A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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 <email@example.com> wrote: