NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Position lines, crossing.
From: Dave Walden
Date: 2006 Dec 12, 17:29 -0800
From: Dave Walden
Date: 2006 Dec 12, 17:29 -0800
More from monte-carlo. Using 3 LOP's 120 degree apart, no bias and normally distributed errors, I find that for 4% of the observations (based on 1,000,000 runs) the distance from the true postion to the most probable is greater than 10 times the length for the cocked hat side. That is, a small 'cocked hat' but a large distance from the true postion. 20% of observations are greater than 2 times the cocked hat side. Or, 80% of the time, you're within 2 cocked hat side lengths of the true postion. 72% of the observations are greater than .3989 cocked side lengths from the true postion. .3989 is the radius of a circle with the same area as the cocked hat. So the 28% inside the circle corresponds to the 25% inside the cocked hat. (The difference being the circle includes more area closer the the center where the probablity is higher than the corners of the cocked hat.) Note that for a constant bias, the effect cancels out for equally spaced LOP's. So, the average distance from the true position to the MPP is still .51 miles if the Std Dev is .5 min. Everything scales, so avg dist is 1.02 miles if std dev is 1 min. As expected, the monte-carlo for this case shows 100% of observations are inside the very large cocked hat if we use 1min std dev and a 5 min bias. The 3 equally spaced lines case can be thought of as a generalization of the 2 line 180 degree difference case. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---