Indirect approach to invariant point determination for SLR and VLBI systems: an assessment

We assess the accuracy of some indirect approaches to invariant point (IVP), or system reference point, determination of satellite laser ranging (SLR) and very long baseline interferometry (VLBI) systems using both observed and simulated survey data sets. Indirect IVP determination involves the observation of targets located on these systems during specific rotational sequences and by application of geometrical models that describe the target motion during these sequences. Of concern is that most SLR and VLBI systems have limited rotational freedom thereby placing constraint on the reliability of parameter estimation, including the IVP position. We assess two current approaches to IVP analysis using survey data observed at the Yarragadee (Australia) SLR and the Medicina (Italy) VLBI sites and also simulated data of a large rotationally constrained (azimuth-elevation) VLBI system. To improve reliability we introduce and assess some new geometric conditions, including inter-axis, inter-circle and inter-target conditions, to existing IVP analysis strategies. The error component of a local tie specifically associated with the indirect determination of SLR and VLBI IVP is less than 0.5 mm. For systems with significant rotational limits we find that the inter-axis and inter-circle conditions are critical to the computation of unbiased IVP coordinates at the sub-millimetre level. When the inter-axis and inter-circle geometric conditions are not imposed, we retrieve biased vertical coordinates of the IVP (in our simulated VLBI system) in the range of 1.2-3.4 mm. Using the new geometric conditions we also find that the axis-offset estimates can be recovered at the sub- millimetre accuracy (0.5 mm).