Least-Squares Variance Component Estimation Applied to GPS Geometry-Based Observation Model

Geodetic data processing usually is performed using the least-squares method. To achieve the best linear unbiased estimation، it is necessary to use the proper and realistic stochastic model of the observables. The estimation of the unknown (co) variance components of the observables is referred to as variance component estimation (VCE). In geodetic applications، VCE is also known as the observables weights estimation. In this paper، least-squares variance component estimation is applied in a straightforward manner to GPS observables for determination of the realistic stochastic model. For this purpose، the functional model used in the analysis is the GPS geometry-based observation model (GFOM). The numerical results for two receivers، namely Trimble 4000 SSi and Trimble R7، are presented. The results indicate that the correlation between observation types is significant. A positive correlation of 0. 55 is observed between the code observations on CA and P2 for Trimble 4000 SSi. Also، a significant positive correlation of 0. 64 is observed between the phase observations on L1 and L2 for Trimble R7.