BDS/GNSS Clock And Phase Bias Products Combination For Precise Point Positioning With Ambiguity Resolution

Precise satellite clock products are important for PPP(Precise Point Positioning).In order to provide more reliable products than a single AC(Analysis Center),IGS(International GNSS Service)has been conducting GPS clock combinations since 1994.However,the IGS combination strategy had no further modification since 2001,and it can no longer meet the current developing demand for multi-GNSS precise clock combination,especially for the Chinese BDS system.Besides,IGS ACs have begun providing multi-GNSS phase bias products along with clock products.Reliable phase-bias products are the key to achieving PPPAR(Ambiguity Resolution),which can significantly shorten the convergence time and improve the positioning accuracy of PPP.Currently,there are few studies on multi-GNSS clock and phase bias products combination.To fulfill this actual demand,this paper thoroughly studies the precise clock and phase bias combination method for BDS/GNSS undifferenced PPP-AR,and evaluates the effectiveness of the proposed combination method and the performance of combined products based on multiple examples.An in-depth analysis of the components of multi-GNSS precise clocks and their temporal characteristics is conducted.In addition to the clock datum,modeling errors and initial clock bias,the inter-system bias is also taken into account.Based on those knowledge,this paper proposed a new combination method for multi-GNSS.Compared with the IGS combined clock products of 2019,the new combined method is more robust and performs better in special cases where abnormal clock datum differences exist.It is found that the RMS of clock alignment residuals are 11.6 ps,11.5 ps,45.5 ps,20.5 ps and 26.4 ps for GPS,Galileo,GLONASS and BDS-2/3,respectively.By using the combined products,multi-GNSS(GREC)PPP in static positioning mode can achieve the coordinate repeatabilities of 2.3 mm,1.5 mm and 5.6 mm in the east,north and up components,respectively,which is generally better than the results using single AC's products.This study also discussed the causes of poor consistency between different ACs' GLONASS clocks.It is pointed out that the great tangential and normal orbit differences lead to the linear and nonlinear variation of the clock differences.Based on the multi-GNSS clock combination strategy,this paper proposed a combination algorithm for BDS/multi-GNSS clock and phase bias products.Phase biases are first converted to wide-lane and narrow-lane UPDs(Uncalibrated Phase Delay)and then reconciled with satellite clocks.Finally,the wide-lane UPDs and the reconstructed clocks are combined in turns.The combination results show that about 99.98% of wide-lane UPD alignment residuals are smaller than 0.1 cycle for GPS.The counterparts of Galileo,GLONASS and Beo Dou-2/3 are98.59%,100% and 99.80%,respectively.The RMS of clock alignment residuals are 5.9 ps,6.4ps,10.6 ps and 10.9 ps.By using the combined products,the average wide-lane fixing rates of GPS,Galileo,GLONASS and BDS-2/3 are 91.1%,98.2%,98.2% and 93.1%,respectively.The average narrow-lane fixing rates can reach 96.9%,97.5%,82.6% and 92.7%,respectively.Generally,the combined products are more robust than single AC's products.Based on the combined products,GPS and Galileo combined PPP-AR in static positioning mode can achieve the coordinate repeatabilities of 1.4 mm,1.4 mm and 4.8 mm in the east,north and up components,respectively.Besides,about 75% of stations perform better by using the combined products rather than single AC's products.Coordinate repeatabilities of global BDS-only PPPAR in static positioning mode can reach 2.4 mm,2.5 mm and 7.6 mm for the east,north and up components,respectively.BDS-only kinematic positioning can only achieve the average accuracy of 3.4 cm,2.6 cm and 6.7 cm in the east,north and up components,respectively,which is currently limited by the number of BDS-3 satellites supported by ACs' products.Furthermore,this study demonstrates the effects of attitude products for correcting inter-AC clock differences,which significantly mitigate clock inconsistencies caused by differences aomong AC's attitude models during the eclipse.