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    Re: Poor St. Hilaire
    From: Andrés Ruiz
    Date: 2007 Oct 18, 12:12 +0200
    Re: Poor St. Hilaire

    I am totally agree with George.

    John, the Nautical Almanac Sight Reduction algorithm for n LoPs, (see http://www.geocities.com/andresruizgonzalez/celestial/sr.html) used the St Hilaire process

    You can play for two LoPs with the excel spreadsheet or the CelestialFix.exe software available at: http://www.geocities.com/andresruizgonzalez/celestial/nRA.html, and see how the process go on with one, two , or morte iterations or initial position for this process; reference, assumed or DR


    Andrés Ruiz

    Navigational Algorithms

    http://www.geocities.com/andresruizgonzalez

    -------------------------------------------------------------------------

    .... at some length, that for any

    arbitrary position that you specify, (call it the RP) and a defined GP and

    altitude of a body, the St Hilaire process will generate another position

    (call it the SHP), on the corresponding position circle around the body, as

    close as you can get to the RP, and will do so exactly. And I agree. So

    what?

    That is only a part of the St Hilaire process. The next step is to draw a

    tangent to the position circle through that point, knowing the azimuth

    direction. And the next step is to do the whole thing again for another

    body, and find the position where those tangents intersect.Only then is the

    process completed. And it's those parts of the operation that are affected

    by any errors in choosing the RP, divergent from the true position.

    and John goes on to say-

    | 2.  A List member has stated that the accuracy of the St. Hilaire

    | result depends on how good the initial estimated position is.

    I wonder if that was me? Whether or not it was, I think that it's true.

    | 3. And therefore the St. Hilaire method is really an iterative method.

    And I think that is true also. And indeed, so does St Hilaire. See his

    comments on page B2- 368, in which he writes "It seems to us necessary to

    determine, at least roughly, the approximations that one obtains by the

    calculations and thus to know if it is necessary to make a second

    calculation to obtain a more correct position". And on page B2-375 he works

    an example in which the error from the true position after one calculation

    is 16 miles, which after a second iteration has reduced to 0.2 miles. I

    admit that I've made no attempt to follow these sections in detail, however.

    | We've just seen that all of this is wrong.

    I've seen nothing of the kind. I remain unconvinced, as yet. What am I

    missing?


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