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High-precision global navigation satellite system (GNSS) positioning technology, as a hot spot in the field of satellite navigation, has expanded the in-depth development of the location-based service area, and has been widely used in smart cities, intelligent transportation, autonomous driving and other fields. First, this paper presents the current status and development of GNSS positioning technologies.Then, it explains the common basic theories such as integer ambiguity fixation, functional model and stochastic model fusion involved in multi-frequency multi-GNSS high-precision positioning, as well as the key techniques for improving GNSS positioning performance such as the non-model error processing, the cycle slip detection and data interruption repair. Based on the innovations of basic theories and key techniques, this paper introduces four new technologies for multi-frequency multi-GNSS high-precision positioning applications developed by Tongji University GNSS team in recent years. Finally, we remark the future development trend and challenges of GNSS-based high-precision positioning. [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: BeiDou-3 satellite navigation system (BDS-3) has been officially completed and provides services, network real time kinematic(RTK) is the main means to improve positioning accuracy, we present a long-distance undifference network RTK method based on BDS multi frequency and multi system observation data. Methods: First, the ambiguity resolution model considering atmospheric error parameters is used to determine the integer ambiguity of multi-frequency carrier phase of long-distance BeiDou satellite navigation system (BDS) reference station.Then,the double difference integer ambiguity between reference stations is converted into non‐difference integer ambiguity of each reference station through linear change,and calculate the undifference observation error of each reference station. Considering the weakening of spatial correlation of observation errors between long-distance stations.According to the difference of error characteristics,obtain the correction number of classified undifference error of reference station network.Finally, by inverse distance weighted interpolation method, we calculate the error correction of mobile station, high precision positioning for users. Results: Select the measured data of long-distance continuous operation reference station network for experiment, the results show that: Compared with BeiDou-2 satellite navigation system (BDS-2), BDS-3 increases by 15.7%, 28% and 11.9% in E, N and U directions respectively. Compared with GPS, the positioning performance is equivalent or even better. The ambiguity fixing success rate and convergence time of multi-frequency data are better than GPS dual-frequency data. Dual system positioning results are better than single system, both of which can achieve centimeter level positioning of mobile stations. Conclusions: This method can avoid the correlation effect of double difference observations, high efficiency of spatial error calculation, mobile station positioning is more flexible, shows the advantages of BDS multi frequency observation data. [ABSTRACT FROM AUTHOR]

Objectives: In order to make full use of the observed value information of each frequency, an undifferenced and uncombined integer ambiguity resolution method between BeiDou satellite navigation system (BDS) long-range reference stations is proposed. Methods: First, the error observation equation is established directly by using the observations of different frequencies, and the relative zenith tropospheric wet delay error and ionospheric delay error are estimated by random walk strategy to increase the constraint between epochs. Second,a linear calculation method of undifferenced integer ambiguity real-time is used to obtain the undifferenced integer ambiguity of all satellites in the current epoch of the reference network. It solves the problem that ambiguity needs to be inherited or re-superimposed on normal equations in the reference star transformation. Because the information of each frequency observation is fully utilized, the influence of linear combination amplification noise on integer ambiguity fixing is avoided, and the ambiguity fixing success rate of uncombined method is much higher than that of ionosphere-free combination method. Results and Conclusions: The results show that the average fixed speed of ambiguity of each reference station is 20 epochs (sampling interval 1 s). The integer ambiguity resolution of the carrier phase of the reference station can be realized quickly. [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]

