Statistical analysis of position fixing in three dimensions

This paper sets out a statistical analysis of the errors of position inherent in any position-finding system which utilises a number of ‘position-fixing planes’ and takes the point of maximum likelihood as the required position in 3-dimensional space. Formulas are given for the mean-square errors associated with the co-ordinates of position and also the covariances of these errors. A simple example is used to illustrate the use of the mean-square-error information, and expressions which give the co-ordinates of the maximum-likelihood point are derived for general application.