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Re: How good is St. Hilaire? was: Advancing LOPs for precision fixes
From: George Huxtable
Date: 2010 Feb 27, 13:52 -0000
From: George Huxtable
Date: 2010 Feb 27, 13:52 -0000
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.