Can you guide me about the purpose of fine alignment in inertial navigation systems?
I was a Doppler Radar &amp; INS specialist for the Air Force in the 80s, and learned systems for the F4 (flying brick) and the triple carousel system for the C-5A. These systems used mechanical gyros in combination with accelerometers to establish a "Stable Platform". The carousel idea was state of the art then and rotated 1 revolution per hour to greatly reduce drift.

BATH was used for course alignment, which is an acronym for Best Available True Heading and local gravity to start level. It would then spin up and do fine alignment by sensing Earth rotation to determine True North. Typically this took about 30 minutes. Modern systems us laser gyros which aren't affected by mechanical drift.