Generalized Least-Squares Adjustment, a Timely but Much Neglected Tool

Abstract

A considerable amount of work has been done to make least-squares adjustment a more versatile tool, and it is the purpose of this article to give brief descriptions of all generalized least-squares adjustment techniques that have been developed so far. Algorithms have been established which will allow one to work with problems in which any number of (possibly correlated) observations occurs explicitly in any of the nonlinear condition equations, and in which at least a subset of the adjustment parameters may be known to be samples from a multivariate normal distribution with known covariance matrix but unknown modes. Furthermore, “filtering” algorithms have been developed which allow one to take advantage of previous results in finding revised adjustments when either the set of observations, or the set of adjustment parameters or both have been augmented over the sets on which the previous adjustment was based. The most recent generalization, in which the condition equations are not available explicitly but only through the differential equations whose solutions they are, was presented during this Colloquium. (Kallrath et al.,1992)