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George, all this talk of simulations and errors makes me wonder how anyone can 
discuss simluations at all before one has even enumerated the possible errors 
and error conditions.

Without knowing exactly what errors need to be simulated in each case--and the 
errors will be different depending on the observer's habits and equipment in 
each case, although many will be similar--any talk of a computer simulation 
is meaningless, it would merely simulate a "condition" which has no confirmed 
relevance to the actual situation being simulated.

Consider if you will a case which everyone has omitted so far:
 Three bearings, observations, LOPs are noted. Two happen to be dead on, 
literally dead on within the width of the finest pencil. Only the third 
happens to be off, because the observer sneezed. Now, does the real position 
lie inside the cocked hat or outside the cocked hat?

 Well, in fact it lies at the intersection of two LOPs and the cocked hat is 
now an artifact generated by the fact that the third bearing--and only the 
third--was pushed to the side. It seems like all the neat math telling us 
that the position was really here or there, has omitted three finite 
positions each of which may be acccurate.


 Which brings me back to the real point: None of this matters, and it is 
arguably of no real use at all to argue whether the exact position lies here 
or there. That is the mistake of the GPS user who says "I am exactly HERE" 
while the other end of the boat hits the rocks. If you've plotted a cocked 
hat, you also plot a circle of error around it, and you say "I am in this 
circle" not in (or out) of the cocked hat. If you say "I am here" there is 
always an inference that a circle of error exists and it needs to be stated 
and quantified--unless one wants to join the novice GPS user, wondering how 
those rocks didn't get charted correctly.

   

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