NavList:

Arguably, the older word "fix" is the real problem here.

The idea that you cross your lines of position and put a teensy-tinesy dot at the center of the triangle, call it a "fix", and then brag to your friends about the very small size of your triangle and the accuracy of your "fix", is deeply ingrained in navigation culture, but it's nonsensical. It's navigation LORE. 

Go into almost any navigation app on a smartphone, and you will see an uncertainty circle about a central point. Users get immediate feedback reminding them that the central dot is not their "real" position because they know their real position is not there. It's just the center of the error ellipse (usually displayed as a circle). Celestial navigators need to be re-trained to understand that the "fix" and the "most probable position" are nothing more than the center of the error ellipse. You're somewhere near the fix, somewhere near the MPP, but your probability of being exactly where you see the dot is, of course, zero.

This shouldn't be a difficult thing to get across to navigators (note: that's "navigators" with a small "n", meaning "people who navigate" --not officers in services who have trained for years as expert "Navigators"). The problem is cultural. Many of the same people who take pride in "navigation" also adhere to cultural attitudes that decry statistics. As soon as someone starts to explain that you only have some statistical probability of being within a certain distance of the spot marked as the fix or the MPP, they roll their eyes and start muttering about the evils of statistics and the good old days when a fix was a fix. Yet there are analogies we can apply to help understanding.

Most navigators today (again, small "n", as above) have gotten to the point rather early in their education where they understand that the exact instant of local noon cannot be observed by watching the Sun's altitude. The maximum altitude is the top of a locally very flat curve of changing altitude. For several minutes the altitude doesn't change. You can "call" noon, but the real, exact noon might be a minute before your call or two minutes after, or anywhere within several minutes of your call... It can't be specified exactly by observation of the Sun's altitude. The "most probable position" or in the older lingo, the position "fix" similarly represents the peak of a very flat curve of probability distribution. 

Note: the above is an analogy for teaching purposes, to get the ball rolling. If you're dealing with students that have better mathematical preparation, or who are accustomed to looking at error ellipses in smartphone apps, you probably don't need an analogy like this.

Frank Reed