NavList:

I have just read "The Ice Diaries" (2008) by Captain William Anderson.  Captain Anderson piloted the Nautilus to the North Pole under the ice.   He and his crew were the first to do so.

In this book, Captain Anderson gives us the accuracy of generation 1 inertial navigation equipment as compared to his celestial equipment.  So without further ado, Captain Anderson states that after a 2000 mile journey under the polar ice cap the difference between his inertial navigation equipment and his celestial fix was 1 nautical mile.  Call it 1 part in 2000!

Captain Anderson permits us a peek into his celestial equipment.  It is a thru periscope SCAR (Sperry Corporation Altitude Recorder), gen 1.  For those who have ever observed through a US Navy periscope, you know the optics are superlative (this is available to the general public at the Submarine Museum just outside of New London, CT).  Further submarines have exquisite sense of horizontal, referring to it as "the bubble".  Therefore, vertical is known as well.  In combination, the ability to get a fix must have been phenomenal.  No need for a horizon with perfect optics.  Just record the altitudes and reduce to a fix.

The inertial navigation equipment was also generation 1.   It was adapted from the guidance system for the sophisticated Navajo missile designed by North American Aviation.  Captain Anderson states it was lucky that it fit down the hatch. 

After his final (celestial / radar) fix, the Nautilus submerged for the North Pole journey, near the Bearing Sea.  Crossing under the ice, he navigated strictly by inertial equipment through 90 north (you pick the longitude, as he states) and out from under the ice into the North Atlantic.  He was unable to surface the entire time due to ice, and therefore no other fix was possible.  Its an interesting read.

Upon surfacing in the North Atlantic, his quartermasters performed the celestial fix and came up with the figure of merit.  1 nautical mile.

Which one was out and which one was correct is not stated. 

That was 1958, using gen 1 equipment.  I'd like to think it got better over the last 56 years.

Brad