low voltage with GPS solution

sort of an oxymoron, I understand. The polling of gps is a voltage resource hog.
I know some assembly language and some C++ and I want to start playing with drones and arduino
What would be a good low voltage/light weight solution be for minimal gps polling?
Are there any pitfalls to watch out for?

The polling of gps is a voltage resource hog.

No, it isn't. The GPS itself is a current hog, regardless of whether you collect the data it produces, or not. In any case, the voltage is a constant 5V (OR 3.3V).