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 multi-stationadjustment, i.e. the problem of computing the positions of severalstations observing the Doppler shift on radio frequencies emittedby several artificial satellites passing over the horizon. Amodification of an algorithm due to Golub and Plemmons, forsolving large linear least-squares problems where the observationmatrix has a block dual angular form, is proposed in this framework.This modification is shown to reduce substantially both datatransfer between the tracking stations and the main computingcentre, and the total computational effort required to obtainthe solution of the problem. Preliminary numerical results arediscussed and some further comments presented.