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Objectives: In October 2019, the International GNSS Service(IGS) began the third data reprocessing campaign(repro3). To enable more robust ambiguity resolution(AR) in precise point positioning (PPP), one of IGS important tasks is to combine satellite clock and code/phase bias products. Methods: We elaborated the precise satellite clock product model, code/phase bias product model, as well as prior corrections and specific processes for the combination of global navigation satellite system(GNSS) satellite clock and code/phase bias products. What􀆳s more, entrusted by the IGS Analysis Center Coordinator, we combined the clock/bias products of repro3 from 2000 to 2020 successfully. Results: Through the statistics of the combination, it is concluded that the integrity rate of combined clock can reach more than 95% after stabilization, which is superior to most of the products of IGS Analysis Centers. The average root mean square error of GPS and Galileo satellite navigation system satellite clock reach 6.13 ps and 5.63 ps respectively, which prove that the correction models in the combination can significantly improve the consistency. The average weight of Graz University of Technology participating in the combination reaches 21.83%, which has better precision than that of other analysis centers. The weight of phase/integer clock is higher than that of legacy clock, with better stability and precision. Furthermore, 103 stations with uniform global distribution were selected for the static PPP-AR solution to validate the positioning precision of the combined products. The results showed that the average fixed rates of GPS wide and narrow-lane ambiguity based on combined products are 90.16% and 86.72% respectively, and those of Galileo are 97.11% and 93.77% respectively, which are about 1-5 percentage points higher than those based on Center for Orbit Determination in Europe (COD) repro3 products. The average positioning precision based on combined products in the east, north and high directions is 0.154, 0.178 and 0.542 centimeters respectively, which is 20% to 30% higher than COD. Conclusions: The multi-GNSS satellite clock and code/phase combination method can effectively solve the problems of the consistency among products of analysis centers,and enable more robust ambiguity resolution in PPP-AR. Moreover, the combined products have been officially downloaded (IGSMAIL-8248:https://cddis.nasa.gov/archive/gnss/products/repro3/). [ABSTRACT FROM AUTHOR]

Objectives: Global navigation satellite system (GNSS) satellite chip shape distortions lead to individual biases in the pseudorange measurements. These biases are the results of the correlator's tracking response and thus depend on the correlator and front-end design of the receiver. As a result, different receivers are likely to exhibit inconsistent biases, called receiver-related pseudorange biases. The researches show that the receiver-related pseudorange biases cannot be absorbed by clock offset, which will affect GNSS precision applications. Methods: We estimate the receiver-related pseudorange biases of global positioning system (GPS)/BeiDou satellite navigation system (BDS) /Galileo satellite navigation system (Galileo) from 9 short/zero-baselines stations from the multi-GNSS experiment network using double difference method. The baselines are divided into three groups according to the combinations of two receivers of one baseline. Results: The results indicate that the receiver-related pseudorange biases of receivers with different manufacturers even the same manufacturers with different models cannot be neglected. For base‐lines with receivers from different manufacturers,the inconsistences of pseudorange biases can reach up to 160 cm. Conclusions: Among GPS, Galileo and BDS, Galileo shows the smallest pseudorange biases, while BDS in general is the largest. Furthermore, the stability of pseudorange biases is analyzed, the results suggest that estimated receiver-related pseudorange biases are quite stable with the standard deviation less than 12 cm for the three systems. We investigate the effect of receiver-related pseudorange biases on integer ambiguity resolution and pseudorange relative positioning, with the pseudorange biases correction, the root mean squares of fractional parts of double difference Melbourne ‐Wübbena combination are decreased by 17%, 22%, and 14% for GPS, BDS, Galileo, respectively. An improvement of pseudorange relative positioning accuracy is also confirmed, the 3D positioning errors of GPS, BDS, Galileo are reduced from 84.4, 77.3 and 60.0 to 80.1, 72.1 and 57.0 cm, respectively. [ABSTRACT FROM AUTHOR]

