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Nicolas, you wrote:
"There is one significant advance that was introduced some ten years ago:
the FOG (Fibre Optic Gyro). Combined with acceleration sensors these
produce very high quality motion reference units and even inertial
navigation systems. Initially developed for military rocket application
the downgraded versions of these instruments are widely used in
hydrography and other businesses."

Well, I did mention ring-laser gyros, at least. From my point of view,
ring-laser gyros and fiber optic gyros are basically identical (they're
Sagnac Effect devices). But you make a good point that these inertial nav
systems provide a measure of the vertical. I'm wondering whether this could
be relevant to any hypothetical "independent" automated celestial navigation
(which was the context in which this was brought up). That is, if we take
the implied vertical coming from a ring-laser gyro or fiber optic gyro
inertial navigation system, could we measure stars relative to that vertical
and get a fix that's better than the position fix that the inertial system
is already supplying? I don't want to annoy anyone by discussing something
that is clearly not traditional navigation, but since it's strictly at the
level of relating it theoretically back to the principles of celestial
navigation, I hope no one minds for now.

A modern laser-based inertial navigation system is dead reckoning gone mad.
The laser gyros determine three fixed directions in space and hold those
directions no matter how much you vehicle turns, spins, bounces,
accelerates, or does whatever it will do. Except for a little drift, the
gyros continue to tell you exactly where those original directions are
pointing. Using output from accelerometers tied to those same three
directions, the system then calculates velocities in those directions, and
from the velocities it calculates changes in position. Without looking at
the outside world, an inertial system can navigate like this for hours. In
addition, the system can keep track of true north and the local vertical as
part of its inertial solution. Of course, these systems are not perfect so
gradual drift occurs and the laser gyros will slowly shift away from their
original orientations. Soon enough, the position data becomes inaccurate.
And soon enough, the calculated vertical becomes inaccurate.

An inertial system can be re-aligned by looking at the stars. Fundamentally,
this is nothing more than using the stars as a compass, to tell the
laser-gyros which way they're pointing after some drift has occurred. Then
the system will re-calculate velocity, position, and local vertical. So
although it's using the stars, it can't get a fix from them that's any
better than the new inertial fix. But there's an interesting possibility for
sophisticated inertial systems: if the solution for the vertical is *better*
than the solution for position, then the system could do real celestial
navigation, using the inertial vertical to determine the zenith and
measuring astronomical zenith distances from there. The celestial fix would
then directly reset the inertial navigation allowing it to, in effect, start
over from a new departure. I don't know enough about these systems to say
whether the solution for the vertical might in fact be better than the
solution for the position (the best such systems are classified anyway), but
now that I think about it more, it's actually possible that they do get a
better solution for the gravitational vertical than they do for position. If
the system includes a fast gravity gradiometer able to detect the local
tidal field (the very local deviations in the Earth's gravitational field),
or if the math of the inertial solution by itself lets the inertial
navigation system itself function as a gravity gradiometer (?), then it may
well happen that the system can track the local vertical. And in that case,
a stellar-inertial system could do something more than just using the stars
as an astro-compass, which would certainly be interesting! I'll have to
think about that some more...

You also wrote:
"I am a regular user of these systems (and did several performance tests
with them as well for the Dutch government) and know from experience
that the direction of the vertical is not influenced by lateral
motions/accelerations."

Yeah, that's a normal property of a good inertial system. Almost all modern
airliners also use these amazing laser gyros and keep an almost exact
vertical at all times as part of the inertial navigation solution. And they
look cool, too (at least with the case removed). Ever seen a ring-laser
navigation system all lit up? Few things seem more like science fiction made
real...

 -FER

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