NavList:
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 20, 09:37 -0700
From: Chuck Taylor
Date: 2004 Oct 20, 09:37 -0700
--- Herbert Prinzwrote: > If Peter has in mind a simple visual approach with > paper and pencil when he > speaks of "best fit", I can accept that. But > bringing Microsoft into this stage > of the sight reduction game is a severe faux pas. Microsoft Excel is simply another tool, like pencil and paper. Some people find it easier to make a simple plot with a spreadsheet than with pencil and paper, and I think that is what Peter and Jim were suggesting. Herbert goes on to say: > The US Power Squadron recommends (in fact demands > for the sight folder to be > submitted for graduation from the JN course) that > every altitude sight be > repeated at least three times and be checked for > 'consistency'. Such a group of > sights the call a 'run'. (Junior Navigation, 99/01, > p. 2-11 and Appendix G) > They specify what 'consistency' means: A rising body > must show a steady growth > in altitude, a setting body a steady decrease. The > consistency rule is waved for > sights near the meridian. (N.B. Alexandre: Altitudes > above 75 deg are > discouraged, but admitted!). I am a member of the national USPS (United States Power Squadrons) committee that oversees the Junior Navigation and Navigation courses, and have been teaching both courses and grading USPS sight folders for I-don't-remember-how-many years. High-altitude sights are admitted for the Navigation course, but not for the Junior Navigation course. The same applies to low-altitude sights (below 15 degrees), because temperature and barometric pressure corrections are not taught until the Navigation course. > In the USPS course, averaging the sights within a > run is an option. One is > supposed to record all sights in a log (Form ED-SL > (98)) and enumerate them. The > instructions on the back of the form say that for > the reduction you can either > pick one sight from a run, or average several ones. > The only guidance given is > to dismiss obviously 'inconsistent' sights. This is not so. One run of 5 averaged sights is required for the Navigation course, but averaged sights are not otherwise admitted. USPS teaches sight averaging as one technique for compensating for random error such as might occur on a small-ish sailboat in rough weather. The instructions cited on the back of the form refer to the one instance in which averaging is required, and not to any run. (I have just re-read those instructions to be sure.) Herbert went on to discuss the appropriateness of fitting observed altitudes with linear models. > First, the altitude grows in a linear fashion near > the prime vertical. There, > you would use linear regression. Near the meridian > you would have to use a > parabolic fit. That's also easy. But what kind of a > fit do use in-between? ... I am reminded of the words of a famous statistician by the name of Oscar Kempthorne, who taught at Iowa State University: "All models are wrong; some are useful." Certainly a straight-line fit, whether by eyeball or by linear regression, is not rigorously correct in this situation. Still, within appropriate limits, it is useful for highlighting possible outliers. As Kempthorne pointed out, a good statistician does not necessarily *believe* his or her model. Standard procedure for plotting a line of position using the St. Hilaire method calls for plotting a straight line, when we know that what we "should" be plotting is the arc of a great circle. Still, the straight line is useful. -- Chuck Taylor 47d 55' N 122d 11' W __________________________________ Do you Yahoo!? Yahoo! Mail - You care about security. So do we. http://promotions.yahoo.com/new_mail