There may not be a reason for GPS to not work at the poles... but I have seen 
GPS receivers that had hiccups at  the equator and know of some that had 
problems at the poles...   seems to be caused by math degenerating at 0 and 90 
degrees.   

The equator problem manifested itself as a reflection of latitude from negative 
latitude to positive latitude within a couple of km of the equator... this was 
before the days of well proven GPS simulators.  It caused some problems 
starting King Neptune's court on time...  
https://en.wikipedia.org/wiki/Line-crossing_ceremony

I also know of a modern receiver that has problems crossing 90 degrees west 
(-90 degrees) longitude... It was a device developed in the far east and 
apparently never tested with a GPS simulator.

------------------

> I have been watching the thread and there is no reason for GPS not to work
at the poles.
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