This is a discussion of problems with David Wilson's
otherwise excellent averaging analysis...
In model0.gif the Y axis has had the log taken of it.
The RMS range would have easily fitted in without the
log. This makes the results of this graph less
obvious. The short term results appear bad, but
actually that is almost entirely due to the log, the
results are actually very good, as you can see from
my own non-log graphs. Thus it is difficult to be
able to make comments of the first 3 minutes being
"correlation effect dominating", whatever that might
mean.
At this point the derivative should have been taken,
to show clearly what effects were happening at that
time. But there was no derivative done. As you can
see from my own graphs, the derivative tells a very
different story.
The tables show RMS error, mean error, median error, 95%
error and max error (which is even more distance
calculations than I have provided), but no mention of
search area. Given that some/many applications are
search area problems, those figures should have also
been included, as part of a general discussion of the
various ways the waypoint may be being used.
There is also no mention of how the cost of averaging
has a bearing.
Next we have...
> Although in theory it is always better to average, due to the
... it's not just in theory, it's in practice too, as his
own empirical measurements show beyond a doubt. The reason
he made a statement like this at all is because of an old
argument about the value of short term averaging. The bias
is obvious.
> correlation of errors, averaging for only a couple minutes does
> not improve the accuracy (error distance from the true position)
> to an amount that is worthwhile for most users.
"worthwhile" is something that generally means "cost-justified".
Given that there is no mention of cost in the analysis, nor
any discussion about the various uses of a waypoint, this
all-encompassing statement does not bear close scrutiny.
In actual fact for "most users" the time taken to enter the
waypoint name is usually completely free averaging time, and
is thus the MOST worthwhile, infinitely more valuable than
any subsequent for-cost averaging. Secondly, even assuming
linear cost, as you can see from my own graphs, the most
worthwhile averaging period is generally quite low, e.g.
5 minutes 7 seconds for average search area applications.
Here is a sample of some figures provided from John
Galvin's data, dealing with RMS, not average search area...
The 2 minute average produces 2.01 metres reduction per minute in RMS.
The 4 minute average produces 2.29 metres/minute
The 8 minute average produces 2.02 metres/minute
After that, it just gets worse, so a 15 minute average actually
is LESS "worthwhile" than a 2 minute average.
Also there is also no mention of the fact that the first
10m of RMS reduction is generally more important than the
last 10m, making the short term averages even more valuable.