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Dear Andres,

QUITE INTERESTING DISCUSSION FOR OUR COMMUNITY HERE, AND I WOULD WELCOME ANY COMMENTS ABOUT THE FOLLOWING.

Yes ! If we decide to treat FER's data as simple "standard shots", then I fully agree with your computed position numerical results.

Your latitude is 47.71582� (I find 47�71613) and your Longitude is W -087.93211� (I find W +087.93162� :-)) as I have NOT followed the latest recommendation to treat Western longitudes as negative values ****, and I find the LOP dispersion equal to 1.5 NM ).

Our computed positions fall 53 meters apart, i.e. less than 2" only. Possible reason for this difference might (most) probably be (minor) variations in height reductions, unless it might come from the apparent SUN coordinates computation but I would guess that you are using full VSOP87. It also means, which is now quite visible under such an "extreme" case, that we also most probably use the very same data crunching mathematical process / computation.

I unfortunately cannot clearly view your error ellipse which must be very "flat" and long. You certainly included it as you (always) do, but I have difficultes to single it out. It is simply so long. Certainly, and given your numerical published results, Statistics warn us of the very low confidence level of the computed fix, since for the Confidence Ellipse, you published the following :

Prob = 0.9500 , k = 2.4477

theta = 44.4592 (I would assume that it is the orientation of the great axis)

a = 48.7271 (I would assume that it would be the value in NM of the great axis)

b = 1.2957 (small axis in NM ?)

HOWEVER ... we both find positions which are 19.7 NM away from true position, simply because we are dealing here with a quite high Dilution Factor (all our 10 LOP's are more or less parallel), and this would be a REAL concern in true world.

IN OTHER WORDS, OUR POSITIONS ARE WRONG BY ALMOST 20 MILES, WITH LOP'S ALMOST PARALLEL AND WITH INDIVIDUAL KNOWN OBSERVATION ACCURACIES OF SOME 1 NM. SO, WHAT IS THE REAL OPERATIONAL VALUE OF ANY FIX DERIVED UNDER SUCH CONDITIONS ???

If I were a Skipper - Aircraft Carrier, Big Container Ship or small sailboat whatever - and as indicated yesterday, from this set of observations, I would MOSTLY and UNIQUELY keep the main and almost ONLY information they can confidently give : i.e. just one LOP as depicted yesterday. Anything else seems to me HIGHLY SUBJECT TO CAUTION.

Only in high open oceans, and far away from everything, would I give such Fix precedence over to my DR position. Unless I am totally lost without any DR whatsoever, in which case ... better "a little something" than a "big nothing" ... But in such a case I would have to be be prepared for a big position update sooner or later.

Please do not take me wrong Andr�s and I am sure you will not. I am not at all questioning neither your mathematical comprehensive and very clear and instructive approach, nor the mathematical validity of your results (otherwise I would do the same for my own case), but I am just taking the opportunity and unique "chance" of this real world example - thank you again Frank - where we DEFINITELY KNOW our computed postion error (i.e. 19.7 NM far from TRUE position) to point out that under certains conditions, just taking a computed fix postion as "Scripture" might lead to some most regrettable consequences if we do not exercise proper good sense caution.

In other words, I keep (again) questionning in this specific example the mere concept of any kind of "Fix" here, while 99 % (and maybe even 99.1 %) of the information we can extract from this real world example is only a sound and reliable LOP - no less but no more in my own viewpoint - which might be extremely useful and could nonetheless be PRICELESS in order to clear dangers (shoals or reefs) off.

Thank you for your Kind Attention, Andr�s, and thank you also for your always very professionnal results (I like accurate results, you know ... ), and

Best Regards from

Antoine M. "Kermit" Cou�tte

**** Better immediately close this "off topic" subject because it might become a lenghty one (see also Jean Meeus's strong point in his celebrated book ASTRONOMICAL ALGORITMS in its chapter "Transformation of Coordinates") !!!
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