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    Re: Rejecting outliers: was: Kurtosis.
    From: Gary LaPook
    Date: 2011 Jan 1, 11:15 -0800
    Another way to improve the accuracy an an LOP derived from a series of sights on one body is to take the mid point of the times and the median of the altitudes. This is the principle used in many "averagers"incorporated in bubble octants for use in flight such as the A-7, A-10, A-12 and others, These all use disks or drums attached to the altitude adjustment knobs onto which you impress pencil marks my pressing a plunger when the body is collimated with the bubble. The A-10A makes a mark every second by use of a solenoid activated plunger triggered by a clockwork mechanism. At the end of the series you visually find the median between the marks and use that for your Hs and the mid time of the series as the time of the observation. Since the times of the observations are not marked down and, except for the A-10A, the marks are not evenly spaced in time, using the midpoint of the time doesn't really represent the time of the median sight but is close enough. Even when using a bubble octant in flight that doesn't have this type of averager the navigator records only the start and end time of the series and then the series of altitude readings. He then finds the average of the altitudes and used the mid point of the time for his observation.

    Obviously, these methods do not produce LOPs with the precision of a least squares fit or other methods discussed on this thread but good enough for flight navigation.



    --- On Sat, 1/1/11, Geoffrey Kolbe <geoffreykolbe@compuserve.com> wrote:

    From: Geoffrey Kolbe <geoffreykolbe@compuserve.com>
    Subject: [NavList] Re: Rejecting outliers: was: Kurtosis.
    To: NavList@fer3.com
    Date: Saturday, January 1, 2011, 8:58 AM

    Peter Fogg wrote:

    I've added some simple diagrams to text to try and show that its the other way around; apparent outliers tend to reject themselves because they stubbornly refuse to join a 'line of best fit', but whereas in the past I've been able to place text and diagrams directly here I can't this morning, for reasons unclear.

    Therefore the next least-worst alternative has been adopted, and I've attached my reply as a PDF file.  Hope you can open it.  Its only about 60KB, thus a file of modest size.

    Thankyou Peter, and a good morning to you.

    Actually, that diagram is a very good example of what I am trying to get across. On seeing that data, my first question would be, "Are my sights usually such a good fit to the line?" In other words, is the standard deviation on the random error of my altitude data usually as small as indicated by the four points that sit very close to the line?

    If the answer is yes, then there is very little doubt that the orphan point up at the top does not belong to the data set that sits so nicely on the line. It is so far out that I would be pretty certain that there was some difference in the circumstances that prevailed for that measurement against the four others.

    When taking a run of sights like that, I find that a steady rhythm is established, so it is fairly easy to pick out errors in timing. If the altitude was off by a whole degree then an error in reading the sextant would seem likely. Because of this, I would be particularly suspicious of the fact that the orphan data point is not the first or the last in the run of data.
    But if those and the other usual suspects are discounted, then it starts to become increasingly likely that there is some "systematic" problem, like a loose index mirror on the sextant which, for one of the sights, moved slightly in its seating. Now, if something like that was the problem - as would seem likely with the outlier so far out - we suddenly have good reason to mistrust all the data.

    Your response, I gather, would be to discard the outlier and carry on as though it never existed.

    Fine, I have said what I needed to say.


    Geoffrey Kolbe
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