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    Re: Exercise #11 AM star fix
    From: Andrés Ruiz
    Date: 2008 Jun 9, 08:47 +0200


    Fix(14.935384780070354, 145.122785888988830) ( 14º 56.1' 145º 7.4') LopLSSR

    Fix(14.935382506928963, 145.122781472048672) ( 14º 56.1' 145º 7.4') KaplanSR_Bm = 0


    I have attached:

    - The LoPs for those who want to do the traditional plotting

    - the plot for the Lops and the 95% Confidence Ellipse.

    - the solution by LS SR. (A PDF file is found at my web site explaining the method in detail)

    - the circles of position

    - the input file for CelestialFix.exe




    Note: the method used in the program "Navigator"  http://www.tecepe.com.br/nav/inav_met.htm is the traditional one, and the astronomical position is found using the average of all the LOPs intersections, as follows:

    L= Sum ( Lij . cos aij ) / Sum( cos aij )

    Is a way to obtain the position, the weight is the cos Z


    Traditionally by hand, one obtain the cog of the cooked hat as the fix, or bisectors of azimuth angle are used, (formed at the intersection of
    the two LoPs, it has the important property that is free from systematic errors, ie is the line of position when the error made in the two LoPs is the same).



    Other algorithms gives:

    B [0-90][+N/-S]

    L [0-360][+ W->E]

    Fix(14.923884650446535, -145.113092015913367)  ( 14º 55.4' -145º  6.8')     MatrixSRtIter [1]

    Fix(14.935396000607037, -145.122802550769308)  ( 14º 56.1' -145º  7.4')     MetcalfSRtIter [2]


    [1]. Watkins. R. and Janiczek. P. M., Sight Reduction with Matrices, NAVIGATION, Journal of The Institute of Navigation, Vol. 25, No. 4, Winter 1978-79, pp. 447-48

    [2]. ON THE OVERDETERMINED CELESTIAL FIX Thomas R. Metcalf and Frederic T. Metcalf. NAVIGATION Vol. 38, No. 1, 1991




    -----Mensaje original-----
    De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de Anabasis
    Enviado el: viernes, 06 de junio de 2008 10:06
    Para: NavList
    Asunto: [NavList 5343] Exercise #11 AM star fix



    Exercise #11 AM Star Fix.


          On 29 May 2008 (local date), a ship was sailing course 158 degrees

    True at a speed of 14.7 knots.  Around 05h 25m ZT (ZD -10), a round of

    sights was taken.  The DR is Latitude 14deg 56’ North, Longitude

    145deg 07.5’ East.  Height of eye is 106 feet, Temp/Press is 82 F/

    1010 MB.  Index Error is 0.0.


    Here is the sight information, all times in _Zone Time_.


    Alpheratz: Hs : 49deg 05.8’ {at} 05h 13m 38s


    Fomalhaut: Hs 40deg 09.4’ {at} 05h 15m 58s


    Vega: Hs 45deg 59.6’ {at} 05h 20m 08s


    Deneb: Hs 58deg 16.8’ {at} 05h 21m 35s


    Jupiter: Hs 43deg 52.4’ {at} 05h 22m 31s


    Moon (LL): Hs 59deg 45.4’ {at} 05h 24m 43s



    Determine a star fix at 05h25m local time.




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