NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Running fix Monte Carlo analysis
From: Paul Hirose
Date: 2013 Oct 28, 20:44 -0700
From: Paul Hirose
Date: 2013 Oct 28, 20:44 -0700
I wrote: > But what about accuracy? Unable to answer the question > 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). http://home.earthlink.net/~s543t-24dst/running_fix/ 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 angles between about 25 degrees and 90 degrees, the traditional running 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. --