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    Re: MP through linear fit of randomly timed observations
    From: Jaap vd Heide
    Date: 2012 Jan 26, 11:29 -0800

    I know, but your method is the other way around.

    I can now do the fitting by hand & eyeballing (if it needs be) achieving a reasonable fix with the aid (besides a sextant, almanac and a watch set to UTC [and thus to UT1 for the near future :)] ) of a single sheet of letter size paper, a ruler and a pencil.

    Fits my "needs" as a cannoeist better than having to take along a laptop or the likes.

    For fiddling with your own data, I attach one of my test-worksheets (MS Excel 2007).

    A2:A8 hold randomly picked times around a known MP of the sun on 21 April 2012 on the probable venue of the 4th Dutch Song of the Paddle meet. (hence SotP)
    [http://www.songofthepaddle.co.uk/forum/showthread.php?30707-Forth-Dutch-SOTP-meeting-20-22-april-2012-leiden-and-surroundings]

    B2:B8 hold the apparent altitude of the sun as virtually determined with the aid of Stellarium 0.11.1

    In C2:C8 a random error is introduced.

    D2:D7 hold the average value (time) of each pair of observation times (t_i+t_i+1)/2

    E2:E7 hold the average change of altitude over t_i - t_i+1 (average rate)

    D10:E14 hold the parameters of the Excel line estimation function

    D17:E18 hold two points based on the outcome of the line estimation.

    H18 holds the estimated time of MP. (in this case, the expected outcome was 11:40:23 UTC - I am not sure yet where the systematic error of 12-15 seconds I see results from; it might be in the implementation of the used time format, or in the excel least squares estimation function)

    If anybody would like to fool around with this, he/she would have to replace the Dutch functions in C2:C8 and D10:E14 by the language version of their own version of Excel. Excel function translations can be found here: http://wwwhome.cs.utwente.nl/~trieschn/excel/excel.html
    Have fun. :)

    As said, all of this could also be done by hand on a piece of paper.

    Regards,

    Jaap
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    File: 117984.sotp-mp-positioning-test.xlsx
       
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