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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Linear regression and other tools
From: Antoine Couëtte
Date: 2018 Oct 12, 02:36 -0700

RE : Linear-regression-other-tools-TonyOz-oct-2018-g43046

Dear Tony,

As understand your suggestion: you would start from a series of different linear regressions and "extend" some of them a number of minutes of time (say e.g. up to 10 or 15 minutes) into past or into future so that at a convenient chosen time you would have at hand "simultaneous" linear regressions for this same instant, a procedure which - as you expect - could improve your fix accuracy.

It looks a quite interesting idea.

However I am not sure things would be so simple.

As a general case - and to the accuracy of +/- 0.1' - the geocentric height variation of a body with respect to time is linear during a time span of only 4 to 5 minutes of time. Outside this time span higher order terms can quickly exceed 0.1', then 0.2', then 0.5' .... depending on the body to observer configuration.

Hence "extending" too much into future or into past a linear regression in order to match it with other later or sooner linear regression[s] could certainly be a very good idea if your various linear regressions are closely spaced with respect to elapsed time. But it will likely and quickly degrade the end results if you extend one or two linear regressions too far away from their averaged times.

Another reason for this caveat is that your observed/computed Linear regression "slope" is different from the actual one. And the bigger the time interval [around the averaged time of this observations set] during which your consider your heights to be exactly linear with respect to time, the bigger your potential systematic error near the ends of this interval.

Antoine M. "Kermit" Couëtte

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