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    Re: Navigational Algorithms - required assumed position for SR ?
    From: George Huxtable
    Date: 2006 Oct 19, 11:49 +0100

    Andres Ruiz wrote-
    
    Indeed using the "DeWit/USNO/Compac Data", least squares algorithm for 
    reduction of n sights, you can suppose any assumed position far away 
    from the real position. Because it do an iterative find of the fix, if 
    a solution exist, after few iterations it is found.
    
    If the assumed position is near the estimated one, DR, or the 
    celestial position, only one or two iterations are required.
    
    Try it with the software available at my web page: n LOPs Fix 
    (SR_LS.zip)
    
    The algorithm is described in the Nautical Almanac and at [n LOPs Fix] 
    :
    
     Andr�s
    
    http://www.geocities.com/andresruizgonzalez
    
     =======================================
    
    Comment from George-
    
    In the case when there are only two bodies observed, then there must 
    always be two solutions, at the two crossing-points of the circles, 
    which are usually easy to distinguish, but under unusual circumstances 
    may be close together.
    
    Depending on the assumed position you choose to start with, a 
    least-squares algorithm homes in on one or the other, which may 
    possibly not be the one that's relevant.
    
    How do you ensure that both possible solutions have been flushed out, 
    then?
    
    I have discussed this some time ago with Herbert Prinz, who, as best I 
    remember, suggested that having found one solution, starting from your 
    best guess at assumed position, you then started it off again from the 
    antipode of that assumed position, which should be sure to end up at 
    the other solution. It made sense, to me.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    
    
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