star positional errors

Barron and I spent part of the afternoon discussing various approximations by which we can estimate the uncertainty in a measure of a star's centroid. In principle this is easy, when the centroid is some kind of first moment. However, astronomers have learned that first moments do not deliver the most accurate centroids. The best centroids come from the fitting of paraboloidal tops to star peaks in the image, and the errors are determined by propagation through the fit. However, this propagation is non-trivial to perform correctly; it is even non-trivial to perform it approximately!