Saw a detailed radar tracking/plotting of the last part of the flight. I think we can disregard the self-designed GPS theory. From what I saw, the aircraft looked for and then followed exactly the motorway , until one point where it left it to head roughly towards the airport, but in a wrong general direction ( off track by approx 20-30 degr) . The aircraft also made a few brief left/right turns while descending lower .
Looks more like trying to get visual contact with ground than following a GPS track . Icing is another possibility/factor as Spangdhalem nearby was reporting Freezing Fog at the time . But pure speculation. The guys of the BFU Investigation Team who have access to far more data may get the answer in the end.