Inductor for a GPS active antenna
The question is how did they reach the value of 82nH? and how the other parameters of the inductor are chosen.


This inductor is to filter VBAT power noise as the GPS is very sensitive. 
I designed some GPS boards with different modules and in my experience the filter you need between the GPS module and the rest of the circuit depends heavily on the power source and the rest of the circuit and there is no rule of thumb that is cheap and also realible.

In my experience the best strategy is to test different filters until it works as you expect. A cheap and good option is to use a ferrite bead or ferrite choke that has high impedance at 1.5GHz (the GPS frequency). But if the power source is noisy you may need to add a linear low noise regulator.