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I wrote:

> For modern use, the fastest and safest algorithm [for a lunar distance] would
> be right in the spirit of St. Hilaire: heuristic and iterative. The distance
> is a function of time. Starting from a reasonable "assumed time", compute the
> corresponding "computed distance", compare it against the "observed
> distance", make a correction  and iterate until the difference between
> computed and observed value is small enough.

Steven Wepster asked:

> I don't see what Marc St Hilaire has to do with it. I associate him with
> the intercept method; quite something different. But maybe he has made
> other contributions to astronavigation?

Marcq St. Hilaire seems to be appreciated for the wrong reason, or at least so
in the English speaking community. Neither did he coin the name 'intercept',
nor did he invent the method of sight reduction that is nowadays known under
this name, or even his own.

He invented a concept that he called "point rapproche". This name is much more
to the point (!) for what he actually did: He introduced an indirect method
(today we would say "trial and error" or "successive approximation") into
practical nautical astronomy. To be sure, such methods have long been used in
astronomy (known as "regula falsi") but were by far too tedious to be used at
sea. St. Hilaire and others (mainly Y. Villarcau and A. de Magnac) adopted it
within a totally reformed system of position line navigation, which they called
"Nouvelle navigation astronomique".

In short, St.-H.'s method went like this: Starting from a reasonably good
estimated position, find an improved position which satisfies the observation
and is nearer to the true position (hence the name "point rapproche"). Then
using that new position as estimated position, repeat the process with a second
observation. This way, one obtaines two "points rapproches" with two position
lines through them that, when intersected with each other, give the most
probable position of the vessel.

The method has no significant advantage (if any) over Villarceau's or De
Magnac's, which we know nowadays under the name of "intercept method". Its
merit is solely that it was the first indirect method to be used on board of a
ship (as early as 1874). A main issue of  the Nouvelle astronomie was to find
the exact conditions under which a one step linear  approximation would be good
enough or whether second order or higher terms needed to be introduced, as
continued iteration still was not an option at sea. Today, of course, it would
be foolish to consider second order terms, since computers happily iterate a
first order approximation ad nauseam until the result converges with the
estimated position. Interestingly, no instruction manual on the market that I
know tells the student that the intercept method is by nature an iterative
method. But the careful reader of the U.S.N.O. Nautical Almanac, pp277-283 has
known this for a long time.

It was this spirit that I invoked when I suggested to apply the method of
successive aproximation for lunar distances in those cases where accuracy and
efficiency rather than historical emulation are of the essence. Since George
Huxtable has in the mean time outlined such an algorithm in great detail, I
believe that any further explanation would amount to carrying owls to Athens.

Best regards

Herbert Prinz (from 1368950/-4603950/4182550 ECEF)

   

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