what makes my nav start moveing when I did not start it yet
Is it possible that you released the emergency brake / parking brake first before you started the SUV? This MAY have caused this, even if the transaxle is still in Park. Just a guess on my part.
The new GPS III and GALILEO systems will be able to measure and correct their own inaccuracies. The WAAS or EGNOS systems have inherent and slight inaccuracies. If your nav says you have moved, but you know you haven't - don't worry. You are not delusional, it's just a grimlin in the system. You will have to decide if it is so bothersome that you need to replay the Nav unit. You could contact your dealship and inquire if a re-calibration is an option on your Nav unit.
The OP is referred to his Lincoln Navigator, when he says "Nav", not the Navigation Unit.
Looking for a Used Navigator in your area?
CarGurus has 3,747 nationwide Navigator listings starting at $1,795.
Search Lincoln Navigator Questions
Lincoln Navigator Experts