Aiming at the problem of rover positioning in Chinese Mars exploration mission Tianwen-1, the related research and accuracy analysis have been carried out. Methods: According to the existing measurement and control system and considering that the rover has no ground ranging data, we proposed a method to locate the rover using same-beam very long baseline interferometry (SBI) data of the orbiter and rover. Since it is not possible to determine the ambiguity using SBI and ranging data while deter‐ mining the orbit and positioning the rover at the same time, the proposed method which only uses SBI data for the rover positioning under the fixed orbital situation is analyzed. Results: The results show that the rover positioning error decreases with the increase of orbital accuracy. If the orbital accuracy is increased from 1 km to 100 m or 10 m,the rover positioning error using 6-hour SBI data can be reduced to hundreds of meters. Conclusions: More data can further reduce the positioning error and the positioning accuracy can be improved obviously with an elevation constraint. [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: Precise point positioning (PPP) combines the advantages of standard point positioning (SPP) and relative positioning, which can achieve centimeter level positioning. With the development of BeiDou satellite navigation system (BDS), more and more BDS satellites begin to provide global positioning, navigation and timing services, which also promotes the development of multi⁃frequency and multi⁃system PPP. For a long time, because of the atmospheric delay and hardware delay of satellite and receiver, the ambiguity of PPP is not an integer. PPP needs a long time to converge, which greatly limits its application. The ambiguity can be restored to integer and the convergence time can be shortened with the help of fractional cycle bias (FCB). Methods: In order to improve the effect of precise point positioning⁃am biguity resolution (PPP⁃AR) of BDS as a whole, we estimate the FCBs of GPS and BDS based on the observation data from August 1 to August 31 in 2020 of globally distributed stations. The single difference between satellites is used to eliminate the influence of hardware delay at the receivers, and the single difference ambiguity vector is solved by the whole network adjustment to obtain the FCB estimation of each satellite. Results: The results of the time series of BDS⁃3 wide lane (WL) and narrow lane (NL) FCBs show that the WL FCBs has long term stability, the change of BDS 3 WL FCBs in 31 days is less than 0.2 weeks, and the change of GPS WL FCBs is less than 0.1 weeks. The FCBs of BDS⁃3 NL can keep stable for a period of time, and the change is less than 0.1 weeks. The percentages of GPS WL and NL FCBs residuals within 0.15 weeks are 99.8% and 99.3% respectively, and the percentages of BDS 3 are 99.7% and 98.1% respectively. In order to reflect the improvement effect of FCBs on PPP, static and dynamic PPP⁃AR tests were carried out at 8 stations around the world. The results show that under the static condition, the average fixed time and convergence time of BDS⁃3 are 31.5 min and 24.9 min respectively, which is 24.8% shorter than the float PPP. The errors in E, N and U directions are 1.03 cm, 0.60 cm and 1.72 cm respectively, and the fixed rate is 89.8%. Under the dynamic condition, the average fixed time and convergence time of BDS⁃3 are 33.3 min and 50.7 min respectively, which is 17.4% shorter than the float PPP. The errors in E, N and U directions are 2.57 cm, 2.29 cm and 3.71 cm respectively, and the fixed rate is 83.9%. Conclusions: PPP⁃AR can shorten the convergence time of PPP to a certain extent, but the improvement of positioning accuracy is not obvious after complete convergence. BDS 3 FCBs stability is limited by precision products and observation data, and its PPP⁃AR is slightly worse than GPS. [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]

Objectives: Network real-time kinematic (RTK) technology can provide real-time and high-precision positioning service for users over the wide range, however, the current technology depends on high density of satellite navigation and positioning (SNAP) reference station network. To satisfy the high-precision positioning requirements based on the sparse reference station network, this paper recommends a net- work RTK service method based on virtual atmosphere constrait (VAC).Methods: Firstly, a non-combined double- difference observation model is constructed to solve and fix the network RTK baseline ambiguity quickly. Then, the baseline atmospheric delay is extracted and the slant path ionosphere and zenith trop- sphere are established respectively. Finally, the interpolated atmospheric delay and its accuracy information are regarded as virtual observations to improve the positioning performance of the terminal RTK. Based on a 205.1 km station spacing SNAP network from a northwest region， China, six rover stations inside and outside the network are used for termininal RTK verification. Results: The results show that the VAC net- work RTK service method can meet the needs of high-precision positioning users over large-scale reference networks. The terminal positioning accuracy and initialization speed by the VAC method are significantly improved by 61.64% and 9.96% compared with the traditional virtual reference station method. In this service mode, the average horizontal and vertical root mean squares of the fixed solution for the six terminals are 1.19 cm and 2.73 cm. Initializing RTK solution by a lot of times, 88.78% of periods can be fixed within 2 epochs for the six rover staions. Conclusions: The VAC service mode has good adaptability to both users inside and outside the large-scale SNAP base station network. [ABSTRACT FROM AUTHOR]