Objectives: BeiDou-3 navigation satellite system (BDS-3) has been fully completed and pro‐ vides reliable positioning, navigation, and timing services to global users. In order to achieve compatibility and interoperability with other global navigation satellite systems (GNSS), B1C and B2a signals have been modulated by BDS-3 based on BDS-2, which enable frequency multiplexing with E1 and E5a signals of Galileo. The inter-system biases (ISBs) are important for the fusion processing of different GNSS. Methods: This paper proposes an ISB estimation and application model based on the single-differenced observations and analyzes the ISBs between the overlapping frequencies of BDS-3 and Galileo. Based on several receivers of the new trackable BDS-3 signals, the characteristics of ISBs between BDS-3 and Galileo are revealed, and the real-time kinematic (RTK) positioning performance of BDS-3 and Galileo is analyzed. Results: The results show that the ISBs of B1C-E1 and B2a-E5a exist in different types of receivers but not in the same type of receivers. In addition, compared with BDS-3-only and Galileo-only, the combination of BDS-3 and Galileo has an improvement of more than 10% in both the success rate of ambiguity resolution and positioning accuracy. Conclusions: The multi-constellation RTK positioning performance with the introduction of ISBs is more advantageous than that of a single constellation [ABSTRACT FROM AUTHOR]

Objectives: The stochastic model of observation information describes the accuracy of observation information and its correlation, and also plays an important role in parameter estimation, quality control and accuracy evaluation. In the process of global navigation satellite system (GNSS) precision positioning, an accurate stochastic model is essential for improving the accuracy of float solution, enhancing the success rate of ambiguity resolution, increasing the accuracy of gross error detection, and obtaining the accurate and reliable positioning results. Methods: An optimization method for stochastic model of BeiDou navigation satellite system (BDS) is proposed by handling the properties of four classic elevation-dependent stochastic models based on the relationship between BDS satellite observation information and elevation. Firstly, the accuracy of BDS four-frequency observation information is evaluated by the simplified Helmert variance estimation method. Then, the model parameters could be fitted based on the estimated precision of observation information. Finally, the statistical characteristics of four stochastic models, including piecewise function, sine function, cosine function and exponential function, are tested by the overall test and ω-test methods. Results: The results show that the accuracy of pseudorange and carrier phase for BDS-3 satellite are related to elevation, and the correlation degree is different by GNSS observation types. The stochastic model of exponential function shows the best performance in the fitting error, the overall test and the ωtest. The maximum fitting errors of pseudorange and carrier phase are 0.029 m and 5.484 mm, respectively. The false alarm rates of the overall test for the float solution and the fixed solution are 5.1 % and 4.9 %, respectively. In addition, the maximum false alarm rates of the ω-test are 5.8 % for the pseudorange and 6.8 % for the carrier phase. Conclusions: The stochastic model of exponential function can get the shortest convergence time and the highest positioning accuracy for BDS-3 quad-frequency precise point positioning. It can also accurately describe the accuracy of BDS observation information and improve the accuracy and reliability of BDS precise positioning results. [ABSTRACT FROM AUTHOR]

Objectives: High-accuracy and high-reliability satellite orbit is the fundamental requirement for precise applications of low earth orbit (LEO) satellites. Due to the uncalibrated phase delay (UPD) originated from receivers and satellites, the phase ambiguity cannot be estimated as integer values. Fixing phase ambiguity to proper integer number is one of the key issues to improve the precise orbit determination (POD) accuracy. The algorithms and methods of single-difference (SD) ambiguity resolution (AR) based on integer clocks are demonstrated. The reduced dynamic POD and kinematic POD with SD AR are implemented and the performance is analyzed. Methods: Integer clock is the precise clock product that absorbs satellite UPD. By applying integer clock products, the receiver UPD can be eliminated by forming SD am-biguities between two global navigation satellite system (GNSS) satellites. And the SD ambiguity recover its integer nature and can be fixed to integer value by a rounding strategy. The onboard gravity recovery and climate experiment follow on (GRACE-FO )data (GRACE-C/D) and integer clocks from Centre National d’ Etudes Spatiales/Collecte Localisation Satellites (CNES/CLS) of April and May 2019 was employed to evaluate the improvement of reduced dynamic POD and kinematic POD accuracy with SD AR. Results: The wide-lane ambiguity fixing rates of both reduced dynamic and kinematic POD reach 99% and the narrow-lane fixing rates are about 95%. For reduced dynamic POD, the 3D root mean square error (RMSE) values of overlapping orbit difference reduced from 7.1 mm and 7.4 mm to 4.2 mm and 3.6 mm for GRACE-C/D, respectively. The standard deviation values of satellite laser ranging (SLR) residuals decrease from 15.9 mm and 14.4 mm to 10.8 mm and 11.0 mm, with improvements of 32% and 24%. Besides, the RMSE values of K-band ranging residuals reduced from 8.0 mm to 2.9 mm, demonstrating that SD AR can also improve the relative position accuracy of LEO satellites. As for kinematic POD, the 3D RMSE values for orbit difference with precise science orbit (PSO) of ambiguity-float solution are 37.5 mm and 36.4 mm, while those of ambiguity-fixed solution are 27.7 mm and 25.5 mm, with improvements of about 28%. Moreover, the SLR residuals results also improved by 20%. Conclusions: With the integer clock products, SD AR can be achieved using onboard observations of a single LEO satellite. The SD AR can significantly improve both the reduced dynamic and kinematic POD accuracy of LEO satellites. [ABSTRACT FROM AUTHOR]

