How big a ground plane does a gps antenna need?
Ublox have a detailed application note on GPS Antennas that states the following for ceramic patch antennas which is the style of element normally used in those:


  Patch antennas are ideal for situations where the antenna is mounted on a flat surface, e.g. the roof or the dashboard of a car. Patch antennas can show a very high gain, especially if they are mounted on top of a large ground plane (70 x 70 mm). Ceramic patch antennas are very popular because of the low costs and the huge variation of available sizes (40 x 40 mm down to 10 x 10 mm; typical 25 x 25 mm).


That seems to line up with the specifications I had on hand for a few similar end-user antennas:


Peak gain: 4 dBic ( based on 70 mm ×70 mm ground plane)


Having said that I agree with the comments that they work fine without an additional ground plane at all (there's a small one internally) and keeping them clear of obstructions and sources of multipath is more important in my experience. That especially applies with newer receivers that are much more sensitive than their older counterparts and often more antenna gain doesn't give any real performance benefit.

However if you do find perform isn't optimal without a ground plane the above document contains a graph of ground size versus gain for a few common ceramic patch sizes. It appears you'd get about 6 dB of gain for a 25 x 25 mm patch by using a 70 x 70 mm ground plane over the small internal one: