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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: Fix Maximum Probability Positions
From: Hewitt Schlereth
Date: 2013 Mar 24, 14:13 -0700

```John -

You wrote, "But the traditional advancing of the previous LOP to the DR position, ..."

This is a puzzling statement to me, and may not be what you mean.

In what you term the 'traditional running fix,' (TRF) an LOP is not advanced
TO the DR. The earlier LOP is advanced the distance and direction run between
DRs. The earlier LOP virtually never lands on the DR plotted for the time of
the sight for the most recent LOP.

Hewitt

On Mar 24, 2013, at 12:52 PM, "John Karl"  wrote:

>
> From GK:
> In figure 1 of your paper, you show a circular area of uncertainty around
your DR, which given no other information is reasonable enough.  But in
figure 5 you show an elliptical area of uncertainty, for which I can see no
justification.
>
> From JK:
> We’re assuming that with no other info, the DR uncertainty grows equally in
all directions.  After the first DR position with the circular symmetry,
Figure 2 starts with the oval narrow dark-blue line, its width uncertainty
determined by the LOP’s accuracy (for CN), and its length uncertainty formed
by the previous DR uncertainty’s size and shape (light blue).  It grows all
directions in size while retaining this the oval shape.
>
> From GK:
> Suppose, in figure 5, your course had been along the LOP1 so that DR1 was in
fact on LOP1. What would your area of uncertainty around DR1 look like then?
Since your original DR started out as a point (as shown in the figure) it
would be circular, just as in figure 1.
>
> From JK:
> It would still be oval, with it’s long axis parallel the LOP1, because it
grew from expanding equally it all directions from the oval narrow dark-blue
section on LOP1.  The uncertainty area would only be circular when the origin
of the DR run is a true fix of two or more LOPs.  So in Figure 3 all the DR
uncertainty areas are oval.
>
> From GK:
distance run is that it does not create a new DR position, as you attempt to
do. It retains the LOP as an LOP, but makes use of the estimated course and
distance run information in a reasonable way to re-locate the LOP.
>
> From JK:
> The estimation approach uses all available info, makes no unnecessary
assumptions, and no contradictions.  (This seems to be a difficult principle
accept.)  After a DR run with its associated uncertainties (in all
directions), we are indeed at a new DR location.
>
> But the traditional advancing of the previous LOP to the DR position, and
placing RFIX at its intersection with the new LOP, makes a very unreasonable
assumption – it can even be viewed as a contradiction:  As I’ve written many
times this tradition assumes that our reckoning over the last run has a
perfectly accurate component perpendicular to the advanced LOP, while at the
same time, has a perfectly inaccurate component along that advanced LOP.
Furthermore, the selection of these components is entirely dependent on the
orientation of the advanced LOP, which obviously has no connection whatsoever
with DR errors along the run between LOPs.  Apparently, tradition has faith
that the stars know how to command the drift and currents to force perfection
on one component of our DR track, but not the other.
>
> From GK:
steered, distance run, or your most probable current position, which is what
"navigation" is about - having a good idea where you are at any given moment
in time. Position fixes using celestial bodies are a way to get an
independent check on your DR position. The navigation method used is actually
dead reckoning first, last and always.
>
> From JK:
> Doesn’t “navigation” include all types, from GPS to depth contours, to spotting of land birds?
>
> From GK:
> It follows then that polluting your celestial fixes with where you
arrogantly think you are is a dangerous way to proceed. It throws out the
independent check.
>
> In your figure 5, if your LOP2 is good, then that should give you cause for
concern that your course steered was not what you thought it was. There may
well be a current flowing to the East which you had not suspected. You,
however, are not treating CN as a check on your DR, you are using CN in
combination with estimated course and distance run to create a DR, which - I
respectfully submit - is dangerous.
>
> From JK:
> The EPRF does not pollute information, it uses all known info, and no more,
i.e., it doesn’t invent any info (like the TRF does with its perfect
perpendicular distance between the LOP and its advanced version).  In the
estimation approach when the DR is updated with a new LOP, it usually doesn’t
fall on the DR location (very unlike the TRF, where without justification the
advanced line is always plotted exactly through the DR location).  It’s the
EPRF that gets an indication of error (the distance between the new LOP and
the DR location).  In contrast, it’s the traditional running fix that ignores
this independent check – and with that advanced LOP drawn exactly through the
DR it’s certainly not independent of it!
>
> Furthermore, since the RFIX distance-to-the-DR location is largely
determined by crossing angles of the LOPs, that measurement is pretty
irrelevant for evaluating the DR error.  So for these reasons, it’s the
traditional running fix that does a darn poor job revealing the DR error.
>
> IN SUMMARY:  The EPRF uses all available info, makes no unjustifiable
assumptions, and makes no contradictions.  The TRF makes assumptions that are
clearly false, and gives unrealistic estimations (some zero, some hundreds of
miles) in arbitrary directions of the dead reckoning errors (determined only
by the stars).
>
> BTW, one traditional example of the EPRF is the old consecutive noon-sun
latitude sights.  They give consecutive parallel LOPs of latitude, with
longitudes determined by dead reckoning.  The updated ship’s position is
plotted by dropping a line from the previous DR position perpendicular to the
new latitude LOP.  Nobody’s ever complained about that.
>
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```
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