A modification of an algorithm by Golub and Plemmons for large linear least squares in the context of Doppler positioning

This paper considers the solution of the geodetic Doppler multistation adjustment, i.e., the problem of computing the positions of several stations observing the Doppler shift on radio frequencies emitted by several artificial satellites passing over the horizon. A modification of an algorithm due to Golub and Plemmons, for solving large linear least-squares problems where the observation matrix has a block dual angular form, is proposed in this framework. This modification is shown to reduce substantially both data transfer between the tracking stations and the main computing center, and the total computational effort required to obtain the solution of the problem. Preliminary numerical results are discussed and some further comments presented.