Rigorous and fast constraints transformations at the solution level: case studies for regional and global GNSS networks

The study introduces an efficient methodology to perform the transformations between station coordinate and velocity solutions where either minimum or redundant datum constraints have been imposed employing the estimated state vector and the covariance matrix thereof. The analytical methodology presented herein facilitates the datum alignment of large-network solutions, especially for the GNSS technique. The computational complexity reduction is achieved by avoiding the expensive normal equation system reconstruction and the subsequent inversion thereof, which is the current norm, in favor of an elegant approach involving the inversion of an up to 14-order matrix. All information parsed in our algorithm is readily available in the widely used space geodetic solution files following the Solution Independent Exchange (SINEX) format. Our transformation approach is evaluated in two globally distributed GNSS-derived solutions and one terrestrial reference frame with a spatial concentration in South America. The results prove the equivalence of the current and proposed algorithm and that our approach is at least an order of magnitude faster. In addition, we test the Fast Constraints Transformation (FCT) through simulated networks, with a size of up to 5000 stations. The FCT presented here accelerates the transformation by almost 140 times compared to the commonly used strategy.