Best unbiased estimation of variance-covariance components: from condition adjustment to a generalized methodology

In this paper, we consider the general linear stochastic model in which the variance‒co-variance matrix of the observations is a linear function of the variance‒covariance components. Hence, first, we derive the formulas for the BIQUE (Best Invariant Quadratic Unibased Estimates) estimator of the variance‒covariance components in the functional model of the condition only. Next, from these particular formulas, the general procedure for the BIQUE variance‒covariance components is derived, which can be applied to all least squares adjustment functional models (condition only, Gauss‒Markov, Gauss‒Helmert, Gauss‒Helmert with constraints among the parameters).