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EP Running Fix vs. the Traditional Running fix -- Part II.

Yes Rob, there are explicit assumptions in both methods.  Here's a
summary of the way I see it:

(1)  To correct error in the DR, the EP running fix (EPRF) uses all
possible information in the newly acquired LOP (the distance
perpendicular to the new LOP), while retaining all possible info in
the DR that is not constrained by the new LOP (the distance along the
new LOP).  These are examples of the kinds of explicit assumptions
universally valid in estimation problems.  See the first figure below.

(2)  The traditional running fix (TRF) explicitly assumes that the
orientation of LOP1 is unchanged and that the estimated track
component perpendicular to LOP1 is accurate.  The first assumption is
good in most celestial applications (although not in others, such as
in some coastal running fixes).  The second assumption means that the
component of estimated track parallel to LOP1 is completely ignored.
This seems to be an arbitrary assumption, which is never allowed in
estimation problems.  See the second figure below.

Now let's muse a bit on these TRF assumptions:  Consider after running
a couple of days with no sights, we see the sun peek through the
clouds.  We think to ourself,  "This is really going to be wonderful.
Somehow that sun line will know that my careful dead reckoning over
the past couple days is correct perpendicular to my last moon line,
And in addition, that old sun will know what my DR error is along my
old moon line.  All this, even though the sun can't even know the moon-
line orientation!  Ain't that old-man sun marvelous?  I guess I'll
muse on him some more".

And Rob I agree, it seems that since both methods are estimates, and
both would give the correct result if there were no DR errors, the
navigator should be able to use either method to improve DR
estimates.  But again, the TRF is flawed because of its assumptions.
Since it gives the same RFIX for all tracks with arbitrary components
along LOP1 (and having the same track component perpendicular to
LOP1), it can't yield any information about this parallel component.
When one component is missing, we know nothing about the revised
track.  On the other hand, the EPRF uses only the DR estimate,
corrected by LOP2, which is indeed a measure of the accuracy of our
dead reckoning.  Specifically, the along-track cross-track components
of the line from DR to EP2 in the first figure would be the subject of
our revised DR thinking.

JK

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