A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2018 Oct 12, 10:03 -0700
By "linear regression" I mean a straight line which minimizes the "vertical" sum of the squared distances from the various samples to this straight line.
Lars just gave us a good and simple example in "Linear-regression-other-tools-Bergman-oct-2018-g43044".
We could use higher order terms regressions of course, such as a quadratic one. However, the x2 coefficient derived from such a limited number of observations can be quite false and misleading, thus bringing [much] more harm to the problem it is supposed to cure.
This is why the x2 coefficient could [and should] be a priori replaced by its theoretical value which can be derived from the Observer's (approximate) environment. Hence it would only be necessary afterwards to "linear regress" on the remaining terms once the effects of the the x2 coefficient have been taken in account. However, this is starting to become "complicated" as it most often requires iterations which are not bringing much definite practical interest. Such mathematical treatment and hassle is not justified at all for plain "traditional" CelNav L.O.P.'s.
I do not recommend either going into the sine/cosine regressions as they are not fit at all to our current cases. If it is perfectly true that during the course of a day the successive heights of a given body do follow a [rather regular] increase/decrease pattern, but nonetheless the period of these phenomena is close to 24 hours ... while most likely your hand held calculator will compute much shorter sine/cosine periods which are totally disconnected from physical reality.
Hope it helps.
Warm[er] Regards too from N47° (vs. N60°)
Still +22°C here as I just got a good 15 minutes swimming in the Atlantic Ocean. :-)