Satellite Doppler observations made in the translocation mode and processed by `short arc' and `orbit relaxation' techniques can lead to very substantial improvements in relative positioning accuracies over those achieved by individual position determinations. Assessing the relative merits of different mathematical solution models is a difficult task which can only be solved by comparing them with an `absolute' standard. This has been done by using satellite Doppler observations carried out at nine stations forming part of the Edinburgh-Malvern-Dover precise traverse. This 900 km long traverse, whose stations also form part of the primary triangulation of Great Britain, has full astro-geoidal data and has been reduced and adjusted on the OSGB 77 ellipsoidal datum. The resulting coordinates are accompanied by a corresponding variance-covariance matrix. The Doppler data obtained along this traverse in the translocation mode were processed by using the newly developed Nottingham `orbit relaxation' program as well as other commercially available `short arc' programs.