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

Abstract

To achieve the best linear unbiased estimation of unknown parameters in geodetic data processing a realistic stochastic model for observables is required. This work is a follow-up to work carried out recently in which the geometry-free observation model (GFOM) was used. Here, least-squares variance component estimation is applied to global positioning system (GPS) observables using the geometry-based observation model (GBOM). The benefit of using GBOM, rather than GFOM, is highlighted in the present contribution. An appropriate stochastic model for GPS observables should include different variances for each observation type, the correlation between different observables, the satellite elevation dependence of the observables’ precision, and the temporal correlation of the GPS observables. Unlike the GFOM, in the GBOM two separate variances along with their corresponding covariances are simultaneously estimated for the phase observations of the L1 and L2 frequencies. The numerical results for two receivers—namely, Trimble 4000 SSi (Trimble Navigation, Sunnyvale, California) and Leica SR530 (Leica Geosystems, Aarau, Switzerland)—indicate a significant correlation between the observation types. The results show positive correlations of 0.55 and 0.51 between the CA and P2 code observations for Trimble 4000 SSi and Leica SR530, respectively. In addition, the satellites’ elevation dependence of the GPS observables’ precision is remarkable. Also, a temporal correlation of about 10 s exists in the L2 GPS observables for the Trimble 4000 SSi receiver.