The undifferenced ambiguity is recovered to the integer characteristics after the fractional cycle bias (FCB) product correction, which significantly shortens the convergence time of precision point positioning (PPP). When the uncombined FCB products are estimated, the original L1 and L2 FCB cannot be accurately separated due to the limitation of global ionospheric model accuracy.On one hand, due to the limitation of the accuracy of global ionospheric grid model, L1 and L2 ambiguity cannot be separated accurately in real‐time, which makes the inconsistent for user end using the uncombined FCB products. On the other hand, due to the difference between the ionospheric combined FCB products and the uncombined FCB products, the user end with uncombined PPP model cannot use the ionospheric FCB products. Methods：A partial ambiguity resolution method for uncombined PPP using the ionosphere‐free combined FCB product is proposed, which considers the consistency between the algorithm of generating the ionosphere‐ free combined at server end FCB product and the algorithm of the uncombined ambiguity resolution at user end. Constructing the narrow‐lane ambiguity by using the raw ambiguity and wide‐lane ambiguity of single difference between satellites, the ionosphere‐free combined FCB product is used to fix the ambiguity step by step. Consisting of about 120 global multi ‐ GNSS experiment （MGEX） stations are used to generate the ionosphere‐free combined FCB and uncombined FCB products, and 10 stations which are not in the service end are selected for evaluation and validation. For the server end with 120 MGEX stations, 97.3% of the wide‐lane ambiguity residuals and 96.8% of the narrow‐lane ambiguity residuals are distributed after ionosphere‐free combined FCB products correction. 96.7% of the wide‐lane ambiguity residuals and 97.7% of the narrow ‐ lane ambiguity residuals are distributed after uncombined FCB products correction. Results: The experimental results show that the positioning accuracy of the proposed method is improved by 25.0% and the convergence time is shortened by 21.1% in static condition, 26.7% and 17.9% in dynamic condition, respectively.Conclusions: Compared with the traditional FCB method, the proposed method can improve the positioning accuracy and shorten the convergence time, which can further broaden the application scenarios of PPP. [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 concept of place plays an important role for coupling between human behaviors and geo⁃ graphic environments, and thus provides a human ⁃centric research perspective for geographical analysis. In early place studies, it was difficult to capture and represent the comprehensive semantics of a place in com⁃ puter systems due to the inherent vagueness, uncertainty, and ambiguity of places, as well as the high cost of obtaining place⁃based behavioral data at the individual level. Recently, multi⁃sourced big geo⁃data and ar⁃ tificial intelligent methods have brought new opportunities for place modeling and sensing. Moreover, place modeling is an important component of knowledge representation in GeoAI. This article reviews the prog⁃ ress of two directions of place modeling and place sensing. Place modeling aims to construct a platial knowledge model that is more in line with human spatial cognition and communication, so as to improve the intelligence and human ⁃computer interaction of geographical information retrieval and spatial query an⁃ swering. Place sensing aims to capture human perception and cognition about a place to better understand the intrinsic connections between human activities and the geographic environments, and to represent the rich geographical context of a place. The ultimate objective is to construct “white ⁃ box” place ⁃ based knowledge representation and reasoning for promoting the development of GeoAI. [ABSTRACT FROM AUTHOR]

