NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Real accuracy of the method of lunar distances
From: Trevor Kenchington
Date: 2003 Dec 31, 08:34 +0000
From: Trevor Kenchington
Date: 2003 Dec 31, 08:34 +0000
Jan, Another point for you to consider: You wrote: "you can be statistically sure that your error won't exceed the value of (SE times 3) in 99,7% of observations". You can only be sure of that if the errors in your observations are "Normally" distributed (which is to say that they follow a Gaussian distribution). This sort of "Normal" distribution is not normal at all (at least not with the biological systems I get to run statistical analyses on). If you are estimating the standard deviation as 1/0.6745 times your "probable error", oddities of the error distribution may not matter that much but once you start pushing out to the 99th percentile, even minor oddities would matter a lot. I'm not going to try guessing at the distribution of the error term in an overall estimate of GMT derived from a lunar observation but I do suspect that it has truncated ends. That is: I suspect that a navigator would discard any observation which led him to a position 45 minutes of longitude away from his DR. At least, he would be very suspicious of it and would repeat it next day, then adopt the second observation as the more accurate one. (The chance of getting two lunars in succession, each of which had a probability of 1-0.997 = 0.003 is of course 0.000009 or about one in a million. If you are that unlucky, inaccurate lunars may be the least of your problems!) Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus