A better description! :) I understand a little of 7 languages well enough to read a newspaper but I still depend on Google Translate. When I speak any of these, native speakers smile and start speaking English.
To get this to work as you describe, your transponder (the wifi module+gps) needs to be able to 'talk' to your phone and send it data. I don't think the transponder can do that or rather, the phone can receive the data that way.
Problems
1) Do you have a device that works as a WIFI hotspot and is already connected to a GPS? I am not aware of anything that will do that. Can you tell me about what you have?
2) An Android can pass data between a BlueTooth device and itself without issues. I do not think it is possible to communicate between an Android and another device using WIFI. Someone might correct me. If the phone and the transponder cannot communicate via wifi, you cannot do what you would like to do with your wifi module + gps module. Is this wifi+gps transponder something like an Arduino module?
3) A flat map is imprecise; the maps on the Internet are fairly precise. A flat map will not be as accurate for plotting gps positions as one on the Web.
What is possible? No Internet is a problem.
1) If your transponder were Bluetooth+gps, the phone could communicate with it.
2) If two locations are known (your cell phone and your transponder locations) it is easy to calculate the distance between them. There are several methods.
3) If both locations are known on the phone, both locations can be drawn on a flat map and the separation calculated. The positions of the two locations are placed very accurately on OpenStreet Map or Google Map tiles when using the Internet. If you plot the locations on a flat map instead, the location posted on the flat map is only approximate. The location placement depends on map scaling from World coordinates to your map image coordinates on the Canvas.
"But i don't know, how to use the flat map." Yes you do know , the information I posted earlier (#2) might work for you and explains how. Did you read the link? The coding is
very complicated . It is possible a flat map
might not be suitable for what you want to do. Are you surveying? The flat map will not help you if there is not a way to get the gps coordinates from the transponder to your phone.
--Steve