NavList:

Hello to all,

Frank very kindly and very judiciously brought this to my attention:

"By the way, I think you've created some confusion by calling this "Douwe's Problem". At least in English language navigation literature, Douwe's Problem specifically refers to "latitude by double altitudes with known time interval" (and that's what it was originally)."

Frank, you are 100% right and thanks again. The confusion was only in my mind. In fact careful french writers correctly identify Douwe's problem exactly as you just defined it, e.g. Chapter XIII of the book "La navigation astronomique, Fondements, applications perspectives" by Philippe Bourbon.

For this reason, I suggest to continue our thread under the sole title: "LOP's without DR Position" with no mention whatsover to the Douve's Problem which is a distinct problem which was already solved by the end of the 18th Century.

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In order to reply to both of you Ianno (g30436) and Dave (g30435) our "LOP's without DR position" problem - again totally differnet from "Douwes's problem" - can be simply restated as follows:

You are given a set of observations (2 observations minimum) with only the times of observations, the observed heights, the course and speed of the Observer but NOT his position, and NOT EVEN his approximate DR position. How are you going to process these observations to determine a Celestial Fix ?

The published solutions fall into 2 general families:

Pure Analytical/Calculus Solutions: with one of them (French Air force Colonel) able to accomodate only "perfect and no error data" on a spherical earth for zero parallax bodies, and with another of them published by Philippe Bourbon and able to accomodate moving observers and data with errors. Probably more solutions of this nature.

3D Geometrical Solutions solved through calculus: with what seems a first publication in France in 1976 by Professor Georges Bodenez. Other similar methods have been independently discovered or rediscovered and are routinely used nowadays. These methods are iterative and can accomodate moving observers, data with errors and bodies at a finite distance computed from an ellipsoidal Earth.

The main aim of this present post is as follows:

Our "LOP's without DR" problem is not immensely difficult to be solved through 3D Geometry + Calculus.

I would not be surprised it had been solved and published somewhere [well] before the 1976 publication by Professor Georges Bodenez.

Who else could have done it, when and in which publication?

This question of course does not imply removing any merit or credit whatsoever to whomever independently discovered or rediscovered his own solution.

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Best Regards to all, and thanks again to you, Frank

Antoine