# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Still on LOP's**

**From:**Arthur Pearson

**Date:**2002 Apr 22, 22:18 -0400

I am unable to refute the various arguments for the 25% (or less) probability of the cocked hat containing the MPP. However, this note from Chuck resolves a great deal of my puzzlement over how to improve on the practice of placing my assumed position at sea within a reasonably sized cocked hat from a reliable set of sites. It makes sense to me that while the probability of being within the hat may only be 25%, that 25% probability is better than I can do by placing the MPP in any of the regions outside the hat. The only additional observation I would make is that I don't believe that for a typical set of star sights taken at sea the error around each of the sites will be random and independent error. The horizon is bright on one side, dim on the other, cloud cover intervenes intermittently, and posture and stance vary for the different sites. I frequently feel I know which sites I nailed, and which I bobbled, and those judgments factor into my determination of where I place the MPP. -----Original Message----- From: Navigation Mailing List [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM] On Behalf Of Chuck Taylor Sent: Monday, April 22, 2002 3:46 AM To: NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM Subject: Re: Still on LOP's Trevor wrote: > But, unless I am mistaking something (which is by no means > impossible!), the probability that the cocked hat lies over the true > position is numerically equal to the probability that that true position > lies within the cocked hat. From the point of view of probability theory, it is precisely the probability that the cocked hat lies over the true position that we are talking about. All the uncertainty lies in the measurements and plots of the bearings and hence in the resulting cocked hat. There is no uncertainty in the true position, only in our knowledge of the true position, as represented by the cocked hat. Trevor then went on to mention "the best estimate of the MPP". Even if we grant that the probability is 0.25 that the cocked hat lies over the true position, I would argue that the Most Probable Position (MPP) is still the center of the cocked hat. Notice that the various possible cocked hats in Geoffrey's diagram lie symmetrically about the true position. Even if you believe (with probability 0.75) that your particular cocked hat does not contain the true position, you have no idea in which direction the true position lies relative to your cocked hat, so you can do no better than select the center of your cocked hat as the best estimate of your position given available information. Can anyone refute that argument? Chuck Taylor Everett, WA, USA