Originally Posted by
khorton
Every direction is south, but some of the souths are a better choice than the others.
This is a key point. Neither the concept of heading nor the concept of longitude make any mathematical sense at the north pole. That's not an engineering limitation of any compass, gyro, INS, or GPS system: it's a limitation in the underlying mathematical geometry. To navigate at the pole you need to use a coordinate system which is something other than latitude/longitude, with courses and headings defined relative to that coordinate system.