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The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). The latest IGS Repro3 ERP products, which provided the IGS contribution to the latest ITRF2020, were generated without consideration of the Beidou Navigation Satellite System (BDS) observations. The global BDS, namely the BDS-3 constellation, has been completely constructed from July 2020 and the observing stations are evenly distributed globally now. Two couple dual-frequency combinations, including the B1I/B3I and B1C/B2a combinations, are commonly used for BDS-3 ionosphere-free combination usage. With the goal of identifying the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3, this research evaluated the performance of ERP estimation using B1I/B3I and B1C/B2a combinations. Firstly, we conducted a comparison of the ambiguity resolutions. The mean percentage of successfully resolved ambiguities for the BDS-3 B1C/B2a combination is 86.5%, surpassing that of B1I/B3I. The GNSS satellite orbits and ERP were estimated simultaneously, thus the accuracy of orbits could also reflect the performance of the ERP estimates. Subsequently, we validated the orbits of 22 BDS-3 Medium Earth Orbit (MEO) satellites using Satellite Laser Ranging (SLR), and the root mean square error (RMS) of the SLR residuals for the 3-day arc orbit with B1C/B2a signals was 5.72 cm, indicating superior accuracy compared with the B1I/B3I combination. Finally, we compared the performance of ERP estimation, considering both internal and external accuracy. For the internal accuracy, B1C/B2a-based solutions demonstrated a reduction in mean formal errors of approximately 17% for PM, 22% for LOD, and 21% for PM rates compared with B1I/B3I-based solutions. In terms of external accuracy, we compared BDS-3-derived ERP estimates with the IERS 20C04 products. The B1C/B2a combination exhibited a slightly better standard deviation performance and a significant reduction in mean bias by 56%, 54%, 39%, 64%, and 23% for X, Y polar motion, X, Y polar motion rates, and LOD, respectively, compared with B1I/B3I solutions. In conclusion, the results highlight the excellent signal quality for BDS-3 B1C/B2a and its superiority in ERP estimation when compared with the B1I/B3I combination. [ABSTRACT FROM AUTHOR]

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: 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]

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify due to its reliance on highly variable atmospheric humidity. In this paper, we use the NRTK approach to estimate double-differenced zenith tropospheric delays alongside ambiguities and positions based on a complete set of multi-GNSS data in a sample 6-station network in Europe. The ZTD files published by IGS were used to validate the estimated ZTDs. The results confirmed a good agreement, with an average Root Mean Squares Error (RMSE) of about 12 mm. Although multiplying the unknowns makes the mathematical model less reliable in correctly fixing integer ambiguities, adding a priori interpolated ZTD as quasi-observations can improve positioning accuracy and Integer Ambiguity Resolution (IAR) performance. In this work, weighted least-squares (WLS) were performed using the interpolation of ZTD values of near reference stations of the IGS network. When using a well-known Kriging interpolation, the weights depend on the semivariogram, and a higher network density is required to obtain the correct covariance function. Hence, we used a simple interpolation strategy, which minimized the impact of altitude variability within the network. Compared to standard RTK where ZTD is assumed to be unknown, this technique improves the positioning accuracy by about 50%. It also increased the success rate for IAR by nearly 1. [ABSTRACT FROM AUTHOR]

The Ambiguity Dilution of Precision (ADOP) is a well-known scalar measure that can be used to infer the strength of the Global Navigation Satellite System (GNSS) model of the carrier phase ambiguities involved in precise relative GNSS positioning. Odijk and Teunissen (2008a) derived closed-form expressions for single-baseline GNSS models that allow verifying the factors affecting the ambiguity resolution as well as the probability of its correct resolution as integer values. However, this weighted-ionosphere ADOP closed form assumes that the standard deviation of the ionosphere delay is dependent on a function associated with the baseline length. This means that a baseline of the same length at different locations around the world and in different moments in time would have the same standard deviation, which in practice is not true. This becomes even worse in regions like Brazil, where the ionospheric anomalies are more intense and frequent, especially in periods of high solar activity. In this work, a new method for calculating the ionospheric delay standard deviation that considers the ionospheric scintillation S4 index is proposed to improve the closed-form ADOP performance. Experiments with a baseline of 280 m located in Presidente Prudente, Brazil (magnetic latitude of around −13°), were carried out. The results showed that in periods of both weak and strong ionospheric scintillation, the introduction of S4 into the ionospheric delay standard deviation was beneficial for ADOP. The average improvement of the ADOP closed form was of around 72% in the analyzed period of weak scintillation and of 35% in the period of strong scintillation. In addition, the results showed that in periods of strong scintillation, relative positioning accuracy is around 100 times worse, up to 30 m, when compared to periods of weak ionospheric scintillation. [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]

To derive surface displacement, interferometric stacking with synthetic aperture radar (SAR) data is commonly used, and this technique is now in the implementation phase in the real world. Persistent scatterer interferometry (PSI) is one of the most universal approaches among in- terferometric stacking techniques, and non-linear non-parametric PSI (NN-PSI) was proposed to overcome the drawbacks of PSI approaches. The estimation of the non-linear displacements was successfully conducted using NN-PSI. However, the estimation of NN-PSI is not always stable with certain displacements because wider range of the velocity spectrum is used in NN-PSI than the conventional approaches; therefore, a calculation procedure and parameter optimization are needed to consider. In this paper, optimized parameters and procedures of NN-PSI are proposed, and real data processing with Sentinel-1 in the Kanto region in Japan was conducted. We confirmed that the displacement estimation was comparable to the measurement of the permanent global positioning system (GPS) stations, and the root mean square error between the GPS measurement and NN-PSI estimation was less than 3 mm in two years. The displacement over 2 π ambiguity, which the conventional PSI approach wrongly reconstructed, was also quantitatively validated and successfully estimated by NN-PSI. As a result of the real data processing, periodical displacements were also reconstructed through NN-PSI. We concluded that the NN-PSI approach with the proposed parameters and method enabled the estimation of several types of surface displacements that conventional PSI approaches could not reconstruct. [ABSTRACT FROM AUTHOR]