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Antoine refers to the iterative nature of the  Marcq St Hilaire method, and 
the speed with which it converges, if an initial solution is taken to be the 
the new DR value to recalculate from, a second time, or even a third.

Several years ago, I implemented the least-squares procedure for doing so, 
as described on pages 282-283 of the Nautical Almanac, and also on pages 
66-68 of the AstronavPC Manual (2000-2005). This was done on an old Casio 
730p programmable pocket calculator. Taking the 3 star-sights given on page 
283 of the almanac as an example, the solution was obtained at the third 
iteration. This was even though the convergence test had been set such that 
the computed position had to change by less than 1 mile since the previous 
iteration: quite unrealistically severe.

As Peter Hakel recently assured Gary LaPook, on 18 Feb, in "Advancing LOPs 
for precision fixes", that procedure in the Almanac does indeed allow for 
motion of the observer between observations, but that is by no means 
explicit in the explanation.

Anyway, recently, I tried spooking that algorithm by providing it with an 
initial  DR position, that's the exact antipode of that given as a starting 
DR position in the almanac; that is, E165º, S32º, instead of W15º N32º, with 
everything else unchanged. But it wasn't spooked. It took all of 9 
iterations to work its way around the World from that absurd starting point, 
but ended up once again, back at the same best-position.

So it seems a robust algorithm.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

======================

Antoine Couette wrote, on 26 Feb.,

Excellent insight of yours on Marcq Saint Hilaire's Method. And thank you 
very much.
Since MSH's method is not "stricto sensu" a "full exact one shot 
mathematical method", we should not forget that if 1 st position derived 
after first round of computation is significantly far from initial DR 
position (some 30NM/40NM if you go "manual", or only 10NM for example if you 
have quick semi-automated computation power, or as small as you wish if you 
can parameter this value in fully automated computations), we should use it 
again as an updated DR position. And here, such iteration method/algorithm 
immediately shows MSH's deadly cconvergence rate, with its actual accuracy 
limit being almost always reached to 0.1 NM/0.2 NM after the third iteration 
at the most. Its only limitation - an unavoidable and unescapable one common 
to ALL and ANY other mathematical treament of the same raw data - is both 
(in)accuracy of the measurements and (too) small interception angles of the 
LOP's.

   

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