NavList:

   

Reply

Following Peter Fogg's contribution obout systematic error, let's consider
that topic a bit more carefully.

He rightly separates out the possibility of systematic error in timing, and
its effects on longitudes and latitudes.

But then, the second of his "two sources", is-

| 2. A systematic error in altitude, such as using corrections with the
| wrong sign, damage to the sextant, anomalous refraction, and the like.

and he then continues-

| Correction for systematic error
|
| If the error is systematic, each position line will be displaced equally
by
| the amount and in the direction of the error.

Trouble is, that doesn't accord with his examples above, of what he calls a
"systematic error in altitude".

Take "using corrections with the wrong sign". Well, if you applied the
refraction correction with the wrong sign, it wouldn't make much difference
for high-altitude objects, but would systematically put lower bodies into
the wrong place.

Take "damage to the sextant". I wonder what damage he is thinking about
here. If any such damage has affected the scale calibration, over different
parts of the arc, or given rise to drum eccentricity or collimation error,
or if a user has misinterpreted the sign of the "box corrections" on the
certificate pasted inside his sextant box (or ignored it), these will all be
systematic errors, but all will vary with altitude.

Take "anomalous refraction". I wonder if he is thinking about "anomalous
dip" here, which varies with the low-level refraction in the path from the
horizon to the eye. Yes, that would indeed give rise to a systematic error,
common to every observation. But NOT anomalous refraction, in the light path
from the observed body. That can indeed have serious consequences, as is
clear to anyone who has watched the distortions that often occur in the
shape of the disc of a low Sun, and wondered how its altitude might be
affected. And different altitudes will be affected by different amounts.

Yes, indeed, there are causes that will give rise to a common, equal, error,
in every corrected altitude, and getting the index error wrong is perhaps
the most obvious of them. And only when it's known that the cause is such as
to give rise to equal errors at all altitudes, will the method, that he
described, apply. It applies, not to "systematic errors", in general, but to
systematic common-altitude errors only.

And there's another difficulty, that he doesn't go into, but it's a crucial
one. We have recently gone at great length into the analysis of
error-triangles in which the basic assumption was that all systematic errors
had been corrected, and only random scatter remained. Peter is now dealing
with a case where it's assumed that the errors are systematic ones (and he
says so), and he must be presuming that there are no (or insignificantly
small) random errors. If it was somehow known that the only errors in a
round of observations were common systematic ones and that there was no
random scatter, then I would concur that his construction method, to
eliminate those errors, is a valid one. But how on Earth can anyone TELL
that, from a single round of observations? In fact, both assumptions are
unrealistic; there will always be an unknown mix of random scatter and
systematic error, and how are they to be disentangled?. Only by considering
the statistics of many such rounds of sights could you reach any such
conclusions; not that I'm advocating that.

Just by chance, if there was zero systematic error, one observation in four
will show the displacements all in the same "systematic" direction, which
would indicate to Peter that some such common error was indeed present, even
if it wasn't, and he would "correct" the triangle accordingly. But that
would have been done on the basis of a wrong assumption, so would he have
"improved" anything at all? I doubt it.

The technique Peter puts forward has been proposed a number of times,
notably by George Bennett. I am going back to the example Bennett gave by
distant memory, but as I remember he was teaching a group of students who
were all measuring sextant altitudes of certain bodies. All had arrived at
consistent results except one, and Bennett was later able to show, by a
similar technique to Peter's, that there must have been a serious error in
the index correction that had been used in that case, and to put it right.
You can see that in that particular example, the method was indeed valid.
The consistency of the other students' results showed clearly that random
scatter was indeed small, by comparison with the major errors shown by the
odd-one-out. How often does that apply in real-life?

Peter's conclusions, such as that his "improved" fix will always lie inside
the triangle if the azimuths spread by more than 180 degrees, and, indeed
will be at its centre, are over simplistic, in that they apply only if it is
known that there is no random scatter, or if the systematic error is
sufficiently great as to completely overwhelm it.

Indeed, if you were to find that in every case the three position lines in
such a triangle were indeed displaced in that same "systematic" manner, in a
series of many rounds of sights, that should excite suspicion that somewhere
a systematic error exists, which needs to be tracked down and corrected.

George.

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


--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@fer3.com
To , send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply