How to find inductance of a burnt inductor of a RF matching circuit
I removed the glue and figure out some of the parts. But still cannot understand the whole thing. However, I think @JRE is right and the burnt resistor is not M5002 but M5003 as it is the one that carries the line from the antenna, and for which I have no data.  

Update. 

After loads of reading I could figure out that the burnt inductor was actually a choke to bring power to the antenna. That's why shortcutting the antenna burnt it. The only function is therefore power, therefore it should block all frequencies in the range if gps antenna, as it was a dedicated gps antenna. The right inductor for the job could be a 27nH (max inductance at 1600MHz).

That's what I did, replace it and now the gps is getting signal again!