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    On improving data
    From: Peter Fogg
    Date: 2003 Jan 18, 05:17 +1100

    Dan Allen wrote:
    > ... like my land sights: some are amazingly accurate while
    > others are not.  We know this because we have the luxury of comparing
    > our sextant results with an averaged GPS location or a typographic map
    > location.
    > But how would we do without these crutches?  How would we do on a
    > rolling ship in a storm?  What statistical measures or rules of thumb
    > can be
    > used to help throw out the bad sights and keep the good ones?  This is
    > an
    > area that I am considering more and more.
    The common answer is to 'average' a series of sights. The problem with
    this is that the bad sights pollute the others, and there is no way to
    know just which is what from just looking at the numbers. But there is a
    technique to separate the good from the bad, so telling which is which
    becomes clear with a glance. It has been described before but may bear
    The rate a celestial body appears to rise or fall over a 5 minute period
    can be expressed as a sloping line on a graph. If the sights taken (as
    many as possible of the same body over the 5 minutes*) are plotted above
    this line then a second line can be drawn parallel which best fits the
    pattern of sights - they should also rise or fall. Then any point along
    this 'line of best fit' can be used for the 'time/sextant altitude' data.
    Any sights that are wildly off are ignored, so unlike 'averaging' they
    make no contribution to the result.
    That's it in a nutshell. The bad sights are obvious - they are the ones
    far from the 'line of best fit'. The reasonably good ones will lie just
    above and below the 'line of best fit' - meaning that the line may give a
    more accurate result than any individual sight. And this is my experience.
    Its a technique ideally suited for the 'rolling ship in a storm'. An
    additional advantage is that a precise time for the sight can be chosen in
    advance, by starting the sight taking process a few minutes before and
    extending it a few minutes after the exact time required. Whether you took
    a sight at the right moment and whether that one is any good is
    irrelevant. This enables, for example, a sight when the body is at 90 or
    270 degrees of azimuth, giving a line of position that indicates the
    The alternative seems to be to take sights of multiple bodies and discard
    the LOPs that seem wrong, compared to the others. But this entails much
    more work, lots of sight reduction, improved possibility of error. Then
    you are left with a plotting sheet full of confusing lines. With multiple
    LOPs all over the place I find it difficult to choose the point of fix .
    If some of these bodies have similar azimuths their usefulness is
    questionable - they are more likely to promote further confusion. Better,
    I propose, to have just 3 bodies with nicely separated azimuths, and the
    assurance in advance that they are quite accurate.
    If anyone is interested in more detail about this I will be happy to
    expand further. Its a simple routine and I am mildly surprised that it is
    not more widely known and practiced - it is simpler to do than to
    (PS*This reminds me that I've been reading about how the United States was
    comprehensively surveyed, a mammoth task. They found that the best
    technique was to get their sights done quickly; that extra fiddling with
    the theodolite was counter-productive - it tired the operator and, in any
    case, led to less accurate results.)

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