Objective: The uncertainty of influencing factors of BDS positioning is great in the disaster environment and emergency scene. The applicability and maneuverability of receiver in disaster emergency environment may not meet the needs of positioning. Therefore, the method of augmented positioning between long range stations on smart device was researched to meet the demand high-precision positioning in disaster emergency environment. The augmented positioning algorithm is convenient for high efficiency and easy to realize, and the user can use a very flexible data processing method. Methods: The un-difference error corrections between long-range reference stations was used of augmented positioning. The satellite clock error was eliminated and the atmospheric error and satellite orbit error can be weakened by the un-difference error corrections. The augmented positioning of user including pseudo-range, carrier phase and carrier phase smoothing pseudo-range between long range stations were achieved. And the demand of high-precision positioning of long range was meted by corrections of classified errors. The method of carrier phase smoothing pseudo-range by un-difference error corrections was used. The integer ambiguity was estimated by observations with eliminating errors and the pseudo-range was recalculated by the simple smoothing formula. The user station errors were removed or corrected by the reference station smoothing error corrections.The pseudo-range observations do not involve ambiguity with simple positioning mode and high- real-time performance, at the same time the accuracy of pseudo-range positioning can be improved by carrier phase observations. And this method can be better applied to the demand for high-precision positioning in disaster environment. The augmented positioning for specific receiver equipment was also integrated in the smart device. Results: Three reference stations between long range together with smart device and receiver in North China were used to test the augmented positioning. The positioning accuracy of dm or cm can be obtained by augmented positioning with pseudo-range and carrier phase smoothing of receiver, the accuracy on cm level obtained with carrier phase. The smart device can get the position on dm level of horizontal with carrier phase smoothing augmented positioning, and the augmented positioning with carrier phase was able to achieve the accuracy on cm level by fixed ambiguity or float ambiguity. The kinematic augmented positioning of smart device can get the positioning accuracy better than 1 meter with the test at Liaoning. Conclusions: The smart device can be used as the source of observation and the carrier of data processing for user receiver positioning. The Results: indicate that the method can achieve high-precision positioning with real-time dynamic centimetre, decimetre and sub-meter levels better than 1 meter. [ABSTRACT FROM AUTHOR]

According to the problem of complex data processing caused by the correlation between stations and satellites in the double-difference network RTK(real-time kinematic), an algorithm of BDS un-difference network RTK with triple-frequency is proposed. Firstly, the integer linear relationship among extra-widelane, wide-lane and triple-frequency integer ambiguity is used to determine double-difference integer ambiguity between BDS network RTK reference stations. Then, according to the composition relationship between double-difference and un-difference integer ambiguity, un-difference integer ambiguity between reference stations is quickly determined at single epoch. On this basis, a high-precision region error correction model of BDS un-difference is established to realize the error correction and integer ambiguity fixing of use. This algorithm is tested by the measured triple-frequency data of BDS CORS(continuously operating reference stations) network. The results indicate that the algorithm of un-difference network RTK with triple-frequency can effectively overcome the correlation between station and satellite which is brought by the double-difference network RTK and make the operating type of the network RTK more flexible. [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]

Single-frequency GPS ambiguity resolution on-the-fly has the problem that normal equation is ill-posed. Using epoch-differenced coordinate information between neighboring epochs can mitigate the ill-condition problem to some extent, as a result, the accuracy of the float ambiguity solution will be improved and the convergence time of ambiguity will be shortened. In order to further improve the ambiguity fixing effciency of epoch-differenced method, the epoch-differenced coordinate pseudo-observation error equation and its new variance matrix is reconstructed. The experimental results show that, compared with the previous algorithm with epoch-differenced coordinate information, the new method has higher stability and efficiency. [ABSTRACT FROM AUTHOR]

Pseudorange code biases will influence high precision data processing in BeiDou navigation satellite system (BDS). Based on Melbourne-Wübbena(MW) combination, we have analyzed the effect of code biases on baseline resolution according to the code biases correction models and the residuals of double differenced wide-lane ambiguity of baselines, respectively. The results show that the influence of code biases on double differenced wide-lane ambiguity resolution with MW combination is gradually obvious as the baseline becomes longer. Moreover, the impact on the 300 km baseline may reach up to 0.36 cycles. In addition, the results suggest that the code biases of geostationary earth orbit(GEO) have great influence over both short and long baselines. For inclined geostationary orbit (IGSO) and medium earth orbit (MEO), the code biases have little effect on baseline solution when the baseline is within 300 km, however, the residuals of wide-lane ambiguity of partial satellites have obvious biases when the baseline is over 300 km. Furthermore, the fixing rates of wide-lane ambiguity of these satellites are lower, so we should take into account the influence of code biases on baseline resolution at this time. [ABSTRACT FROM AUTHOR]

