite Systems, but perhaps someone can recommend an open-access publication.
This free eBook (100 pages) may be helpful for general questions on GNSS observations: http://arf.berkeley.edu/files/attachments/equipment/NovAtel-Intro-to-GNSS2015.pdf
The GNSS does use a time source that is accurate to approximately 3 billionths of a second But as the satellite orbits at 20,200 km from earth, the effect of altitude is negligible. The #1 thing that affects accuracy is the number of satellites visible to the GPS device and the number of satellites use in the calculation.
If you are asking about "observation time" the fact is that the more readings you take the better the accuracy can be. The first fix may not be the best.
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