To those questioning the Doppler shift analysis, and trying to rationalize how you could determine a north vs south heading, it's pretty simple. You are analyzing this as if the pings started on the equator, which we know they didn't. If part of the readings indicated the plane was getting closer before it was going away from the satellite, then it was heading south west. If all of the readings indicated the plane was getting father away, then it would be going north.
The fact that the plane didn't start on the equator is what breaks symmetry.