When the sampling rate of base station is lower than that of the rover station, it's impossible to obtain the coordinates of the rover station at all epochs with a conventional differential GNSS post-processing method. To solve this problem, a method based on PPP model is proposed to construct the virtual observation data of the non-sampling points of base station. The method separates the receiver clock error and tropospheric zenith wet delay from the observation error, and estimates them simultaneously with ionosphere ambiguity, after which the distance between the satellite and the station is obtained by base station's real coordinate. On this basis, the method calculates the residual errors of two adjacent epochs, by which the residual errors of non-sampling epochs are fitted. Eventually, the virtual observation data are generated by the non-sampling epochs' residual errors, the distance between the satellite and the station and the estimated errors. Error characteristic of the virtual observation data is maintained, especially the common error between the base station and the rover station; This method only densifies the data of the base station, which will not affect the rover station. The experiment results show that when base station works with a sampling interval within 30 s, the virtual observation data generated by this method are accordant with the real data. In 30s, 15s and 5s sampling intervals, the standard errors of virtual observations of pseudo-range are about 0.2, 0.1 and 0.05 meters, and virtual observations of carrier phase are about 1.2, 0.7 and 0.2 cycles, respectively; In the case of 30 s sampling interval, the positioning result obtained by this method can still meet the cm level accuracy requirements. [ABSTRACT FROM AUTHOR]

In most GPS (Global Positioning System) receivers, the pseudo-range measurement error is bigger than the wavelength of WL (Wide Lane) carrier phase measurement. It will probably cause one cycle WL integer ambiguity resolution error in case the DD (Double Differenced) WL integer ambiguity is rounded by DD pseudo-range measurement according to the WL integer bootstrapping model. In this view of, we propose a modified WL bootstrapping ambiguity resolution algorithm. The proposed algorithm mainly aims at detecting and repairing one cycle WL integer ambiguity error. The WL integer ambiguity error detector is designed according to the characteristic that the integer ambiguity is an integer. The designed detector is compared with the theoretical threshold calculated by the Carrier Noise Ratio (CNR) to judge whether the WL integer ambiguity is wrong. There are only 3 degrees of freedom in all the ambiguities, therefore we fix the wrong ambiguities by the right ambiguities. We analyze the feasibility of the proposed algorithm in Gaussian noise environment. The results show all the carrier phase measurement in normal CNR environment can judge whether the WL integer ambiguity has one cycle error. The maximum carrier phase error is calculated in case we consider the multipath and other carrier phase measurement error. The probability of one cycle WL integer ambiguity error is analyzed with pseudo-range measurement error in different orders of magnitude. Field tests were carried out by using GPS short baseline data. The proposed algorithm increases the success rate of the WL integer bootstrapping ambiguity resolution algorithm from less than 1/3 to nearly 100%. [ABSTRACT FROM AUTHOR]

Tightly-coupled GNSS/INS integration has been shown to provide better performance than loosely-coupled approach in GNSS degraded environments. However， it is difficult to achieve reliable ambiguity resolution (AR) when the number of satellites is below four. In this case, ambiguity search in the ambiguity domain is not possible，which means other AR method should be considered. Also, it is likely to wrongly fix the ambiguities，which will lead to biased state estimate or even filter divergence. In this paper，a tightly-coupled RTK/INS algorithm based on centralized Kalman Filter (KF) is implemented， in which ambiguity parameters are augmented into the state vector. Ambiguity-fixed or -float carrier phase observables can be used to update the filter even if the number of satellites is less than four，and this improves the accuracy of the integrated system in complex environments. A field vehicular test was conducted to evaluate the performance of the tightly-coupled algorithm in terms of the position drift error during GNSS signal outages and ambiguity recovery time after outages. Test results indicate that by utilizing tactical-grade inertial measurement units (IMUs)，the horizontal position drift error is about 0.3m during 30-second partial outage and the average time for reliable ambiguity recovery is 1 to 2 seconds when the number of satellites in view is three. Besides, the performance of float solution is only slightly worse than the fixed solution for shout-time (e.g. 60 seconds) partial outages, but both of them are much better than the case of full GNSS outages. [ABSTRACT FROM AUTHOR]

