Two new methods for solving large scale least squares in geodetic surveying computations

This paper considers the solution of linear least squares problems arising in space geodesy, with a special application to multi-station adjustment by a short arc method based on Doppler observations. We recall briefly the widely used second-order regression algorithm due to Brown for reducing the normal equations system. Then we propose two algorithms which avoid the use of the normal equations. The first one is a direct method that applies orthogonal transformations to the observation matrix directly, in order to reduce it to upper triangular form. The solution is then obtained by backsubstitution. The second method is iterative and uses a preconditioned conjugate gradient technique. A comparison of the three procedures is provided on data of the second European Doppler Observation Campaign (EDOC-2).