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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Averaging
From: Chuck Taylor
Date: 2004 Oct 19, 11:11 -0700
From: Chuck Taylor
Date: 2004 Oct 19, 11:11 -0700
George Huxtable wrote, concerning the concept of averaging observed sextant altitudes over time: "But I don't see how you would apply that technique to a quantity that was changing systematically, in the way that observed altitudes change rather steadily with time (either increasing or decreasing), with a bit of random scatter superimposed." Alex Eremenko commented: "To reduce random independent errors in a measurement of a quantity that changes linearly (or does not change at all), average is the proper thing to compute." The question is, "Does it make sense to average a quantity that is varying systematically over time, such as observed sextant altitudes?" We are talking about two components of variation, one systematic and one random. As Alex pointed out, averaging is certainly useful in eliminating random variation when there is no systematic variation. I would argue that it also makes sense when the magnitude of the random variation overwhelms the magnitude of the systematic variation, such as might occur at sea in rough weather on a relatively small vessel. Peter Fogg proposed a method that in effects allows one to average observations with variation taken into account: "...the process for averaging sights is simple and effective. As many sights as possible taken over about 5 minutes of time are plotted. Time is the horizontal axis, observed altitude on the vertical. The slope of this group of sights either rises; obs to the east, or descends; to the west. This slope is then compared to a calculated line, which is then best fitted to the slope of sights. Any extreme outliers are disregarded (probably best, although it goes against ideal statistical practice). Simple and effective." This gives you the best of both worlds, with the averaging done visually. As Jim Thompson pointed out, this is quite easy to do with a computer spreadsheet. The only issue is converting altitudes and times to decimal fractions. Chuck Taylor 47d 55' N 122d 11' W _______________________________ Do you Yahoo!? Declare Yourself - Register online to vote today! http://vote.yahoo.com
