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Indeed a fine synthesis, Antoine !

Just a few comments about your contents :

1. About 4G1, "my" MPS (Methode du Plan des Sommets) can take into account as many stars as you like, in the same computation. The celestial DOP is traced during the computation, in order to eliminate geometry problems met by Georges Bodenez -and other ones later-.

2. About 2G1, MPS is applicable as well, but the computation is iterative (the sphere is not approximated by a local plane, as proposed by Georges Bodenez).

3. About 2A1, I could find again the original publication of Carl Friedrich Gauss. This method was limited to equal altitude observations, in order to compensate instrumental errors. The same method has been reused by Observatoire de Paris. Suzanne Debarbat told me she has practiced it a lot when she was young (but she is still young !).

As I said in a previous message, Franz Brunnow introduced a full analytical (trigonometric) method on 1860. Antoine Yvon-Villarceau introduced not only 3D methods, but also a full analytical 2D method, is an appendix of his book "Nouvelle Navigation" (1877). It was based on hyperbolic trigonometry, but sh and ch functions were not tabulated at this time. So he asked to his wife to tabulate them, what she made perfectly. She was honoured by the Scientific Community as being the first women to act in this field ! 

4. About 2A3, I had contacts with James A. Van Allen. His method was 3D and similar to Georges Bodenez approach, but  later on. I know that in a US congress he met Georges Bodenez who said him that Yvon-Villarceau was the pioneer of such a method...

5. About 3A1, I had a wink on the method of General G. Hounau when I wrote my own book. It is a full analytic method starting from cosinus equations of 2 observations. I can send  you a copy of the publication, Antoine (if I find it again in the same cupboard as you !). By the way, it was prefaced by Georges Bodenez !   

6. About 3A2, the method used by Philippe Bourbon in his chapter XIV is an optimisation approach with Lagrange multipliers. I used myself a more general formulation to validate the MPS. See  PCSL (Planes with weighting, Sphere following Lagrange), in an appendix of my publication on 1996. But this PCSL had counterparts.

7. About the Earth as an ellipsoïd: It is not difficult to take the ellipsoïd into account (but the mean error is only 0,1'). I made it in a MPS derivative. It is necessary when you make a direct hybridation with GNSS measurements. But the last problem behind is the vertical deviation from the geoïd, which should need a gravitometry lab on board !

8. About LAN: many comments could be done ! If I remember well, James Cook (and his astronomer) used to process LAN by hand. When the sun was not visible at noon, he tried Douwes solution with 2 sun sights, using Douwes table he had on board.

What an interesting discussion, thank you Antoine  !

Best friendly,

Yves Robin-Jouan