Elliptical Gaussian fits are used in astronomy for accurate measurements of fundamental source parameters such as central position, peak flux density, and angular size.The full value of a noise-limited image can be realized only if the effects of noise on the fitted parameters are estimated accurately.This paper presents the equations of error propagation for two-dimensional elliptical Gaussian fits in the presence of Gaussian noise plus a new method that simplifies the use of a priori size constraints to reduce amplitude errors.
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J. J. Condon (1997) studied this question.