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    Re: Making an artificial horizon, and leveling thereof
    From: Gary LaPook
    Date: 2011 Jan 22, 21:52 -0800
    Lower case"sigma" is the  Greek letter used to represent "standard deviation." When looking at a series of measurements a "normal distribution" will have more measurements near the average and progressively fewer as you move away from the average. Standard deviation  is determined from a formula used to analyze the distribution of measurements. It turns out that the calculated sigma will contain about 68% of the measurements, 95% of the measurements will be within two times sigma (2 sigma) and 99% of the measurements will be within 3 sigma of the average. Only 1% will be outside 3 sigma.

    Looking at the sigmas derived from my artificial horizon measurements and, for convenience, combining all of them we end up with an overall sigma of about 0.37 minutes of arc, 0.37 nm in the plotted LOP. So, I should expect that 68% of the altitude measurements that I take in the future with my artificial horizon will have errors less than 0.37', 95% will have errors less that 0.74' , 99% will have errors less than 1.11' and only 1% will exceed 1.11'.

    When looking at the accuracy of fixes derived from these measurements, since we are looking at errors (or uncertainties) in two dimensions, it turns out that only 39.35% of the fixes will be within 1 sigma of the actual position, 50% will be within 1.177 sigma (this radius is also know as "circular probable error, CEP), 90% within about 2.1 sigma, 95% within about 2.5 sigma and 99% within slightly more than 3 sigma.

    So using my sigma of 0.37 nm, half of my fixes should be within 0.44 nm, 90% within 0.78 nm and 99% within 1.12 nm.

    See links to prior discussions about this.






    --- On Sat, 1/22/11, Alan <alan202@verizon.net> wrote:

    From: Alan <alan202@verizon.net>
    Subject: [NavList] Re: Making an artificial horizon, and leveling thereof
    To: NavList@fer3.com
    Date: Saturday, January 22, 2011, 8:48 PM


    Here in Western PA, in late January, it's often cold, though recently The Weather Gods and or Goddesses have gone a bit wild, to much of the proverbial "good thing".

    BTW, while at this time of the year, the water in one's AH might freeze, we don't worry about earthquakes.

    The "sigma" numbers you mention, a statistics term that I do not understand, though I assume it references "error" being a small seeming number, must mean that your shots were pretty good, right? Think that after the next "big one", that the scientists fortell as "coming", they cannot say when, will end up with realtors peddling "ocean front propertry" in Arizona and or Nevada?


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