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But looking at your "uncertainties" diagram, the RFIX falls within the
range of uncertainty. So if your actual position at the time of LOP1 was
at "A" and not at "EP1," which is possible based on your diagram, then
your course and distance takes you to the RFIX which makes sense. This
illustrates what I wrote before that the RFIX corrects the error in
"EP1" and you should go back and determine where the reverse of your
course, as plotted starting at RFIX, cuts "LOP1" near "A."  Then go back
over your previous work and find out what caused you to plot "EP1" in
the wrong place.

gl


John Karl wrote:
> Lu & Gary,
>
> Yes, there are cases where the LOP accuracy is less than the accuracy
> of the estimated track.  But I said at the outset that I'm considering
> the opposite case, where the LOP accuracy is significantly greater
> than the track accuracy.  This occurs quite frequently with running
> fixes, such has in a one, or more, day's run with no new LOPs.
>
> In the first attached figure (labeled Uncertainties) regions of
> uncertainty are show in blue, the LOPs are drawn as lines, indicating
> that the uncertainty perpendicular to them is negligible.  When LOP1
> was acquired, the uncertainty surrounding EP1 was effectively
> collapsed to a line by LOP1.  After a run of some length, the dark
> blue line at EP1 expands equally in all directions as shown.  A MAJOR
> OBSERVATION is that the distance from DR1 to EP2 is always less than
> the distance from DR1 to RFIX.  (These distances are equal if the two
> LOPs are perpendicular.)
>
> That is, unless more is known about the shape of the uncertainty
> region surrounding DR1, EP2 is always a better estimate than is RFIX.
> Dropping a perpendicular from DR1 to LOP2 is a better estimate than
> the traditional running fix.
>
> The second figure (labeled Weird Uncertainties) shows an example where
> by some weird circumstance the DR uncertainty just happens to have
> grown, known to the navigator, more along the advanced LOP1 than
> perpendicular to it.  It's difficult to image a practical situation
> where this would happen.
>
> All this is simply said by noting that the Estimated Position concept
> fully honors the new LOP2 while retaining the information in the DR
> that is not contradicted by LOP2.
>
> And Lu, the two tracks in my previous figure need not be the same
> length.  They are just an example of two tracks that have the same
> perpendicular distance between LOP1 and its advance (speeds and even
> times can be unrelated).
>
> JK
>
>
>
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