Objectives: It is difficult to effectively evaluate and weaken the impact of observation environment change on data quality. To solve the problem, this paper studies a multi-point hemispherical grid model which can be applied to various satellite navigation systems.Methods: It integrates the observations of different global navigation satellite system (GNSS) satellite pairs in different observation periods to establish a global optimal multipath model. GNSS multipath error can be estimated effectively using multi-point hemispherical grid model (MHGM), image-based inverse of multipath effect and reflect the orientation of interference sources in the observation environment around stations. Results: To a certain extent the observation environment around stations can be modelled. The test under deliberate high multipath environment reveals that using MHGM significantly improved the root mean square error (RMSE) of the double-differenced carrier phase observation residuals in the period of fixed ambiguity, reducing the mean RMSE from 0.983 cm to 0.318 cm, a 67.7% improvement. In addition, the abnormal areas with large value of correction in the MHGM results is consistent with the direction of the baffle mounted at the corresponding stations. This model indicates multipath effects on GNSS carrier phase observations in different directions from the station. The test with International GNSS Service historical observations shows MHGM can effectively reflect the influence of changing multipath interference around stations on carrier phase observations, with an average improvement of 29.5% in the RMSE of residuals over the past 18 years. Conclusions: This model can be used to evaluate the changes in observation environments surrounding stations over time. It has potential application value to improve the accuracy and reliability of augmentation system products. [ABSTRACT FROM AUTHOR]

Objectives: In precise point positioning (PPP) technology, the correct fixing of ambiguity is al⁃ ways an essential part of achieving high-precision positioning. However, the wrong fixing of ambiguity will lead to serious positioning errors. Therefore, it is necessary to optimize the selection of the ambiguity sub⁃ set to ensure a more reliable fixing of PPP ambiguity. Methods: This paper proposes a PPP partial ambiguity resolution (PAR) method that combines quality control and Gram-Schmidt orthogonalization. By utilizing the multi-GNSS(global navigation satellite system) experiment (MGEX) observations in the un-differenced and un-combined PPP model, the PAR method based on Gram-Schmidt orthogonalization was com⁃ pared and analyzed with the selected reference satellite method with maximum elevation, and the performance of ambiguity resolution and positioning was assessed under the multi-GNSS conditions. Results: Experimental results show that the average epoch fixing rate of each day and each station based on the Gram Schmidt method is improved by 7.74% and 11.46% in the static mode, and 7.90% and 7.78% in the pseudo-kinematic mode, respectively, compared with that of the selected reference satellite method considering the maximum elevation. Meanwhile, time-to-first-fix (TTFF) of each day and each station based on the Gram-Schmidt orthogonalization can be significantly reduced by 22.30% and 25.42% in the static mode, corresponding to an improvement of 20.44% and 19.65% in the pseudo-kinematic mode, respectively, compared with that of the selected reference satellite method considering the maximum elevation. As far as multi-GNSS PPP AR is concerned, multi-GNSS PPP AR has a significant improvement on the convergence time of BDS (BeiDou navigation satellite system) only. The convergence time of horizontal components is shortened by 20.00 min on average at 95% confidence level, and the vertical components are shortened by 19.00 min on average. For the positioning accuracy aspects, the positioning accuracy of horizontal components is improved by 1.50 cm on average, while that of vertical components is improved by 1.12 cm on average. Conclusions: The PPP PAR algorithm based on the Gram-Schmidt method can significantly improve the performance of ambiguity resolution and positioning accuracy. [ABSTRACT FROM AUTHOR]

