| Real-time Precise Point positioning(PPP)technology has become a research hotspot of domestic and foreign scientific research institutions and scholars because of its advantages of accuracy and availability.Unlike relative positioning,PPP does not need a high-density reference station.It can obtain high-precision station coordinates,receiver clock deviation and atmospheric delay with a single receiver.Therefore,PPP has been widely used in precise positioning,timing,atmospheric monitoring and other related geoscience fields.The traditional ionosphere-free PPP eliminates the influence of the first-order ionosphere in positioning,but because the linear combination reduces the number of observation equations and enlarges the noise of observation values,it will bring some adverse effects on the reliability and accuracy of positioning.However,the un-differential un-combined PPP directly utilizes the original observation value of GNSS without any linear combination,which provides more abundant measurement information,improves the redundancy of adjustment and retains ionospheric information,and is more suitable for the future development trend of multi-frequency and multi-system PPP.Many scholars at home and abroad have studied the location model of GNSS un-differential and un-combined PPP systematically and deeply,but the filtering convergence time of real-time PPP still lasts for 30 minutes or more at present.Compared with the current network RTK(Real-time kinematic),the convergence time of real-time PPP still has a long distance,which mainly limits the application of real-time PPP in some engineering fields.For the fixed solution of real-time PPP ambiguity,the CLK 9X mount point of CNES analysis center broadcasts multi-frequency un-combined phase biases products in real-time.However,few domestic and foreign literatures have clearly described the product,and no scholars have systematically analyzed this products.The research on the application of this product to three-frequency real-time PPP ambiguity fixing is very limited.Therefore,with the continuous development of real-time PPP technology,the fast convergence of filtering and the fixed un-differential ambiguity of multi-frequency and multi-system are still a difficult problem in current research.To address these needs,this paper aims to deeply study the GPS/Galileo real-time PPP positioning theory,systematically introduce the main error sources affecting positioning and their processing methods,compare and analyze the positioning performance of single/multi-system dual-frequency un-differential and un-combined PPP float solutions.Around the fast convergence of GPS/Galileo PPP,the mathematical models of single-frequency and dual-frequency real-time PPP with ionospheric constraints are expounded.A method for precisely determining the variance of ionospheric constraints is proposed to accelerate the convergence speed of filtering and improve the positioning reliability after convergence.In the aspect of GPS/Galileo PPP ambiguity fixing,the relationship between integer phase clock and un-combined phase biases in CNES analysis center is introduced in detail,and the influence of triple-frequency ambiguity fixing on positioning performance is analyzed from the aspects of convergence performance and positioning accuracy.The main work and contents of this paper are as follows:(1)The mathematical model of traditional dual-frequency ionosphere-free combination and un-differential un-combined real-time PPP is sorted out systematically.The main error sources and processing methods of PPP are described in detail.Based on the observation data of MGEX network and the real-time products of CNES analysis center,the satellite visibility,convergence and positioning accuracy of single/multi-system real-time PPP floating-point solution are analyzed.The results show that the single GPS system has the following advantages: The total number of visible satellites is about 11-13,PDOP is about 1.25-1.55.When Galileo satellite is added,at least 18 satellites can be observed worldwide.In some areas,the number of visible satellites is even as more as 22,and the number of observable satellites has nearly doubled.In terms of filtering convergence time,the un-differential and un-combined real-time PPP of single GPS system is in static and kinematic positioning mode.The average convergence time is 32.4 min and 48.3 min respectively,while the average convergence time of GPS/Galileo combination in the two positioning modes is 26.2 min and 33.8 min,and the improvement rates are 20 %and 30 % respectively.After filtering convergence,compared with single GPS system,the positioning accuracy of GPS/Galileo real-time un-differential and un-combined PPP in horizontal and vertical directions can be improved by 26% and 7.8%respectively in static mode,and 15% and 14.7% respectively in kinematic mode.(2)Starting from the undifferential and uncombination mathematical model of GNSS real-time precise single point positioning,the PPP mathematical model with additional ionospheric constraints is analyzed,and the difference between the real-time ionospheric correction provided by CNES analysis center and the post-processing GIM products of CODE is compared.In view of the difficulty in determining the weight ratio between real-time ionospheric corrections and observations,this paper proposes an ionospheric constraints weight factor search algorithm which takes historical information into account.The variance of prior ionospheric corrections is adjusted by weight factors.The optimal weight factor is found by searching according to the principle of minimizing the sum of weighted squares of posterior residuals and dynamic adjustment of post-fit residuals.The variance of the prior ionospheric correction is used to improve the positioning results.In order to analyze the positioning effect of this method applied to PPP with additional ionospheric constraints,the PPP experiments of kinematic dual-frequency,kinematic single-frequency,static dual-frequency and static single-frequency based on30-day GPS/Galileo measurement data from 30 MGEX tracking stations are carried out.The results show that the convergence speed of the new method can be increased by 36% compared with the traditional constrained algorithm.Compared with PPP without ionospheric constraints,the proposed method not only improves the convergence speed obviously,but also achieves the same positioning accuracy when the filtering has converged.(3)The mathematical model of triple-frequency GPS/Galileo undifferential and uncombined float solution is introduced in detail.The correlation among the parameters to be estimated and the reason why the undifferential ambiguity can not be fixed as an integer are expounded.The conversion formula between the integer phase clock model and the uncombined phase biases product is deduced in detail.Based on the open source software PPP-WIZARD from CNES analysis center,the performanceof the uncombined phase biases is evaluated.Meanwhile,the positioning accuracy and convergence performance of various strategies are analyzed and compared from the GPS/Galileo data of a large number of MGEX observation networks.The results show that the uncalibrated fractional offsets of GPS/Galileo single-difference wide-lane and narrow-lane show an approximate normal distribution with the mean value close to 0.The percentage of absolute deviation of single-difference wide-lane and narrow-lane with uncalibrated fractional offsets less than 0.25 cycle for GPS satellite is 97.8 % and 92.1 %,respectively,while that of Galileo satellite is 96.7 %and 87.1 %.Compared with the floati solution,the fixed triple-frequency ambiguity improves the positioning accuracy in both vertical and horizontal directions after filtering convergence.In the static positioning mode,the rate of improvement in both directions are about 20.12 %,33.33 %,and in the kinematic positioning mode,the rate of improvement are about 21.13 % and 43.52 %,respectively.In terms of filtering convergence time,the convergence time of fixed triple-frequency ambiguity strategy is better than that of other two strategies.Compared with the convergence time of float solution,the convergence time of fixed triple-frequency ambiguity in static and kinematic positioning is reduced by about 13 % and 7 %,respectively. |
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