Study on calculating rigorously lateral link-up error in GPS tunnel control network based on variance-covariance matrix of coordinates

Aiming at covering the insufficiency of the approximating theory in calculation of the mean square error of lateral link-up in the GPS tunnel control network, considering the principium of GPS control network adjustment and calculation of the mean square error of tunnel lateral link-up utilizing the variance-covariance matrix of coordinates, this paper discusses a method to calculate the posterior mean square error of weight unit in the GPS tunnel control network, and to transfer the space rectangular coordinates variance-covariance matrix of the GPS control network in WGS84 to the plane rectangular coordinates variance-covariance matrix in the tunnel independent coordinate system by employing the theory of coordinate transformation and law of variance-covariance propagation. This method educes the formulae of the variance-covariance matrix of coordinates, which is used for calculating rigorously the mean square error of lateral link-up. The algorithm is developed to implement the rigorous calculation of the mean square error of lateral link-up in the GPS tunnel control network, which is also operated in the Beitian Mountain GPS tunnel control network.