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    Re: Advancing LOPs for precision fixes
    From: Gary LaPook
    Date: 2010 Feb 18, 23:37 -0800

    Andres' site is really impressive and it is well worth looking at.
    
    It has been at least 40 years since I tried doing matrix math so his 
    explanation left me in the dust. But, in looking at his formulas and 
    those in the N.A. I think, conceptually, that the first two formulas 
    provide for adjusting the A.P. (of E.P.) for the movement of the vessel 
    so I guess that this is what allows for a moving fix but, I must admit, 
    I don't understand why it works.
    
    His methodology for determining a fix by least squares makes sense and 
    reminds me of how attacked this problem in the past. In the late '70's I 
    programed my TI 52 calculator to come up with an approximation of a fix 
    from three LOPs. Lacking Andres' math skills and working with a lesser 
    level of accuracy commensurate with flight navigation, I programmed the 
    calculator to determine the intersection of the first two LOPs.Then it 
    used this position as the AP for computation of the third LOP. Then, to 
    approximate the center of the triangle of position, my program took the 
    bisector of the first two azimuths and then moved the fix 2/3rds of the 
    distance of the third intercept along that bisector from the 
    intersection of the first two LOPs and took this as the position of the 
    fix. Not elegant, not perfect,  but close enough for flight navigation..
    
    gl
    
    
    Andres Ruiz wrote:
    > At my web page my article:
    > "Celestial Fix Nautical Almanac Sight Reduction algorithm for n LoPs", gives 
    a detailed information of the algorithm.
    >
    > Originally the references are:
    > * Optimal Estimation of a Multi-Star Fix, C. De Wit. NAVIGATION, Vol.21 , No. 4, Winter 1974-
    > 75, pp 320-325
    > * Compact Data for Navigation and Astronomy for the Years 1991-1995, Cambridge University
    > Press ISBN 0-521-38731-0. Yallop B. D. and Hohenkerk C. Y. (1991).
    > * The Nautical Almanac. USNO
    >
    > Also the free program "CelestialFix.exe" implements the method, see pic.
    >
    > Regards,
    >
    > Andr�s Ruiz
    > Navigational Algorithms
    > https://sites.google.com/site/navigationalalgorithms/
    >
    >
    > -----Mensaje original-----
    > De: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] En nombre de Gary LaPook
    > Enviado el: jueves, 18 de febrero de 2010 11:41
    > Para: NavList@fer3.com
    > Asunto: [NavList] Re: Advancing LOPs for precision fixes
    >
    > Have you tried using the method in the N.A. to which you refer? I may be 
    > missing something but I don't see anywhere in the given formulas where 
    > you input course and speed which would be necessary if the method was 
    > allowing for advancing the LOPs to a common time.
    >
    > gl
    >
    >
    > P H wrote:
    >   
    >> As John Karl writes in his book:
    >> "The Nautical Almanac gives an iterative procedure for calculating a 
    >> fix from several intercepts and azimuths determined from their St. 
    >> Hilaire sight reductions."
    >>
    >> I would add that this procedure does take the vessel motion (assumed 
    >> to be constant during the round of observations) into account.  I am 
    >> confident that I am simply restating a fact that is well-known among 
    >> NavList members.  Also, I think it is not unreasonable to assume that 
    >> the content of the Nautical Almanac reflects common (standard, 
    >> recommended, accepted, etc.) practice.
    >>
    >>
    >> Peter Hakel
    >>
    >>
    >> ------------------------------------------------------------------------
    >> *From:* hch 
    >> *To:* NavList@fer3.com
    >> *Sent:* Tue, February 16, 2010 8:20:41 AM
    >> *Subject:* [NavList] Re: Advancing LOPs for precision fixes
    >>
    >> Gary,
    >>  
    >> You said ... "It is common practice to ignore the movement of the ship 
    >> during the time period needed to take a round of sights ...", and I 
    >> am unable to dispute this assertion in the light of today's "it's good 
    >> enough" approach to Celestial Navigation. I can, however, state in no 
    >> uncertain terms that this was not the traditional approach - LOPs 
    >> generated in a round of sights were always advanced or retarted to a 
    >> common time, so long as the distance run between individual sights was 
    >> measurable, if for no other reason than professional pride.
    >>  
    >> Regards,
    >>  
    >> Henry
    >>
    >>
    >>     
    >
    >
    >
    >
    >   
    >
    > ------------------------------------------------------------------------
    >
    
    
    
    

       
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