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Since the full system deployment of BDS-3 in July 2020, it has provided stable and reliable positioning, navigation and timing (PNT) services for users around the world. It is an urgent task to explore the potential performance of precise point positioning (PPP) based on the full constellation of BDS-2/BDS-3. This research presented the global satellite visibility of BDS-2/BDS-3, analyzed the stability and accuracy of BDS-2 and BDS-3 rubidium clocks and hydrogen clocks, jointly estimated the BDS-2 and BDS-3 fractional cycle biases (FCB) and evaluated the PPP performance with ambiguity resolution (AR). Due to the fact that International GNSS Service (IGS) precise products have a great impact on narrow-lane (NL) FCB estimation, the FCB obtained by using the precise products from CODE (Center for Orbit Determination in Europe) and GBM (Deutsches GeoForschungsZentrum) in two different analysis centers and the FCB obtained by using GBM precise products with different calculation strategies are analyzed. In addition, the experimental data from Multi-GNSS Experiment (MGEX), EUREF (EPN) and Germany (GPN) observation networks are used to evaluate the influence of orbital errors on BDS FCB estimation. For wide-lane (WL) FCB, MGEX WL FCB has the highest accuracy, followed by EPN and GPN. On the contrary, for NL FCB, MGEX NL FCB has the worst accuracy, followed by EPN, and GPN is the best. Eventually, numerous experiment results showed that compared with the static float solution, the PPP fixed solutions in East (E), North (N) and Up (U) directions are improved by 32.9%, 27.7%, 13.8% for BDS-3 and 10.0%, 7.5%, 3.8% for BDS-2/BDS-3. Compared with the kinematic float solution, the PPP fixed solutions in E, N and U directions are improved by 27.9%, 23.4%, 16.6% for BDS-3 and 15.9%, 8.9%, 5.3% for BDS-2/BDS-3. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) network analysis benefits from precise point positioning with undifferenced (UD) or double differenced (DD) integer ambiguity resolution (IAR). Position time series with UD-IAR and a practical DD-IAR are compared for a mixture network consisting of 57 global and 82 regional stations with 4-year observations. The sparse global stations are more affected by different IAR methods than the regional stations of Crustal Movement Observation Network of China (CMONOC). The most significant differences between UD-IAR and the practical DD-IAR are observed in velocity estimations, with averages of 0.15 and 0.30 mm/yr for the horizontal and vertical components, respectively. UD-IAR can achieve smaller root mean square at 70–83 % of the daily solutions than the practical DD-IAR for global stations. Nevertheless, moderate differences of frame parameters and annual variations are introduced by different IAR methods. The IAR is also proved to be one of the potential origins for Global Positioning System (GPS) draconitic signals and white noise at high frequency. [ABSTRACT FROM AUTHOR]

With the capability for single-receiver AR (Ambiguity Resolution), real-time GNSS (Global Navigation Satellite System) satellite integer clock has been the research hotspot of GNSS community in the past decade. Robust ambiguity datum is one prerequisite for high-quality integer clock. In this paper, with undifferenced AR model derived, a robust ambiguity datum definition method is proposed to isolate the signal biases from the integer ambiguity. Firstly, based on the ambiguity graph, the ambiguity datum is selected with the minimum spanning tree algorithm. Secondly, the ambiguity datum is transferred to the subsequent epochs through signal bias connection. Moreover, additional datum ambiguities are introduced to accommodate the arising of receiver and satellite in real-time circumstance. With the combination of ambiguity graph and signal bias, the efficient definition and smooth transition of ambiguity datum are assured for the real-time processing. To validate the approach, simulated real-time integer clock estimation for GPS/Galileo/BDS-3 satellites are conducted with one-month (January 2022) data from about 100 global IGS (International GNSS Service) network stations. Experiments show that the proposed robust ambiguity datum can produce accurate real-time integer clock. The average WL (Wide-Lane) and NL (Narrow-Lane) fixed rates exceed 99 % and 95 %, respectively, for most of the GPS/Galileo satellites. While comparable WL fixed rate is achieved for the BDS-3 satellites, the NL fixed rate is about 5 % lower as a result of poor orbit quality and imperfect measurement model. With eclipsing satellites excluded, the standard deviations between real-time integer clock and post-processed reference clock reach 0.018 ns and 0.016 ns for the GPS and Galileo constellations, respectively, which are 28 % and 24 % smaller than those of corresponding float clocks. In contrast, the standard deviations of float and integer clocks are similar for the BDS-3 constellation. Further improvements on the background models, including unconservative force modeling, satellite attitude modeling and antenna calibration are required to achieve ultimate accuracy, especially for the BDS-3 satellites. [ABSTRACT FROM AUTHOR]

