Application of Least-Squares Variance Component Estimation to GPS Observables

Abstract

This contribution can be seen as an attempt to apply a rigorous method for variance components in a straightforward manner directly to GPS observables. Least-squares variance component estimation is adopted to assess the noise characteristics of GPS observables using the geometry-free observation model. The method can be applied to GPS observables or GNSS observables in general, even when the navigation message is not available. A realistic stochastic model of GPS observables takes into account the individual variances of different observation types, the satellite elevation dependence of GPS observables precision, the correlation between different observation types, and the time correlation of the observables. The mathematical formulation of all such issues is presented. The numerical evidence, obtained from real GPS data, consequently concludes that these are important issues in order to properly construct the covariance matrix of the GPS observables. Satellite elevation dependence of variance is found to be significant, for which a comparison is made with the existing elevation-dependent models. The results also indicate that the correlation between observation types is significant. A positive correlation of 0.8 is still observed between the phase observations on L1 and L2.