I tried to figure out how accurately one can possibly measure a proper motion, given a heterogeneous data set. I have an approximate expression, and it seems to agree with my code (ie, my code seems to hew close to the best possible errors), but I don't yet have a proof. One interesting consequence of this exercise is that the proper motion accuracy does not depend explicitly on the number of images you take, only their time span (measured appropriately) and the total signal-to-noise with which you have detected the source. For this reason, if you are concerned to beat down systematics with redundancy, go to town: Take many short exposures at many epochs rather than a few long ones. Of course this is all provided that you are gutsy enough to measure the proper motions below the individual-epoch detection limits!
David,
ReplyDeleteThat's right: accuracy should go as (image size)/(time span)/(total SNR). I have been lurking here because of WISE and faint asteroids. But how about computation time and storage?
-Ned Wright
I don't have a storage or computation time estimate, but I am looking into ways to greatly speed the calculations. There is a lot of stuff that can be pre-computed and stored, and there are a lot of hypotheses that can be ruled out without doing the full-blown chi-squared measurement.
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