With the rapid progress of Global Navigation Satellite Systems (GNSS), integer ambiguity resolution has gradually become one of the key factors that affecting Precise Point Positioning (PPP) to achieve high-precision positioning results and fast convergence. Fortunately, the proposal of observable-specific code/phase biases (OSB) has greatly alleviated this problem tremendously. Different from obtaining OSB by dual-frequency linear combinations, this research proposed BeiDou Navigation Satellite System (BDS) OSB estimation method from raw observations. This method allows for more flexible estimation in a global network, without the need to compose the complex linear combinations when involving multi-frequency measurements processing. The BDS-3 observation data collected from 112 stations over one month (October 2022), containing B1C/B1I/B2a/B2b/B3I frequencies, were used for five-frequency phase OSBs estimation. Subsequently, static and kinematic PPP were executed utilizing two different ambiguity resolution strategies to corroborate the efficacy of this method. The results revealed that the BDS-3 five-frequency phase OSBs possessed good monthly stability, with standard deviation less than 0.3 cycle. High position accuracy was achieved in the static mode by fixing the ambiguity directly, with root mean square (RMS) of 3.0, 4.8 and 9.9 mm. Meanwhile, the ambiguity fixed rate was maintained at a high level around 96 % in multi-frequency tests. Simultaneously, the kinematic mode also presented the centimeter-level dynamic positioning results and the positioning accuracy improved by 55, 31 and 17 % in the East, North and Up components, respectively. Compared to the float solutions, the adoption of multi-frequency OSBs significantly accelerated the convergence speed by 55 % on average. [ABSTRACT FROM AUTHOR]

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases. [ABSTRACT FROM AUTHOR]

• An improved SICB correction model is proposed based on elevation and azimuth angles. • The parameters are estimated for each BDS frequency with node-separation of 1°. • The threshold of elevation for the new model is determined based on the statistics. • Weight-average algorithm with SNR is used to obtain the optimal MP deviations. The satellite-induced code bias (SICB) resulting in code-phase divergences of nearly 1.0 m has been observed in the code measurements of BeiDou navigation satellite system (BDS). Since the SICB is proved to be elevation- and frequency-dependent, several SICB correction models have been proposed to remove the systematic bias, but most of them only consider elevation angles, overlooking the influence of azimuth angles, which would limit the accuracy of the correction models, especially for Medium Earth Orbit (MEO) satellites. To deal with this problem, we proposed an improved SICB piecewise correction model as a function of elevation and azimuth angles and estimated parameters for each BDS un-GEO (Geostationary Earth Orbit) satellite and each available frequency with node-separation of 1°. The epoch-difference method is employed to remove the effect of stable terms, such as phase-ambiguities, receiver- and satellite-dependent hardware delays. Moreover, to reduce the effect of code noise and multipath at low-elevation conditions, the threshold of elevation angle for the improved model is determined based on the statistics of Multipath (MP) combinations. Besides, weight-average algorithm is used to obtain the optimal MP deviations and improve the accuracy of proposed correction model in consideration of signal-to-noise (SNR). The experiment results with real GNSS data show that the SICB models are more suitable for BDS-2 MEO satellites than Inclined Geosynchronous Orbit (IGSO) satellites. The code measurements on B1 signal are more susceptible to the SICB than that on B3 signal. After applying the improved SICB correction models, the RMS errors of MP series are significantly reduced for BDS-2 un-GEO satellites. However, for BDS-3 satellites, only centimeter-level SICB deviations can be detected for all frequency-bands, and the RMS of MP variations have slight changes after applying the SICB corrections, indicating that the systematic bias in MP combinations is not obvious, especially for BDS-3 MEO satellites. [ABSTRACT FROM AUTHOR]

Nowadays, the BDS-3 satellites transmit new signals B1c and B2a that are compatible with GPS and Galileo, which is meaningful to fully take advantage of the BDS positioning capability. However, further research and analysis are needed to investigate the precise point positioning ambiguity resolution (PPP-AR) performance of the new BDS-3 signal combination. In this manuscript, the characteristics and quality of differential code bias (DCB), inter frequency clock bias (IFCB) and uncalibrated phase delay (UPD) of BDS-3 new signals are analyzed based on 30 days observation data from 70 multi GNSS experiment (MGEX) stations. The results show that the mean value of IFCB between B1I/B3I and B1C/B2a is 1.18 cm, which indicates that the IFCB can be ignored when performing the clock errors reference conversion of BDS-3 satellites. Besides, the DCB of the new BDS-3 signals varies within 0.2 ns over 30 days, and with a difference of 0.08 ns compared to the DCB product provided by chinese academy of science (CAS). The percentage of the estimated residuals less than 0.25 cycles for new signals WL UPD and less than 0.15 cycles for new signals NL UPD are 99.76% and 97.19%, respectively. The above results demonstrate the reliability of the DCB and UPD products, which can be used to estimate the carrier phase observable specific signal bias (OSB) product for the new signals. The average positioning errors of the BDS-3 new signals static PPP-AR in the N, E and U directions is 0.50 cm, 0.43 cm and 1.62 cm respectively, with an improvement of 18.3%, 28.3% and 11.5% compared to the ambiguity float static PPP. The average positioning errors of the kinematic PPP-AR are 2.09 cm, 2.67 cm and 4.79 cm in three directions, respectively, with an improvement of 17.1%, 23.9% and 15.7% compared to the ambiguity float PPP. The convergence time of the static and kinematic PPP-AR are 26.36 min and 29.12 min, respectively. [ABSTRACT FROM AUTHOR]

