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    Re: Poor St. Hilaire
    From: John Karl
    Date: 2007 Oct 18, 07:08 -0700

    
    It looks like it's boiling down to our definition of the St. Hilaire
    intercept method.
    
    To quote from the 1962 edition of the glossary in Bowditch:  "St.
    Hilaire -- The establishing of a line of position from the observation
    of the altitude of a celestial body by use of an altitude difference
    and azimuth".
    
    This is also the definition in other glossaries, and is used in the
    books I have seen.  In St. Hilaire's original papers he doesn't bother
    with a one-line definitions, of course,  but discusses all sorts of
    sight reductions under a general section headings.
    
    I had hoped that it was clear that I'm using the traditional Bowditch
    definition of the method - establishing a single LOP.  As I've stated,
    the error in the straight-line approximation is only due to the
    curvature of the true LOP compared to the distance along the straight-
    line LOP.
    
    This error is well known and can be corrected without iterations.  HO
    229 has a table of offsets that does exactly this (or you can
    calculated them yourself).  When it comes to comparing the St. Hilaire
    LOP to other information, such as another altitude observation, again
    there are several methods.  And yes the Almanac presents an iterative
    method using intercepts.  My book presents a direct calculation (no
    iterations) at the bottom of page 77.  It uses the same two equations
    of the St. Hilaire method, five times.  Whereas a two-body St. Hilaire
    fix uses four of these equations.  So with just one more equation, of
    the same type, we eliminate the straight-line approximation, using no
    iterations.
    
    Yes, one CAN use St. Hilaire iterations to improve the straight-line
    approximation, using other information.  But the St. Hilaire method
    itself as defined by Bowditch (and others) doesn't use iterations.  So
    this part of the discussion has boiled down to semantics.  I was using
    the traditional Bowditch definition when I wrote
    
    >  Now if members think that this is unnecessary and unproductive nit-picking
    >  of terminology, consider that:
    
    >  1.  All CN books (well, all that I have seen) either don't attempt to 
    explain the reason for the > assumed position, or they explain it 
    incorrectly.  For example, some say that an
    >  assumption is necessary because the distance between
    >  the sun's GP and the ship is too great to plot, some because there's insufficient
    >  information to plot the LOP,
    >  and others because we don't know how to plot the exact LOP.
    
    >  2.  A List member has stated that the accuracy of the St. Hilaire result depends on how
    >  good the initial estimated position is.
    
    Speaking of a single LOP now, I thinks it's more accurate, and
    informative, to say the accuracy depends on the distance along the
    straight-line LOP compared to the curvature of the true LOP.  I think
    it's misleading to say it depends on an estimated position.  After
    all, no matter what AP (or estimated position) is used, my accuracy
    statement still applies.
    
    >  3. And therefore the St. Hilaire method is really an iterative method.
    
    If we want to expand the definition of St. Hilaire method to include
    iterations, that's a new usage to me - and considering that this whole
    discussion is about the wisdom, and implications, of certain
    terminology, I'm not sure it's a good idea.
    
    >  We've just seen that all of this is wrong.  This misunderstanding may not stem from the
    >  unfortunate
    >  terminology of "estimated" position and "assumed" position.  But if it doesn't,
    > where does it come from??
    
    So let's forget iterations.  My major point is item (1) above.
    
    John Karl
    
    
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