Apparatus for measuring surveying parameters, such as distances and angular displacements between an instrument survey station and a mobile survey station, with improved accuracy. The invention combines a differential satellite positioning system (DSATPS), available with positioning systems such as GPS and GLONASS, with electromagnetic measurements of distances and optically encoded angles by a conventional electro-optical survey instrument to provide survey measurements that can be accurate to within a few millimeters in favorable situations. The DSATPS relies upon pseudorange measurements or upon carrier phase measurements, after removal of certain phase integer ambiguities associated with carrier phase SATPS signals. The SATPS may be retrofitted within the housing of the conventional electro-optical instrument. In a first approach, a remote station provides DSATPS corrections for the mobile station and/or for the instrument station. In a second approach, the mobile station provides DSATPS corrections for itself and for the instrument station. In a third approach, the instrument station provides DSATPS corrections for itself and for the mobile station.