Ambiguity resolution (AR) is critical for enhancing the orbit accuracy in precise orbit determination (POD) for low earth orbit (LEO) satellites. While orbit estimation using single-difference (SD) AR has been widely researched, the investigation of orbit estimation using undifferenced (UD) AR for LEO satellites is limited due to time-varying hardware biases at the LEO receiver end. To address this deficiency, we propose an improved UD AR method for LEO satellite orbit determination. The method employs the optimal integer datum ambiguity for a 1-day observation arc, and the random-walk clock model is utilized to transfer the integer ambiguity datum to the other epochs, which enables the arc-wise ambiguities to regain the integer property within the time frame. To validate the effectiveness of our improved method, numerical experiments are conducted. Moreover, we assess the performance of the random-walk clock model for a spaceborne ultra-stable oscillator (USO). The high frequency stability of the USO establishes the satisfactory requirements for this study. Both in the kinematic and dynamic modes, the AR success rates of our improved method are ∼ 2% higher than that of the current SD AR method, and the orbit results indicate a slight improvement. The 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences between JPL precise science orbits (PSO) and our orbits are reduced by up to 4% and 5% for kinematic and dynamic orbits, respectively. The subtle benefit is also proven by K-band ranging (KBR) system validations. In the case of the Gravity Recovery and Climate Experiment Follow-on (GFO) satellites, the results indicate that the effect of our improved UD AR can be equivalent to that of SD AR. Our improved UD AR method can be a good alternative for its superior ability to generate hardware delay at the LEO receiver end. [ABSTRACT FROM AUTHOR]

In addition to the legacy B1I and B3I signals, the BeiDou global navigation satellite system (Beidou-3) are capable of transmitting B1C/B2a/B2b/B2 several new navigation signals. The multi-frequency signals of Beidou-3 are expected to benefit precise point positioning with ambiguity resolution (PPP AR). Currently, most international GNSS service (IGS) analysis center adopt the Beidou-3 B1I/B3I ionosphere-free (IF) combination to estimate the satellite orbit and clock products, the Beidou-3 B1C/B2a/B2b/B2 phase biases should be aligned with satellite B1I/B3I clocks. Therefore, in this paper, the multi-frequency phase observable-specific phase biases (OSB) estimation method is developed for Beidou-3 system, which is compatible with satellite B1I/B3I legacy clock. Experimenting on the Beidou-3 multi-frequency observations over 30 days from the globally distributed stations, the characteristics of the estimated Beidou-3 multi-frequency phase OSB and the positioning performance of the IF kinematic PPP AR with different frequency combination are assessed. After the OSB are used in the raw observations, the results demonstrate that the wide-lane ambiguities residuals within ± 0.25 cycle are approximately 97%, 94%, 97% and 93% for Beidou-3 B1I/B3I, B1C/B2b, B1C/B3I and B1C/B2a combinations, respectively. When the OSB and satellite B1I/B3I legacy clock are used in different dual-frequency combination PPP AR tests, over 94% of the corresponding narrow-lane ambiguities are within ± 0.25 cycle. In addition, owing to the low noise of the B1C/B2a combination, the positioning performance of B1C/B2a PPP AR outperforms that of the other frequency combinations. More specifically, in case of B1I/B3I PPP AR, almost 22.7 min is required to successfully achieve 10 cm for east, north and up components, while only 18.8 min is needed for B1C/B2a PPP AR. The results show that such phase OSB, along with Beidou-3 satellite B1I/B3I legacy clock, can fully recover the PPP ambiguities based on all available frequency choices and observable combinations. [ABSTRACT FROM AUTHOR]

