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I have struggled a bit in reading some posts here about the cocked hat and the "symmedian point".  I feel like I walked into the middle of a conversation, and searching did not really seem to get me in on the beginning of that conversation...at least not in a way that I could understand.  Wikipedia was of no help.

I have seen a statistical analysis suggesting that where errors in LOPs are plus-or-minus some amount, that the odds of your actual position being inside the cocked hat are around 25% (MWSnap007.bmp).

I played around with this graphically, and came up the other attached images (MSsnap001 to 006).  I would appreciate help from you all in testing my inferences from these images.

First, as I look at the overlapping areas of uncertainty around the LOPs, it would seem that my most-probable-position lies in an area that includes the cocked hat, but extends outside the cocked hat into triangular zones lying outside the cocked hat, and sharing a side with it. This is the zone that has the darkest shade of grey.

Second, it may be that I can't REALLY pick a single point for a "fix"...but if I do it anyway, I could choose a point at the center of the cocked hat (the dashed-blue lines)...OR I could choose the center point of the rather larger triangle that includes the cocked hat, but lies outside it (the dashed-yellow lines). This is the zone that the darkest shade of grey due to the overlapping zones of uncertainty.

Third, if there is a use for this visual approach to determining uncertainty around the cocked hat, it could possibly be done while at sea, on a plotting sheet, by using three different colors of highlighter, drawing zones to either side of each of my LOPs...such that I could end up with different colors on the page...with presumably the darkest color zone representing a zone of most probable position.

Thank you all in advance for thinking with me on this.

Bob

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