RigorousVariance Component Estimation in Weekly Intra-Technique and Inter-Technique Combination for Global Terrestrial Reference Frames

Abstract

The rigorous variance component estimation (VCE) is a nonlinear procedure for estimating variance components of covariance matrices within a linear Gauss-Markov Model (GMM). The VCE results are strongly dependent on the structure of the covariance matrices for a given GMM. Here VCE is applied to the li-near model of intra-technique combination with SLR input solutions and of the inter technique combination with DORIS, GPS, SLR, and VLBI input solutions, both with an observation range of one week -except VLBI with a session range of 24 hours. The parameters to be estimated are weekly 3D station coordinates and daily earth orientation parameters. The data sets used here are taken from the official input solutions of ILRS and ITRF2005. After having introduced the VCE formulae for this special combination model the characteristics between intra-and inter-technique combination w.r.t. VCE are outlined. For the SLR intra-technique it is shown by examples how VCE results are used not only for the weighting of the input solutions, but also for the formulation of outlier and fail/pass criteria within automatic processing. In the inter-technique combination the VCE processing is more complicated, because two additional problems exist: the handling of different parameter set sizes (e.g GPS sets are much larger than VLBI sets) and of the stochastic behaviour of local tie sets. The question here is whether VCE is also suitable for weighting and outlier analysis in the inter–technique case. First simulation results are presented here which prove the sensitivity of VCE to deterministic and stochastic variations and hence the suitability of VCE for automatic weighting and outlier search.