The Modeling Of BDS Group Delay Variations

Beidou satellite navigation and positioning system(BDS)has been operating continuously and steadily since it announced to provide regional services in 2012.The positioning performance of the system service in the Asia-Pacific region has satisfied the design precision.With the further development of the BDS,the performance of the system has also been gradually improved steadily.At the same time,the application of the BDS in the field of positioning,navigation and timing,especially for the high-precision users is becoming increasingly widespread.However,high-precision satellite signal ranging information is one of the prerequisites to achieve high-performance positioning.The accuracy of navigation satellite signal ranging is affected by many factors.Expect for those common error sources in GNSS signals,such as satellite clock errors,ionosphere,troposphere and etc,an unmodeled error source in the code observations of GPS,which is also called the Group Delay Variation(GDV),have been observed by many researchers during recent years and it was found that the GDV varies with satellites,receivers,frequency and direction of signal.These studies help weaken the system biases in GPS code observations and imporve the positioning accuracy of single-frequency PPP in the vertical direction.And it should not be ignored in the estimation of TEC and DCB.As for BDS GDV,a lot of researches mainly focused on BDS satellite code bias but have few systematically studies and analyses for the BDS GDV.Therefore,it is of great significance to study the characteristics of BDS GDV and establish correction models for GDV considering that it can do great help improve the performance of BDS.In this paper,the existence of BDS GDV is verified.The main factors affecting BDS GDV are studied and analyzed.The BDS GDV model is established and verified.The main work and contributions of the research are as follows:The basic theory and method of BDS GDV extraction was introduced systematically.The existence of BDS GDV was verified by the data of ground stations.The main factors influencing GDV were analyzed in detail from satellite and receiver:GDVs of different satellites and different frequencies vary with nadir angle of GNSS signals,and the GDV is also affected by the elevation angle and azimuth angle of GNSS signals at the receiver end.There are differences between different receiver types and antenna types.In addition,it is found that the GDV relate to the environment temperature at some stations.In order to solve the problem that the satellite-related and receiver-related factors cannot be modeled separately,the "two-step method" model was proposed.Based on the observation data from ground station,four groups of BDS GDV models for each satellite were established using spherical harmonics model for different combinations of receivers and antenna types.Considering that some receiver-related GDVs were found to be correlated with temperature,a temperature-dependent third-order polynomial model is designed for GDV modeling individually.The effects of the BDS GDV model were verified and compared.The time series of MP combination,MW combination,and TEC based on dual-frequency pseudo-ranges were calculated at several stations.The effects of the GDV model were compared with the original time series and the correction model of BDS satellite code bias proposed by Wanninger.The BDS GDV model can eliminate the systematic bias in these time series and is better than the correction model of BDS satellite code bias as there were still trend item in some corrected station-satellite pair;The observation data during 1-week was used to verify the positioning performance of PPP with BDS GDV model applied.The results show that the positioning accuracy of the single-frequency PPP was improved by approximately 7.3%and 25.3%in the horizontal direction and the vertical direction respectively at the 95%confidence level.Compared with the known correction model of BDS satellite code bias,the accuracy in the horizontal direction was comparable while the positioning accuracy was improved by approximately 12.6%in the vertical direction.The convergence time of dual-frequency PPP was improved by about 28.7%and 37.7%in the horizontal and vertical component for positioning accuracy to be better than 20 cm at the 95%confidence level,respectively.And compared to the correction model of BDS satellite code bias,the convergence time in the horizontal direction was comparable,while the convergence time in the vertical component was improved by approximately 18.6%.Experiments show that the positioning accuracy of BDS single-frequency PPP and the convergence speed of BDS dual-frequency PPP have been improved after the BDS GDV model applied.