Least-Squares Fit of a Gaussian to Radio Sources

Abstract

A general program is described for the least-squares fit of a Gaussian to an observed scan or to a re- stored lunar-occultation record. The program is written as a Fortran subroutine and will be sent to any place on request, together with a detailed description. It consists of 650 cards and occupies about 4000 memory words. The program solves for four parameters : position #, width ß, area F, and height of zero line r. It per- forms five tasks: (1) It finds a “first guess” for & and ß from the input data. (2) It iterates (by varying & and ß, and solving directly for F and r) until final values for the four parameters are obtained. (3) It gives the mean errors for these values. (4) It calculates the diameter of the source and its mean error. (5) It makes two independent reliability tests, yielding the level of significance for any systematic deviations of the data from a Gaussian. The program handles both correlated and uncorrelated noise; many checks and safety features are included. The methods chosen for the mean errors and for the reliability tests are not specific for a Gaussian; they can be used for most other cases of curve fitting as well.