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    Re: FOG's, was Re: automatic celestial navigation
    From: Frank Reed
    Date: 2008 Jan 26, 00:32 -0500

    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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