Variance Component Estimation in Linear Models: Theoretical and Practical Aspects on Global Positioning System

Data processing in many fields of applications often relies on the least-squares method, for which a realistic stochastic model of the observables is needed. The estimation of the unknown (co)variance components is generally referred to as variance component estimation (VCE). A review of the existing VCE methods such as MINQUE, BIQUE, and REML is given, and the method of least-squares variance component estimation is in particular discussed. Theoretical and practical aspects of the method are elaborated. In the theoretical viewpoint, an important feature of the method is the capability of applying hypothesis testing to the stochastic model. One can then find an appropriate structure of the stochastic model which includes the relevant noise components into the covariance matrix. In the practical viewpoint, the application of the method to the global positioning system (GPS) observables is presented. Issues like time-correlated noise, satellite elevation dependence, and correlation between different observation types are of particular interest.