This paper proposes a new method based on relationship of multiple receiver ambiguity to solve the re-convergence problem in kinematic PPP due to the satellite signals interruption. The method makes full use of multiple receivers located in different locations of the survey vessel. Because of the different locations, the signal interruption may be not simultaneous for different receivers. The method establishes the relationships of ambiguity between different receivers and then obtains the priori ambiguity of the receiver that need re-convergence, and then completes the re-convergence of kinematic PPP. Experiments show that the success rate when fixing double-differenced ambiguity with baseline length constraint is more than 99%; when fixing double-differenced ambiguity, no matter how long the satellite signal is interrupted, the proposed method can complete re-convergence of kinematic PPP in one epoch. Moreover, the positioning accuracy after re-convergence is as same as the before. [ABSTRACT FROM AUTHOR]

The bridge displacement responses can move from several centimeters to several meters induced by a combination of four major types of loading due to wind,temperature, highway,and rail-way. One of the main challenges of InSAR technique is phase unwrapping. One can take advantage of this wide band to split it into sub-bands and determine the phase-frequency gradient between the sub-band interferograms. This simulates a SAR system with a much longer carrier wavelength than the actual one, which makes it possible to monitor the meter-scale deformation. This paper presents the theory and method of split bandwidth interferometry in detail, and the effectiveness and advantage of split bandwidth interferometry was verified in feasibility of monitoring structural deformation of Tsingma Bridge under the influence of different factors. [ABSTRACT FROM AUTHOR]

A single-epoch ambiguity resolution algorithm without a search process is proposed. Four basic satellites are selected, whose integer ambiguities are estimated by using the INS position, then (1,-1) and (-3,4) ambiguity combinations are formed. The ionospheric error of the (-3,4) combination is polynomially fitted. After systematic influences such as the ionospheric error are compensated, the ambiguity combination can be fixed by simple rounding. The ambiguities of each frequency can be determined by the combination and returned to resolve the receiver position. Based on the receiver position, the ambiguities of all other satellites can be calculated directly and fixed by rounding. The algorithm was validated by field test GNSS/INS data. [ABSTRACT FROM AUTHOR]

The ambiguity resolution is one of the primary problems in GNSS carrier phase measurement. To acquire carrier phase integer ambiguity rapidly and accurately, we often take advantage of integer least-squares (ILS) estimation criterion to resolve ambiguity. Due to ILS problem can be regarded as closest vector problem (CLP) in lattice theory, therefore, lattice reduction could help to accelerate ambiguity enumeration process, shorten the search time, and further to improve the computation efficiency of ambiguity resolution. Among many of lattice reduction algorithms, Lenstra-Lenstra-Lovász (LLL) is a most popular and widely used reduction algorithm in many fields. It includes two reduction conditions, size reduction and basis vector swapping. However, size reduction is aimed at all matrix elements and basis vector swapping is only limited to two adjacent vectors, that will result in the unnecessary elements size reduction and excessive basis vector swapping times. Hence, both of them are not conducive to improving the ambiguity reduction efficiency, especially for high-dimensional ambiguity resolution. To overcome this problem, we adopt the greedy algorithm and partial column vector reduction to reduce the number of basis swapping and size reduction, in this contribution the computing complexity of LLL reduction algorithm is reduced, where LLL reduction algorithm has a long time-consuming under high-dimensional conditions. Simulations and real data validations have clearly shown that the modified LLL reduction algorithm can significantly improve the computational efficiency. Therefore our modified LLL algorithm has a certain useful value for fast resolution under high-dimensional case. [ABSTRACT FROM AUTHOR]

The principle of constructing independent vector sets using Gram-Schmidt orthogonal transformation is proposed. The method of setting independent baseline and independent double-difference ambiguity data sets refers to the idea of vertex incidence matrix and vector weight. The three ways to build double-difference ambiguity data sets are discussed. The computing process of selecting independent baselines and independent double-difference ambiguities is provided. An example of orbit determination using global GPS track nets is tested. The result shows that the orthogonal transform algorithm is effective. [ABSTRACT FROM AUTHOR]

