Relative Positioning with Undifferenced Observations: Concept and Application/Experiments with BDS

Abstract

This paper reviews the history and evolution of the relative positioning based on the undifferenced (UD) observation. The internal mechanism of this method is explained by error division, that is, adopting the model of estimating quasi-clock parameter, which absorbs the unmodeled error of the receiver and the satellite to achieve the same effect of eliminating the common error explicitly by double differenced (DD) observation. With UD observation of Beidou Navigation Satellite System (BDS), various experiments are carried out to demonstrate the flexibility of the relative positioning mode presented, including network solution, static/kinematic baseline solution, and kinematic reference (kinematic for kinematic) solution. In the case of the experiment for network solution with baselines up to thousands of kilometers (2000–5000 km), precise post-processed orbit are used to cancel the influence of orbit errors, the repeatability within 1.1 cm in horizontal direction can be reached, the repeatability in vertical direction is less than 3 cm. The relative positioning precision of BDS on the condition of long baseline also needs to be improved because the phase center offset and variation of satellite antenna and receiver antenna have not been accurately calibrated, and there is still a gap of orbit precision between the current of BDS satellite and GPS. In the static baseline experiments, the broadcast ephemeris is adopted. For baseline of 800 m, the repeatability in horizontal and vertical are 3 and 8 mm, respectively, while for 30 km static baseline, they are 10 and 13 mm. In the experiments of kinematic baseline and kinematic reference solutions both horizontal and vertical precisions are in several centimeters; the latter is slightly worse because the coordinates of reference station are not accurate.