A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Antoine Couëtte
Date: 2018 Oct 11, 12:00 -0700
Re : Linear-regression-other-tools-Morris-oct-2018-g43043
The average value of a set - here observations times and heights - belongs to the linear regression of this set.
For a given set of observations, if you are in a position to use only its average value, you are using the whole set to its best. In other words: you are using absolutely all information contained in this set, and you are not discarting any information contained in it.
Hence - for CelNav at least - [absolutely] no need to "linear regress": simply "average".
Whenever possible I personally recommend 5 observations for each and any celestial body over a maximum time span of 4 minutes of time, a duration during which second and higher order terms are always negligible - i.e. less than 0.1' - whatever the height observed. Essential reason for that ? 5 observations reduce random errors by a factor slighly above 2 (actually by the square root of 5). To reduce Random error by 3 would require 9 observations - by 4 would be 16 !!! - which is totally unrealistic as linear regression should then be replaced by at least 2nd Order Regression, which involves many more "guessing fitting" parameters.
Also, up to 4 minutes devoted to one single Body, espacially at dawn or dusk remains acceptable. You should have plenty of time to "multi shoot" at least 2 extra bodies, or even 3 extra bodies.
Observing and averaging 4 different bodies with 5 observations on each of them is an excellent practical trade-off between random error minimizing and the workload of 20 different observations.
Antoine M. "Kermit" Couëtte