Variance Component Estimation and Precise GPS Positioning: Case Study

Abstract

The underlying motivation of variance component estimation (VCE) is to construct an adequate variance-covariance (VC) matrix for the processing of global positioning system (GPS) code and phase data. Prior to developing a full procedure for VCE in precise GPS positioning, an experimental inventory has been carried out to get acquainted with the key issues in the stochastics of the GPS range observables, and hence with the structure of the eventual VC matrix. The experiences of this inventory are shown in this contribution aspect by aspect, using code and phase data of a geodetic dual frequency receiver pair on a zero baseline at a 1 s sampling interval. The paper treats elevation dependent variances, covariances between channels and between observation types, as well as time correlation. For each aspect easy-to-compute formulas are derived and attention is paid to the redundancy necessary to obtain sensible results. For the receiver at hand, elevation dependence of variance, correlation between observation types, and time correlation are found to be significant.