Does resume own navigation refer to your horizontal navigation, or horizontal and lateral navigation?
According to John D. Collins, a CFI (Certified Flight Instructor);
RESUME OWN NAVIGATION – Used by ATC to advise a pilot to resume his/her own navigational responsibility. It is issued after completion of a radar vector or when radar contact is lost while the aircraft is being radar vectored.
Resume own navigation can be issued to a VFR aircraft that is being vectored after the vector, in which case it is not a clearance to fly a specific route, but rather an indication to the pilot that they may navigate by their chosen route.
Notice the word vectors, vectors refers to heading but does not refer to an assigned altitude. It’s not related to an altitude instruction. It becomes very complicated and mucky though if you try to apply what is used in the real world, because it is very varies from group to group in different areas of the world.
To simplify things and create uniformity, Infinite Flight has described it in the following, this from the the ATC Manual:
10.8.3 If you do issue a vector or altitude assignment, once the risk of conflict is no longer present, you should let the pilot know by sending ‘resume own navigation’ and/or ‘altitude at your discretion’ as appropriate (see 10.8.5 below for exceptions).
So, if issued an altitude and heading instruction, the controller must issue an ‘altitude at your discretion’ along with a ‘resume own navigation’, so that the pilot can climb to their intended altitude.
If only a ‘resume own navigation’ is issued, then the pilot must continue to follow the altitude issued until they receive an ‘altitude at your discretion.