Objectives: Satellite clock difference (SCB) is affected by many factors, such as data discontinuity, jump and gross error, among which the gross error is the most representative. Traditional SCB gross error detection method is the median absolute deviation (MAD) method. Methods: With the single difference of SCB as the research object, we analyzed the working principle of traditional MAD method. In view of the deficiency of traditional MAD in SCB gross error detection, an improved gross error detection method was proposed. Firstly, the ambiguity in mathematical expression was eliminated by optimizing the model structure, and then dynamic MAD was generated based on the basic principle of ridge regression, which effectively overcame the interference of some single difference data with significant trend changes on gross error detection. Results: We used International Global Navigation Satellite System Service precision SCB as reference for experiments. Compared with traditional MAD, the detection accuracy and recall rate of the proposed method were better than traditional MAD, especially for the data with obvious change of trend characteristics. Conclusions: The proposed method has obvious advantages in gross error detection accuracy and recall rate and has high application value. [ABSTRACT FROM AUTHOR]

Objectives: The frequency division multiple access technology of GLONASS causes IFB (inter‑ frequency bias) when the receiver receives signals from different satellites, which makes it difficult to fix the ambiguity of GLONASS. It is an important factor that makes the orbit accuracy of GLONASS inferior to that of GPS （global positioning system） . At present, only CODE (centre for orbit determination in Eu‑ rope) among the IGS (international GNSS service) analysis centers provides GLONASS ambiguity ‑fixed orbits. To improve the orbit accuracy of GLONASS, it is necessary to develop a method to fix ambiguity in GLONASS all baseline and all constellation orbit determination. Methods: Based on a GLONASS ambiguity fixing method for long baseline, GLONASS ultra‑rapid orbit determination is propsed. Firstly, the float ionosphere‑free ambiguity with a wavelength of about 5.3 cm is solved. Then the Inter‑frequency phase bias (IFPB) rate will be determined by interval search method to correct the IFPB. After the IFPB is eliminated, the double difference ionosphere‑free ambiguity can be fixed and then the ambiguity‑fixed ultra‑rapid orbit is obtained. Results and Conclusions: The effect of this method in the GLONASS ultra‑rapid orbit determination is verified and analyzed by using globally distributed stations. The results show that the IFPB rates are relatively stable within one month. The fixing ‑rate of GLONASS satellite ambiguity after correcting IFPB decreases with the increase of baseline length. The highest fixing‑rate is 95%, the lowest is 88%, and the average is 94%. After the ambiguity is fixed, compared with the CODE product, the accuracy of the ultra‑rapid orbit is increased by 26.8% and 18% for the calculation part and the 3‒6 hour forecast part respectively, the accuracy of the inner precision is increased by 20% and 13% for the calculation part and the 3 ‒ 6 hour forecast part respectively, which indicates that this method can effectively fix the GLONASS ambiguity and improve the accuracy of ultra‑rapid orbit. [ABSTRACT FROM AUTHOR]

The uncertainty of distance‐related error of global navigation satellite system is gradually increasing with the increase of distance between the reference stations and the rover station. Therefore, the dual ‐sys‐ tems of global positioning system (GPS) and BeiDou satellite navigation system (BDS) network real ‐ time kinematic (RTK) method was presented to meet the demand of high‐precision long range positioning RTK. Firstly, the wide‐lane ambiguities were fixed by the multi‐frequency observation data of GPS and BDS be‐ tween long‐range reference stations. The satellite clock errors can be eliminated by the double‐difference so‐ lution model, simultaneously the atmospheric error and satellite orbit errors can be weakened. Then the double ‐ difference carrier phase integer ambiguities can be fixed by the resolution model including atmo‐ spheric error and carrier phase ambiguity. The method of classification error corrections between long‐range reference stations network was used. The observation errors were classified, according to the characteris‐ tics of observation errors between long‐range reference station network. The ionosphere errors and non‐dis‐ persive errors of the rover station were calculated by using the reference stations’error correction and regional error interpolation. The atmospheric errors and satellite orbit errors of the rover station can be weakened by the method of interpolation. Then the errors of GPS/BDS carrier phase observation of the rover station were removed by the calculation errors. The carrier phase integer ambiguities of the rover station can be fixed by the method of resolution integer ambiguity with multi ‐frequency carrier phase, and the position of the rover station was obtained by the fixed ambiguities. The algorithm validation was carried out by the data on long ‐ range reference station network. Three long ‐ range reference stations and one rover station were used to test in Central China. The positioning accuracy of centimeter can be obtained by the algorithm of du‐ al ‐ systems of GPS and BDS network RTK. At the same time, single system can also get the centimeter level of position and the GPS is better than BDS. The method of dual ‐systems of GPS and BDS network RTK can guarantee the positioning accuracy of the rover station. The results of experiment indicate that the GPS/BDS long ‐ range network RTK can be realized and the centimeter level positioning accuracy can be achieved by this algorithm. [ABSTRACT FROM AUTHOR]

