On Least-Squares Adjustments within the Variance Component Model with Stochastic Constraints

The estimation of unknown, but fixed, parameters from observations requires that an underlying mathematical model exists relating the parameters, the observations, and the nature of their random errors. When least-squares techniques are applied, the estimation process is called Least-Squares Adjustment. In this memorandum, a new observational model called the Variance Component Model (VCM) with Stochastic Constraints and a LEast-Squares Solution (LESS) within that model are introduced. This new model is needed to address the specific situation when prior information exists for the parameters, but it is presumed that the respective dispersion (covariance) matrices for the prior information and the observations do not share a common variance component. This implies that, while the weights among the observations and also those among the prior information are known accurately, there still remains an unknown scale difference between them.