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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Running fix Monte Carlo analysis
From: Paul Hirose
Date: 2013 Oct 28, 20:44 -0700

```I wrote:
> on a theoretical basis, I decided to program a Monte Carlo simulation.

That program has been improved and put online as a Windows executable
with documentation. It's been said the ultimate documentation is source
code, and that's there too (C# language).

Someone reminded me this topic was discussed in December 2009. I had no
recollection. Based on reviewing messages in the archives, it's likely I
put a kill filter on the thread because it seemed to be going nowhere.

In January 2010 Dave Walden gave results of his Monte Carlo analysis.
There was disappointingly little response. Apparently people found an
argument about the running fix more interesting than a scientific
investigation!

http://fer3.com/arc/m2.aspx/Running-Fix-vs-Estimated-Position-Monte-Carlo-assessment-Walden-jan-2010-g11469

He wrote, "First, a plot of average distance from true postion to Rfix
or EP in nautical miles. This shows a number of things. When the
crossing angle between the two LOP's is small, the traditional running
fix can produce large errors. Not surprinsing. In fact, well known and
expected. (And reassuring to find in the result!) When the crossing
angle between the two LOP's is small, the EP does well. Not surprising
after a little thought. The EP is "anchored" by the DR and doesn't get
too far away. At 90 degrees, the two methods give the same result.
Again, expected and reassuring to see. Interestingly, for crossing
fix method gives better results."

The summary on my Web page says, "a large systematic error (relative to
the random error) favors the running fix, the more so as the angle
between LOPs decreases. On the other hand, if the error is entirely
random, the estimated fix is more accurate than the running fix when
there is a large angle between the LOPs, and equally accurate at small
angles."

There appears to be little in common between those paragraphs. However,
the simulations are quite different in the magnitude of the errors,
their distribution (rectangular vs. Gaussian), presence or absence of a
systematic error superimposed on the random error, and dependence
between the separate iterations. Regarding that last, one run of my
program is a single voyage, the vessel proceeding from one running (or
estimated) fix to the next, for as many hundreds or thousands of fixes
as the user desires.

That is significant when analyzing the performance of the estimated fix,
which is more sensitive to systematic error. It might be argued that the
systematic error I used is excessive, since a navigator would surely
notice and remove such error in a long voyage. But with the program
available now, any interested reader (with Windows) can experiment with
his own settings.

--
I filter out messages with attachments or HTML.
```
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