It's 20 years since I had serious math, so I will try a simpler suggestion
Take a chart of high-level airways and use the most probable going in the right direction to get the path over ground.
Then take a bearing to do a triangulation (I assume that you know where YOU are.
The only missing parameter should be the actual FL.
If the aircraft is cruising af FL 300+ and without following an airway, the theory falls short though.. they could go direct to a NATS entry point ?
Regards
Michael