Overdetermined Celestial Fix by Iteration

Abstract

A celestial fix which minimizes the sum of the squares of the sextant altitude residuals is presented as an alternative to constructing lines of position (LOPs) from azimuths and altitude differences. It is especially applicable to multiple sights, from one or several celestial bodies, providing covariance estimates for the longitude and latitude and a basis for discarding wild readings. The iterative algorithm which replaces the sight reduction tables can be programmed in a high-level computer language and is very robust with respect to the observer's initially guessed position. A fix from a series of sun altitudes taken for an hour after sunrise is presented as an example. Geometry makes this particular fix highly accurate in longitude and inaccurate in latitude, while the low sun angles make it liable to refraction error.