Calculation Of Fractional Cycle Bias And Its Application On Precise Point Positioning

Precise Point Positioning(PPP)has been widely used in many aspects because of its flexibility,convenience,and high-precision.However,Uncalibrated Phase Delays(UPD)destroys the integer property of the PPP ambiguities,which limits the further improvement of convergence speed and positioning accuracy.If the fractional parts of UPDs,i.e.Fractional Cycle Biases(FCBs),are accurately estimated,the integer property of the ambiguities can be recovered and the PPP Ambiguity Resolution(PPP-AR)can be realized.This paper mainly focuses on the calculation and application of FCBs.In view of the defects of existing algorithms,we improve the methods for calculating the single-difference and zero-differential FCBs.A forecast method for real-time FCBs is also proposed.The quality control algorithm of ambiguity fixation is modified,and the ambiguity-fixed PPP solutions are obtained based on FCBs.The main work and achievements are as follows:1.A method for calculating the single-difference FCBs for full constellation using one reference satellite is proposed,where single-difference FCBs between indirect common-view satellites are obtained by converting the reference satellite.The robust estimation based on GPHASE initial value is adopted to combine the converted FCB from different sources.The improved single-difference FCBs can effectively reduce the amount of correction data with a 100% availability.The standard deviations of wide-lane(WL)and narrow-lane(NL)FCBs are 62.9% and 42.8% lower than traditional methods,respectively,and their stability is much better.2.The residual processing strategy of traditional zero-difference FCBs is improved.The new algorithm automatically adjusts the observation and residual according to the integer part of the residual,in order to eliminate the influence of the potential rounding function in the observation equation.The utilization rate of observation data for improved zero-difference FCBs adjustment has been increased from 70.73% in the traditional method to 99.01%.3.In this paper,a new quality control strategy of ambiguity fixation is proposed by combining the threshold verification and float solution assistant.Based on the improved FCBs,PPP-AR is implemented.In the static hourly solutions,the improved FCBs can correctly fix 97.2% of the observation period,and the fixed rate is increased by 32.3% compared to the traditional single-reference FCBs.The average accuracy of the fixed solutions in the N,E,and U directions is 0.49 cm,0.48 cm,and 1.45 cm,respectively,and the three-dimensional error is reduced by 46.8% compared to the float solution.In the kinematic solutions,the average convergence time of the fixed solutions is 14.32 min,which is 37.5 % shorter than that of float solutions,and the position accuracy after convergence is 4.85 cm.4.The FCBs of BeiDou Navigation Satellite System(BDS)are generated in view of the characteristics of the BDS,while WL FCBs changes less than 0.1 cycle in seven days,and the NL FCBs of MEO and IGSO satellites have the same stability as GPS.However,GEO satellites' NL FCBs can change more than one cycle in a day.By fixing the non-GEO satellites' ambiguities,the PPP-AR of BDS is implemented.The convergence time of the static fixed solutions is 78.31 min,which is 58.2% faster than that of float solutions,and the average 3D accuracy is 2.78 cm.The kinematic fixed solutions need 161.4 min to converge,and its positioning accuracy is 9.83 cm.5.In order to meet the demands of real-time applications,this paper adopts least-squares linear fitting to forecast NL FCBs for a short interval of 5 min,and 90.53% of the forecast errors are less than 0.05 cycle.The WL FCBs of the previous day are used as the value of the current day,while 92.4% of the forecast errors are less than 0.01 cycle.In real-time PPP-AR solutions: the static fixed solutions have a convergence rate of 83.33%.The accuracy in NEU directions are 1.51 cm,1.64 cm and 2.18 cm respectively,and the 3D error is reduced by 44.56% compared to the float solutions.In kinematic modes,the fixed solutions need 24.36 min to converge on average,and the 3D accuracy after convergence is 4.92 cm.