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I need help/suggestions on which metric/approach to use.
I am trying to estimate pointing precision by measuring the offset of the experimentally measured values from the real, theoretical values, with multiple measurements but on different quantities although from the same source.

It means I have a list of deviations of exp measured values from the theoretical values. Pretty messy explanation, I know, I will try to explain it in an example.

Specifically, I have a picture of a night sky, and I am measuring offset(angular distance) from the star in the image(experimentally measured value) and its position in the star catalog(theoretical value). And I am doing it for every star in the image. So, if I have 100 stars in the image, I have 100 calculated deviations(angular distances) of the measured values from the real values. With that, I am trying to estimate pointing precision on the random point in the image, regardless if there is a star or not. I could take the average value of all (100) separations.

Or maybe the standard deviation of that separations? Mean of Rayleigh distribution?

What would be an appropriate metric to use? Could someone redirect me to a similar problem, if there is such? Or some material to read?

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    $\begingroup$ I think a good place to start would be determining the systematic errors caused by refraction and telescope/camera pointing angle. Once those are found and your data is corrected for them you could go after random errors and. at that point, techniques like determining standard deviation would be useful. $\endgroup$
    – stretch
    Commented Mar 25, 2022 at 14:29
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    $\begingroup$ You might look at the software ASTAP. It will plate solve the image for you, and tell you what the center point is. Then you can just compare that to the expected center point. Oh, the best part, it's free. If you try to average a bunch of points, lense distortion and atmospheric effects can interfere with your calculations since the star field won't be evenly distributed. $\endgroup$ Commented Mar 25, 2022 at 15:52
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    $\begingroup$ Although the context is astronomical (and so this is on topic) I wonder if the answer is not related to astronomy. Rather is a statistical or data handling question. My limited knowledge of stats would make me think that the root-mean-square of the deviations is the correct metric, but the good folks at Cross Validated might be able to say why that is, or is not, correct. $\endgroup$
    – James K
    Commented Mar 25, 2022 at 18:30
  • $\begingroup$ @stretch Thanks. By standard deviation you mean to calculate std of separation mean, because by calculating separation I am already calculating deviation of measured coordinates vs. true(theoretical) coordiantes $\endgroup$ Commented Mar 26, 2022 at 9:07
  • $\begingroup$ @GregMiller I will look into ASTAP. I am already using Astrometry.net software which gives me RADec of center point, but not pointing at anything particular. These are results from the small camera which is used to measure telescope pointing, and telescope is pointing at the particular source. I have an offset from this camera center of FoV to the telescope pointing. $\endgroup$ Commented Mar 26, 2022 at 9:10

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