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Coming back, after a few days afloat, to this question of systematic error,
and its effect on a cocked hat and on one's best estimate of position, it
seems to me that the wider picture is being lost.

Only one type of systematic error has being considered so far: the error,
such as George Bennett discovered on a voyage, in which all altitudes were
consistently out, by the same amount and in the same direction, as a result
of a wrong value for index error. It's true that if you KNOW that random
errors of observation are small by comparison, and if you KNOW that any
systematic error affects all altitudes in the same way, then it's possible
to apply a procedure such as George Bennett and Peter Fogg have described,
to discover the amount of that systematic error and correct for it.

Another type of error, in that same category, occurs when using magnetic
bearings. If an incorrect value for variation (or deviation) has been used,
it should be possible to deduce what that error was, and allow for it, as
long as you KNOW that incorrect variation (or deviation) was the cause of
the error.

But there are all sorts of things that can go wrong and can give rise to a
systematic error. The difference between a systematic error and a random
error is this: if you repeat the observation, the systematic error (or the
systematic component of the overall error) stays unchanged, the random part
of the error is different each time.

Here are some examples-

Consider taking a round of star altitudes at dusk. When converting from
local time to GMT, you get the Greenwich day wrong: it's horrifyingly easy
to do! This is a nasty systematic error. it puts the geographic positions
of your stars about 1 degree out, in the East-West direction. It puts your
fix nearly 60 minutes of longitude out, East or West, depending whether
you've added a day or lost one. Will that be apparent from the cocked hat?
No, the positions of the three stars remain mutually consistent, and will
give the same small cocked hat as before: but in the wrong position, giving
the wrong answer. So here's a systematic error that doesn't enlarge the
cocked hat.

If a different body, such as the Sun or (even more so) the Moon, with a
different daily motion, had been included as one of the trio instead of one
of the stars, then getting the date wrong would result in an immense cocked
hat. Could you apply some correction procedure for this systematic error?
No, not until you had worked out, somehow, what exactly was going wrong.

Consider taking a round of compass bearings. Two are to landmarks. The
third is to a floating seamark, a buoy or a light-vessel, say. Unknown to
us, the seamark is off-station. Here's a systematic error that will give
rise to a cocked hat. The bearings from the landmarks will intersect at, or
very near to, the true position. If we had known about that dodgy seamark,
it would have been better to just take those landmark bearings, and leave
it at that. But to increase our confidence, we added that seamark. It had
just the opposite effect, and now there's a big cocked-hat to explain. You
might try to explain it in terms of a common deviation error to all three
position lines, and work out some new value for deviation, but because that
argument was based on false premises it would give the wrong answer.

There's no end of possible reasons why things can go wrong in taking a set
of three position lines. No doubt you can add scenarios of your own. The
point I am trying to make here is this- Bennett (and Fogg) have to be
certain that any systematic error that gives rise to a cocked-hat applies
equally to every position line, before their analysis will work. To do
that, they must eliminate all other error-mechanisms of the type described
above. Is it possible to be so certain? I doubt it.

George Huxtable.

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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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