Weighted quasi-stable combined adjustment of two-order horizontal control network using posteriori variance to determine the weight

Abstract

To address the difficulty in reasonably determining the datum in the combined adjustment of a two-order horizontal control network, a new weighted quasi-stable adjustment method is proposed that uses posteriori variance to determine the weight of the datum. First, the most suitable classic datum is selected from the high-order control points to fix the coordinate system, and the posterior variance matrix of the high-order control points is obtained by the classical free network adjustment. Then, keeping the coordinates of the high-order control points unchanged and taking them as the quasi-stable datum, the datum weight matrix is determined according to the posterior variance matrix, and weighted quasi-stable combined adjustment is performed to effectively use all the high-order control points to restrain the error accumulation in the low-order network. Finally, to achieve better conformity between the coordinates of the high-order control points and the low-order observations, the weighted quasi-stable combined adjustment is carried out iteratively until the posteriori variance matrix remains unchanged before and after the adjustment. The proposed method is applied to the combined adjustment of the route plane control network and track control network of high-speed railway as well as the ground and tunnel control networks of a particle accelerator. The adjustment result of this method is compared with the adjustment results of classical free network and annexed network. Experimental results show that the root-mean-square of positional error of the proposed method is close to the result of the annexed network adjustment and better than the result of the classical free network adjustment; the error accumulation is also effectively restrained. The relative positional error of this method is smaller than that in the annexed network, which shows that the proposed method can effectively reduce the influence of high-order control points with initial error on relative positional error.