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Subject: Re: Still on LOP's
WSMurdoch@XXX.XXX
Date: Wed May 08 2002 - 12:56:36 EDT
I am standing on a small island whose position is accurately charted. I take
a round of three sights all equally spaced around the horizon. When I reduce
them with respect to my known position, they can give me two kinds of LOPs;
those are toward (T) and those that are away (A). There are eight possible
combinations all equally probable. In only two of those eight combinations,
A-A-A and T-T-T, will the cocked hat that I draw on the chart enclose my
small island. I will find that I am within the cocked hat only 25% of the
time.
If I get a 'toward' twice as frequently as an 'away' because of a measuring
bias on my part, I will have three different kinds of LOPs; those that are
toward because of the bias (TT), those that are toward (T), and those that
are away (A). The two kinds of towards (TT and T) are together twice as
likely to occur as the one kind of away (A). There are now 27 combinations
of the three kinds of LOPs. There are nine of these that will include my
island; TT-TT-TT, TT-TT-T, TT-T-TT, TT-T-T, T-TT-TT, T-TT-T, T-T-TT, T-T-T,
and A-A-A. With the bias, I will be within the cocked hat 33% of time.
Thus, a skillful navigator will actually be within his cocked hat less often
than an unskilled navigator. I may be on the verge of finding the root cause
of my all too frequent success.
Bill Murdoch
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