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    Re: Optimum number of LOPs
    From: Bill Lionheart
    Date: 2018 Nov 26, 08:30 +0000

    Bob
    
    To clarify your question you want to know how much each extra LOP
    reduces the uncertainty. For example how much it reduces the area of
    the within an elliptical probability contour for a fixed probability,
    in terms of the azimuths and variances for each sight?
    
    I think I can answer that, although most of the answer is in
    Stansfield, Statistical theory of DF fixing, J or the IEE, 1947
    together with the Gauss Markov theorem.
    
    To fully answer your question though we need t decide the value of the
    reduction in the size of the probability contour and if it is worth
    the effort. You could compare for example with taking more
    measurements of the same sights to reduce the variance as at least we
    could compare the time cost.
    
    If you use a computer to do the sight reduction calculate the least
    squares point then there is no significant extra cost of using more
    LOPs, it is just the time taken to measure the altitudes and record
    them with the time.  If you want to compute the least squares point
    and ellipse using ruler and compasses it turns out it is not so hard
    to add extra lines of position. But this involves a neat trick in a
    paper two colleagues and I recently submitted to JoN.
    
    Bill Lionheart
    On Sat, 24 Nov 2018 at 21:30, Bob Goethe  wrote:
    >
    > I have read with interest the discussion on the ever-troublesome cocked hat, 
    and the difficulties associated with assigning a most probable point (or even 
    a least improbable point).
    >
    > If one takes sights on two celestial objects - where he feels equally 
    confident in the quality of the sights - and uses Frank's equation for 
    determining the error elipse 
    (http://fer3.com/arc/imgx/error-ellipse-ratio.jpg.thumb.jpg), to what extent 
    can one say that he has pretty much what he needs to come up with as good a 
    fix as can be had?
    >
    > That is to say, if one takes a sight on a third object, reduces and plots 
    it, could he say that he has done more work with no significant probability 
    that he knows more about his actual position than he had after plotting his 
    initial two LOPs?
    >
    > And if a 3rd LOP represents a poor navigational return on time-invested, 
    presumably a 4th LOP is even less worthwhile?
    >
    > Bob
    >
    > View and reply to this message
    

       
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