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    Navigational Algorithms papers
    From: Andr�s Ruiz
    Date: 2008 Apr 16, 08:27 +0200

    Celestial Fix. Nautical Almanac Sight Reduction algorithm for n LoPs
    I have received several mails from people interested about the calculation 
    method that appears in the nautical almanac. 
    Now I have updated form html to PDF, and expanded the article on my website.
    Andr�s Ruiz
    Navigational Algorithms
    [NavList 4819] Vector Solution for the intersection of two Circles of Equal Altitude
    From: aruiz---es
    Date: 8 Apr 2008 15:28
    Dear George,
    Yes, my paper: "Vector Solution for the intersection of two Circles of Equal 
    Altitude", (not equal amplitude) is in The Journal of Navigation, 2008 Volume 
    61, Issue 02  April 2008, pp 355-365. 
    The Abstract and the appendix not published, (There is always an intense 
    competition for space in the Journal and, the RIN ask me to save space), is 
    at my web site, in the [Papers] section.
    I think there is no omission, the Running Fix algorithm is based on: "Metcalf, 
    T. R. Advancing Celestial Circles of Position, NAVIGATION, Vol. 38, No. 3, 
    Fall 1991, pp 285-288."
    And the appendix is clear enough after reading Metcalf�s paper. It based on 
    iterating until the error in position between two consecutive solutions is 
    less than 10-6, this is the key.
    First thing I did when late in 2006, you kindly sent me your paper, was to 
    check my running fix algorithm against your test. I have attached the 
    results, also the solution by the NA SR algorithm and by Kaplan. The program 
    CelestialFix.exe is available at the download section, and includes the 
    vector solution for 2 CoPs.
    Although the central issue of my paper is to present a vector solution to the 
    two body fix problem, I have also treated the running fix problem, but this 
    is a generalization, you can use any solution for the intersection, like Van 
    Allen�s and the final result is the same.
    For me the best way to solve a running fix problem, is using Kaplan paper, 
    (Kaplan, G. H. 1995: "Determining the Position and Motion of a Vessel from 
    Celestial Observations", Navigation, Vol. 42, No. 4, pp. 631-648.), including 
    the motion as a part of the problem. It is the natural way for many problems 
    in engineering.
    Yours sincerely,
    Andr�s Ruiz
    Navigational Algorithms
    -----Mensaje original-----
    De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de George Huxtable
    Enviado el: martes, 08 de abril de 2008 0:31
    Para: NavList@fer3.com
    Asunto: [NavList 4815] Re: Your paper in JoN.
    In Navlist 4812 I posted the following message. I didn't intend to; it was 
    the result of a bit of finger-trouble, as my intention was to send it 
    off-list directly to Andres Ruiz. . However, no harm done.
    But I didn't explain the topic that Andres was writing about, in his paper 
    in the latest issue of Journal of Navigation, so this message is to fill in 
    that omission. It was "Vector solution for the intersection of two circles 
    of equal amplitude", by Andes Ruiz Gonzalez.
    And the bit I was referring to was his section 2.3, "Correction for the 
    motion of the observer", which stated-
    "When the two sights are not taken at the same time, it is necessary to move 
    the first CoP [circle of position] to the time of the second one, or both to 
    a common instant.Many methods have been presented, but the correct way to 
    move a CoP is to advance or retire the GP [Geographical Position of the 
    first observed body] due to the motion of the observer [refs 6,7]
    Using the technique described in reference [6], the correction is a function 
    of the estimated position of the observer (Be,Le), and his motion: course 
    and speed [C.S]. And since what we are looking for is the true position, an 
    iterative process is required in order to reach the solution for the running 
    fix. The algorithm is described in the Appendix."
    The appendix gives a block diagram of the decision boxes rather than a 
    I have little doubt that Andres understands well how to tackle this 
    question, and get the right answer, as he has explained it to us on Navlist. 
    What I am questioning is his use of the term CoP, or circle of position, to 
    describe the non-circle of the transferred locus of position. Presumably the 
    program calculates the intersection of the second circle with that 
    non-circle, or else with a different circle, which has its centre displaced 
    further, so that it's tangential to the locus in the region that matters.
    This is what I wrote earlier-
    Dear Andres,
    Pleased to see your paper in Jounal of Navigation.
    Coming from an earlier generation, I didn't really take in vector
    mathematics as applied to such problems. So much of your paper went over my
    What I want to ask about are your words in 2.3 about correcting for the
    motion of an observer.
    An observer who has measured the altitude of a star to be, say 30 deg, knows
    that his locus is on a circle radius 60 deg centred at the GP of the star,
    (say, at dec = 0, GHA = 0, as in the example in paragraph 4 of my paper in
    JoN, 59, No3, pages 521-524, which I think you have). And then the  observer
    moves a known distance, say 60 miles North. His new locus is a closed
    figure, somewhat egg-shaped, but NOT a circle any longer. Does your
    algorithm in A2 find the crossings of that non-circle with another circle
    centred on another star (say, at dec = 1deg N, GHA = 45 deg W, seen at 45
    deg alt, as in that example).? What result does it give?
    Yours, 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. 
    Navigation List archive: www.fer3.com/arc
    To post, email NavList@fer3.com
    To unsubscribe, email NavList-unsubscribe@fer3.com

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