Mathematical model for computing precise local tie vectors for CMONOC co-located GNSS/VLBI/SLR stations

The seven co-located sites of the Crustal Movement Observation Network of China (CMONOC) in Shanghai, Wuhan, Kunming, Beijing, Xi'an, Changchun, and Urumqi are equipped with Global Navigation Satellite System (GNSS), very long baseline interferometry (VLBI), and satellite laser ranging (SLR) equipment. Co-location surveying of these sites was performed in 2012 and the accuracies of the solved tie vectors are approximately 5 mm. This paper proposes a mathematical model that handles the least squares adjustment of the 3D control network and calculates the tie vectors in one step, using all the available constraints in the adjustment. Using the new mathematical model, local tie vectors can be more precisely determined and their covariance more reasonably estimated.