Performance Analysis of Combined GPS, GLONASS and BeiDou RTK Based on Single Differenced Observations between Receivers

摘要

The real-time kinematic (RTK) relative positioning uses differential carrier phase observations for precise positioning determination and has been used widely. RTK positioning can be carried out as enough visible satellites (>= 4) are observed, which may not be satisfied in signal shading areas. Since the BeiDou system came into operation in December 2012, there are a total of triple satellite navigation systems offering independent PNT services today. It is obvious that combining GPS, GLONASS and BeiDou will significantly increase the number of satellites in view. In RTK positioning, the ambiguity should be able to be resolved much faster, possibly even with a single epoch of observations. However, instantaneous ambiguity resolution with a high level of reliability is still a challenging task using a single satellite system based on RTK. The available multiple navigation system signals are expected to provide great benefit for fast and reliable integer ambiguity resolution (AR). This paper will focus on combined GPS, GLONASS and BeiDou single-baseline RTK. A measurement model based on single-differenced (SD) observations between receivers has been developed. Based on this new model, an ambiguity datum at each frequency is introduced and SD receiver clock offset, differential code bias (DCB), inter-system bias (ISB) and un-calibrated phase bias (UPB) are estimated as unknowns in addition to the conventional unknowns parameters for position coordinates and phase ambiguities. An estimation procedure will also be described in which abovementioned parameters are not directly estimated, but derived from the preliminary filtering solutions, which is also beneficial to AR involving GLONASS signals because of no additional calculation for the ambiguity of reference satellite. The performance of the combined GPS, GLONASS and BeiDou RTK under different cut-off elevations varying from 10° to 40° with a 5° interval has be investigated for both the single- and dual-frequency case using real data. Satellite visibility, dilution of precision (DOP), ambiguity fixed rate (the fixed epoch number/the total epoch number) and correctly fixed rate (the correctly fixed number/the fixed epoch number) are analyzed and evaluated. According to the obtained results, the combined triple systems get better performance than that derived from using a single system or combined dual systems. The advantage becomes significant in the singlefrequency case or when the mask elevation angle turns to high. Although the cut-off elevation reaches 40°, much enough satellites can be observed, larger than 60% and 90% of all the epochs are fixed and correctly fixed for singleand dual-frequency case. Such a high cut-off elevation can be allowed with the combined RTK, which can significantly increase the GNSS applications available in constrained environments, for example in urban areas. In addition, the obtained results from our experiments indicate that the BDS navigation system performs better than the GPS or GLONASS when using a higher cut-off elevation.