A Procedure for Estimating the Variance Function of Linear Models and for Checking the Appropriateness of Estimated Variances: A Case Study of GPS Carrier-phase Observations

Abstract

In many applications of linear model theory, homogeneous variances are assumed. In practice, however, the variances are frequently heterogeneous. Therefore, to improve the results, the unknown variances have to be estimated. The appropriateness of the estimated variances has then to be checked by a suitable statistical test procedure. Such a procedure is also useful to study models of global positioning system (GPS) carrier-phase observations. While the functional model of GPS carrier-phase observations is widely accepted, the stochastic model is still under development. As well as the neglected correlations of GPS observations, a homogenous variance function is frequently assumed. In Bischoff et al. (J Geod 78:397–404, 2005), we showed by statistical testing that the assumption of constant variances is not appropriate. In this paper, we give a procedure to estimate an individual variance function for a pair of satellites and a procedure to check the appropriateness of the estimated variances. As an example, the approach is applied to double-differenced carrier-phase GPS observations.