# Real-Time Phase Bias Estimation for BeiDou Satellites Based on Consideration of Orbit Errors
###### Abstract  
Correction of the fractional cycle bias (FCB) in the undifferenced ambiguity allows precise point positioning (PPP) integer ambiguity resolution (IAR) to be achieved, which can improve positioning accuracy significantly. In addition, in real-time PPP-IAR, integration of the BeiDou Navigation Satellite System (BDS) can provide a significant reduction in the initial fixing time of global positioning system (GPS)-only PPP-IAR. However, the FCB quality can be considerably affected by the low precision of the BDS orbit, which then severely hampers the GPS + BDS PPP-IAR performance. Therefore, a real-time FCB estimation strategy that takes the BDS satellite orbit error into consideration was developed in this study. The slant orbit error can be absorbed by the ionosphere-free (IF) ambiguity, which can then be recovered by fixing all IF ambiguities from all the tracking stations. The estimated orbit error is then used to refine the orbit, which is broadcast along with the FCBs to enable PPP ambiguity resolution. To evaluate the proposed strategy, an experiment using 60 tracking stations covering the China region is performed in a simulated real-time mode. The a posteriori residuals of both the wide- and narrow-lane ambiguities are checked to validate the efficiency of the proposed FCB strategy. The results show that when the proposed strategy is applied, the effect of the BDS orbit error on narrow-lane FCB estimation is eliminated and more than 94% of the narrow-lane residuals are within 0.1 cycles for both the GPS and the BDS. The fixing percentage within 20 min is 46.3% for the GPS-only solution but is only 4.8% when using GPS + BDS with the traditional method. However, when the proposed strategy is used, the fixing percentage for GPS + BDS improves significantly to 91.7%. GPS; BeiDou Navigation Satellite System (BDS); precise point positioning; ambiguity resolution; fractional cycle bias; orbit error 2018100103390/rs100710099  
integer resolutions can be achieved through application of improved satellite products in which the FCBs have been separated from the integer ambiguities [5; 7; 8; 9]. While major achievements have been reported with regard to ambiguity-fixed PPP, the PPP technique still requires long convergence times of 30 min or more to obtain centimeter-level positioning accuracy or to produce its first ambiguity-fixed solution [10]. Such long convergence times are not acceptable for a wide range of applications. Recently, some researchers proposed use of the Global Navigation Satellite System (GLONASS) to help with global positioning system (GPS) PPP ambiguity resolution. [PERSON] et al. [11] studied the initial fixing time (IFT) improvements by adding GLONASS observations to help with GPS PPP ambiguity resolution, in which only the GPS ambiguity is fixed and GLONASS is left floating. Their results showed that the addition of GLONASS can reduce the IFT by approximately 5% when compared with GPS-only solutions. [PERSON] and [PERSON] [12] performed a similar analysis and found that the average IFT could be shortened by 27.4% in static mode and by 42.0% in kinematic mode. Later, other researchers analyzed the effects of simultaneous fixing of the GPS and GLONASS ambiguities; the results of [PERSON] and [PERSON] [13] showed that the fixing percentage within a 10-min period for kinematic PPP improved from 39.81 to 87.50%, while a similar improvement from 46.8 to 95.8% was reported by [PERSON] et al. [14]. The BeiDou Navigation Satellite System (BDS) has been independently constructed and operated by China and has provided an official service in the Asia-Pacific region since 27 December 2012. The BDS satellite constellation is currently composed of five geostationary Earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites and four medium Earth orbit (MEO) satellites. Given the availability of precise clock and orbit products for the BDS satellites, it is therefore necessary to investigate the GPS + BDS PPP ambiguity resolution performance.