The experimental satellites of BeiDou global navigation satellite system (BDS‐3) broadcast new B1C / B2a / B2b signals that overlap with GPS L1/L5 signals and European Galileo E1/E5a/E5b signals, which provides the opportunity of tightly combined relative positioning for short baselines with observations from GPS, Galileo, and BDS ‐ 3 experimental satellites. In this contribution， we first evaluate the value and time‐domain stability of differential inter‐system bias (DISB) between overlapping frequencies of GPS, Galileo, and BDS ‐ 3. The results show that the DISB of the same type of receiver is close to 0, and its influence can be ignored in the tightly combined relative positioning. Then we preliminarily evaluated performance of single‐epoch tightly combined relative positioning for short baselines with observations from GPS， Galileo， and BDS‐3 experimental satellites. The results show that, compared with the traditional loosely combined model, the tightly combined model can significantly improve the success rate and reliability of ambiguity resolution. The improvement is especially significant (approximately 25% ‐45%) under environments where the observed satellites for each system are limited and only single‐frequency observations are available. [ABSTRACT FROM AUTHOR]

The satellite Fengyun 3C(FY3C) launched in 2013 and carried a global navigation satellite system (GNSS) occultation sounder, which is the first BDS/GPS compatible radio occultation sounder in the world and records both GPS and BDS measurements. It provides an opportunity for investigating the precision realtime orbit determination based on space‐borne GPS/BDS measurements. In order to realize the real‐time orbit determination based on space‐borne GPS/BDS measurements with decimeter‐level accuracy, this paper carries out in‐depth research in the following aspects. Firstly, the real‐time orbit determination mathematical model based on the space‐borne GPS/BDS carrier phase observations is introduced. Then the properties of the errors in the signal’s propagation path that originates from GPS/BDS broadcast ephemeris are analyzed, and the signal‐in ‐propagation path error(SIPPE) statistics of different kinds of GPS/BDS satellites are also presented. Based on the analysis, a pseudo‐ambiguity is modeled as a stochastic process and estimated in the real‐time orbit determmination(RTOD) filter to absorb the SIPPE error, and then the decimeter‐ level accuracy can be realized. The space‐borne GPS/BDS data from China’ s FY3C satellite are em ‐ ployed for the simulative RTOD test using the SATODS software. Results have demonstrated that the position and velocity accuracy of 30 cm and 0.3 mm/s, respectively, are achieved when using GPS/BDS carrierphase data and broadcast ephemeris. Although the accuracy of BDS broadcast ephemeris is obviously worse than that of GPS, orbit results of the GPS/BDS fusion solution with reasonable stochastic models for pseudo‐ambiguities will be slightly superior to that using single GPS data. For example, when the FY3C satellite flew over Asia/Pacific region where more BDS satellites can be tracked, the orbit accuracy can be improved by 10% with the GPS/BDS fusion solution. [ABSTRACT FROM AUTHOR]

Frequency division multiplexing of GLONASS signals causes inter - frequency bias(IFB) in the receiving equipment. IFB significantly prevents GLONASS ambiguity resolution and limits the accuracy and reliability of GLONASS positioning and orbit determination. Therefore, we present a new method for GLONASS ambiguity resolution. Firsly, it weakens the influence of inter-frequency code bias, and wide-lane ambiguities are calculated directly based on the wide-lane combined observations. Then, according to the range of inter-frequency phase bias rate, a step-by-step search schedule is designed to remove the impacts of inter-frequency phase bias on wide-lane and narrow-lane ambiguities. Finally, the ambiguity resolution can be achieved successfully. An IGS experiment network is carried out to verify the validity of this method. Experimental results show that the maximum, minimum and mean success rate of fixed ambiguities within the month were 95.4%, 88.8% and 93.45%, respectively. After ambiguity resolution, the repeatability and root mean square error (RMSE) of N, E, U components were improved; especially for E component, the repeatability and RMSE were improved 20% and 14%, respectively. This proves the validity of this method. [ABSTRACT FROM AUTHOR]

In this paper, the traditional objective function, the quadratic of difference of float ambiguity and integer ambiguity, is replaced by a modified function called sum of Li and L2 pure carrier phase residua squares when searching for a correct integer ambiguity. The integer ambiguities search space is obtained by a floating transformation and building observation model with DD (double difference) C/A code range and wide lane carrier phase. The calculation results from 18-hour static GPS data indicate that the modified is better than the traditional objective function for reliability and usability with a higher success rate [ABSTRACT FROM AUTHOR]