Receiver initial phase biases are significant in integer ambiguity resolution. Based on a study of Beidou receiver Initial phase bias, we derived calculation formulas of single-difference-between-receivers (SDBR) inter-frequency receiver initial phase biases. The analysis results using zero-baseline data indicate that the SDBR inter-frequency receiver initial phase biases do not vary with the satellite elevation angles, which suggests that the biases have a short-time stability. When the receiver is just beginning to track satellites, a certain time is needed for the SDBR inter-frequency receiver initial phase biases to be stabilized. The SDBR inter-frequency receiver initial phase biases are changed after the receiver restarts to track satellites, indicating that the biases do not have a long-time stability. The SDBR inter-frequency receiver initial phase biases on the same combination of two frequencies are nearly identical for different satellites. [ABSTRACT FROM AUTHOR]

Using priori information from known coordinates for reference stations, based on tacombination of ultrarapid ephemeris, a three-step kalman filter algorithm for near real-time estimation of tropospheric wet delay on reference stations is proposed. In this algorithm, wide lane ambiguity and pseudorange multipath error are separated by using a Kalman filter, and then, using the Kalman filter for separating L1 ambiguity and tropospheric wet delay based on na ionosphere-free combination model. After that estimating an accurate relative tropospheric wet delay parameter using the correctly fixed L1 ambiguity back substitution method and rebuilding the Kalman filter. The feasibility and accuracy of the algorithm is verified through numerical examples. [ABSTRACT FROM AUTHOR]

It is very important of deformation monitoring system to ensure enterprises regular operation and protect human lives and properties. According to the real-time and rapid monitoring demand of high slope in open pit mine, this paper aims to design a monitoring system with the integration of Global Navigation Satellite System and Geographic Information System. After its composition and operation principle have been introduced, the direct calculation method is proposed to perform the integer ambiguity fast calculation of GNSS. Subsequently, the software function and integrated development pattern of monitoring system have been discussed in detail. Finally, the open pit mine of Jinduicheng Molybdenum Group Company, located in Shanxi province, which is the biggest molybdenum industry production base in China, is set as an application example. The results indicate that the system can perform real-time and rapid monitoring for the high slope deformation, which provides effective security for mine safety production. [ABSTRACT FROM AUTHOR]

Based on BDS measured data, three pairs of linear independent extra wide-lane (EWL) combinations were selected. Then, single epoch ambiguity resolution was carried out with these selected combinations using the combined geometry-free (FG) and geometry-based method (GB). After this treatment, the original phase ambiguity of each frequency can be resolved. Finally the ambiguity resolved phase measurements are used for precise positioning. Experimental results show that for short baseline situations, reasonable selection of the combination coefficients is decisive for a high success rate in ambiguity resolution. If the coefficients are selected correctly, the success rate of single epoch ambiguity resolution for original phase measurements is 99. 75% in the static mode and 95. 08% in the kinematic mode, so that the traditional exhaustive data preprocessing, such as cycle slip detection, can be avoided and a centimeter level positioning result can be achieved reliably. [ABSTRACT FROM AUTHOR]

A new lattice reduction method is introduced to solve the problem of integer ambiguity resolution in GNSS carrier phase precise positioning. The current LLL reduction algorithm is improved based on a orthogonal Householder transformation with systematic rotation. The comparative range is extended to n. The reduction base vectors are preordered and a HE-LLL reduction algorithm is proposed. Experiments with different time intervals and baseline lengths were executed and a comparison was made between the HE-LLL algorithm and other algorithm concerning condition number, non-orthogonal index, reduction time, and changing trend of the length of orthogonal row vector. The results show that the HE-LLL algorithm has improved reduction efficiency, and can well restrict the length of orthogonal row vector. [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]

As a consequence of a daily data processing strategy, an adjacent IGS final precise clock product displays discontinuity at the junction of two successive days. This will cause a jump in positioning results for the pseudo-range, and change all the related ambiguities. These non-integer cycle slips will require filtering to make them converge. In this paper, the magnitude of the jump of every satellite for a seven day cycle is investigated in detail. Then, based on the full discussion of the data processing strategy of the IGS center, the reasons for discontinuity and the precision of the final clock product are presented. Two counter measures are proposed: one is to insert the jump in the satellite clock datum into the IGS clock product; the other is to estimate the clock datum for adjacent days. Finally the results of the two processing strategies are presented. [ABSTRACT FROM AUTHOR]