Statistical analysis of position-fixing general theory for systems with gaussian errors

Abstract

The paper describes an extension of an earlier theory of position fixing in three dimensions, developed to permit the consideration of systems for which the positional errors of the position-fixing planes are not statistically independent. The general theory is based on the assumption that the position selected is the ‘maximum likelihood’ point, and relatively simple expressions are derived for the mean-square errors in the co-ordinates of this point. Covariance expression are also derived. Two examples of possible practical systems are used to illustrate the value of the theory in system studies.