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Nicol�s You wrote:
"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'." 

How do you suppose the FOG system is keeping this vertical? I've never used 
one, so if I may 'pick your brain' about the ones you've used... When you 
initially set the vertical, does it need some time to get it right? Can it 
be "re-set" while the vessel is in motion? Do you have to "punch a button" 
or otherwise ask it to re-set its vertical, or does it do this 
automatically? And, one more: have you travelled any significant distance, 
say sixty miles, with one of these in operation? The behavior over a 
distance like that should tell us something about what the device is 
actually accomplishing. 

The principle underlying the FOG (and also the ring laser) is simple enough, 
and it lets a set of three preserve exact orientation in three-dimensional 
space. So, for example, we could arrange to point one fiber optic gyro 
towards the North Celestial Pole, another towards GHA=0, Dec=0, and a third 
towards GHA=90 degrees, Dec=0. And now no matter how much we bounce around, 
the system will always "remember" where those directions are. Even if we 
don't have a complete inertial navigation system, which is expensive, it's 
easy enough to include three accelerometers parallel to each of those three 
axes. So how do we use that to get the vertical? 

I can think of a couple of possibilities. First, it could be doing an 
inertial navigation solution internally but without displaying the results. 
IN systems operating near the surface of the Earth determine the vertical 
directly from the calculated position. If the IN system says we've travelled 
ten nautical miles east along the equator then we rotate the vertical by ten 
minutes of arc towards the east. Then the calculated vertical would be just 
as accurate as the inertial fix (so it couldn't be used for a secondary 
celestial fix). Another possibility is that the FOG systems you've used are 
maintaining a vector parallel to the original gravity vector (rotated with 
time, of course). If that's the case, then if you travel ten nautical miles 
east along the equator, the indicated vertical would still be parallel to 
the vertical you left behind but it would be tilted by ten minutes of arc at 
your current location. And if you were to use that as a reference for 
celestial sights, it would happily tell you that you have not moved at all. 
Finally, what is probably the most likely explanation for a system in use on 
a vessel on water, is simple averaging: from the accelerometers and the 
orientations in space you calculate the vector that has the maximum 
acceleration value every second or so. Then you just calculate the average 
vector over the course of, say, ten minutes. There will be lots of small 
accelerations of the vessel over that time period, but they should average 
out and leave you with an excellent estimate of the local vertical. Of 
course, this local vertical will lag behind the vessel but probably not by 
more than a few minutes of arc. If we're zipping along at thirty knots and 
the system is averaging over a period of ten minutes, then the vertical will 
be off by 2.5 minutes of arc --this could be reduced by feeding the system 
some velocity information. 

Every now and then, we hear about military systems that potentially do some 
sort of "super celestial" with 1 second of arc accuracy. While it's 
certainly possible to measure the positions of the stars to that accuracy 
with advanced starseekers, digital cameras, etc., and the calculations can 
be worked at that level of accuracy, the limiting parameter in the fix is 
the accuracy of the vertical. 

By the way, there are some great messsages in the list archive covering much 
of this same material. If you go back to April, 2002, for example, and again 
in December, 2002 (before I joined the group), you'll find Dan Allen, Paul 
Hirose, and George Huxtable hashing out many of the same ideas. Just so 
we're clear, I'm not saying "it's all in the archives, and we've already 
discussed it". I'm saying "there's good stuff in the archives, worth 
reading". For example, here's a quote from George H., "Not so difficult to 
define the direction of a star to that precision, perhaps, but what worries 
me more are the errors in establishing the direction of the vertical 
reference." Here's a link to that post: 
http://www.fer3.com/arc/m2.aspx?i=008070&y=200212. There are others around 
that same date. For example, Paul H, on 8 December 2002 described the B-2 
stellar-inertial system: "Through some magic not clear to me (I worked in 
maintenance, not engineering!) the AINS feeds the measured directions of 
stars back to the inertial portion to correct its errors. Giving the 
otherwise blind inertial system a look at the outside world is enormously 
helpful. As long as it's got a clear view of the sky the AINS will remain 
within[classified] meters of the correct position, worldwide and practically 
independent of mission duration. It doesn't drift away over time like a 
normal INS." 

 -FER 



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