Statistical Determination Of The Constants Of The Atmospheric Refraction Formula

Abstract

In the present paper an efficient algorithm based on the least squares method was developed for the determination of the constants A&B of the atmospheric refraction formula. The principles of atmospheric refraction and the least squares method together with its error analysis were first developed and summarized together with its error analysis. The equations of condition for the problem were then established using N polar stars at their upper and lower culminations. Analytical formulae for the least squares solution of the equations of condition are given.  Analytical formulae of the errors estimate are also established  ,of these are: the  standard error of the fit , the  standard errors for the least squares solutions, the probable errors ,finally, the average squared distance between the exact solutions and the least squares solutions.