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    FOG's, was Re: automatic celestial navigation
    From: Nicol�s de Hilster
    Date: 2008 Jan 14, 09:02 +0100

    I understand your point/concern in how long it would take for a inertial
    system to loose it's vertical and actually that is a good question. The
    FOG's I regularly inspect use are all mounted on ships (and one on a
    vehicle) and are no inertial systems, just motion reference units. These
    are regularly aligned with true vertical by means of levelling and
    normally the alignment error will not be greater than a few hundreds of
    a degree (these FOG's have an resolution of 0.01 degree). The errors
    found are merely levelling errors as these alignments are done under
    dynamic conditions (floating vessel) and we are not concerned of errors
    in the range up to say 0.1 degrees as those will be corrected for in
    later calibrations. As far as I can recall none of those FOG's really
    ever 'lost it'.
    Now these are all based on land/water and therefore have a good
    reference: the earth rotation and gravity pull. I am not sure whether
    the much higher speeds of an aeroplane have different influence on these
    systems and can imagine that in space stuff gets even more complicated.
    The military versions do have much higher resolution and accuracy, which
    should provide enough reference I think for use on board of a vessel
    (although I am not sure, need to check the specs).
    frankreed@HistoricalAtlas.net wrote:
    > 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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