The current GLONASS system suffers from the inter-frequency code bias (IFCB) and the inter-frequency phase bias (IFPB) due to its employment of the frequency division multiple access (FDMA) technology. The IFCB affects the code observation's accuracy and further degrades the positioning accuracy, while the IFPB can be absorbed into the float ambiguity term. With increasing demand on precise point positioning (PPP) in mass market applications using low-cost single-frequency (SF) receivers, the impact of IFCB on SF-PPP with low-cost receivers need to be investigated. In this paper, we propose the use of the University of Calgary (UofC) model to estimate the IFCB in SF-PPP. The feasibility of the proposed approach is first verified using GNSS observations from the IGS stations. Comparing to the traditional SF-PPP model, the UofC model enables more stable IFCB estimations with 80.2% of the maximum changes less than 1.0 ns within one week. Then, the stability of IFCB in the low-cost SF receiver is analyzed with static data collected with u-blox M8T, and the STandard Deviation (STD) of IFCB for each satellite within 5 days is less than 1.5 ns when applying real-time orbit, clock and ionospheric corrections. Further, it's verified that the power off won't affect the IFCB's value significantly in the low-cost receiver. Finally, six different strategies are designed to evaluate the impact of the GLONASS IFCB on SF-PPP. Comparing to those strategies ignoring IFCB, the strategies considering IFCB in SF-PPP can improve the positioning accuracy in both static and kinematic tests. [ABSTRACT FROM AUTHOR]

Tight integration can enhance the model strength and positioning performance by considering the characteristic of differential inter-system bias (DISB), especially in obstructed environments. However, limited work emphasizes the comprehensive analysis of five-frequency DISBs between BDS-3 and other systems considering the receiver type, receiver configuration, and antenna type. In addition, the overlapping DISBs between BDS-3 and BDS-2 are also in great demand for further investigation since they are often regarded as one system. In this study, one DISB-float model is introduced to estimate the DISBs, and one DISB-fixed model and one DISB-free model are formulated to enhance the model strength of tight integration. Four dedicated datasets were collected to estimate the DISBs, which are also comprehensively analyzed considering the receiver type, receiver configuration, and antenna type. The results show that the DISBs between BDS-3 and other systems are rather stable over a certain period and are related to the receiver type and receiver configuration, whereas are not related to the antenna type. More interestingly, the B1I code DISB between BDS-3 and BDS-2 exhibits significant magnitude with a mean value of −1.44 m for the baseline composed of two different receivers. In this case, the B1I code DISB must be considered and the tight integration between BDS-3 and BDS-2 considering its calibration can improve the positioning performance. Besides, the tight integration of the DISB-fixed model can significantly improve the positioning accuracy between multiple GNSS. Compared to the loose integration, the improvement of 60.6 %, 56.6 %, and 61.2 % can be obtained in the E, N, and U directions, when only two satellites are available for each system. In real obstructed environments, the tight integration of the DISB-free model can also improve the positioning performance in terms of positioning availability and accuracy, as well as the ambiguity resolution performance. [ABSTRACT FROM AUTHOR]

• The ISB between the BDS-2 and BDS-3 is considered in UPD estimation. • The time-varying characteristics of ISB and the quality of BDS UPD are analyzed. • The satellite-induced bias of BDS-2 in UPD estimation is evaluated. • The impact of ISB is evaluated from the performance of BDS PPP and PPP-AR. Intra-system biases (ISBs) between BDS-2 and BDS-3 are of critical importance when combining observations from the BDS-2 and BDS-3 systems, which is meaningful to fully take advantage of the BDS positioning capability. Meanwhile, ISBs should also be considered in the estimation of BDS uncalibrated phase delays (UPDs). In this research, we present a BDS-2/BDS-3 joint-processing scheme, as well as a method for estimating BDS UPDs. The characteristics of ISBs and the quality of BDS UPDs are analyzed based on 30-day data from 130 multi-GNSS experimental (MGEX) stations. Our results indicate that the ISBs are related to the type and version of the receiver. The ISBs can be regarded as constant across the course of a given day, and the mean standard deviation (STD) values of ISBs over one month for different types of receivers are generally within 0.2 m. Moreover, to assess the quality of UPD products, the residuals of the estimated UPDs and the utilization rates of the observation data are computed. The results show that the quality of BDS UPDs can be improved by correcting the satellite-induced pseudo-range variations, and by estimating the wide-lane (WL) UPD difference between BDS-2 and BDS-3. The average RMS values of the estimated residuals of WL UPD and narrow-lane (NL) UPD are 0.07 and 0.09 cycles, respectively; moreover, the utilization rate of the observation data of WL UPD and NL UPD can reach above 90 %. The performance of BDS precise point positioning (PPP) and PPP ambiguity resolution (PPP-AR) is analyzed in terms of positioning accuracy and convergence performance in both the static and kinematic modes. Compared with PPP ambiguity-float solutions, the positioning accuracy of PPP-AR is significantly improved, especially in the east direction. The impact of ISBs on PPP and PPP-AR is also analyzed, and the results indicate that ISBs can improve the convergence speed of float PPP, but can be disregarded in PPP-AR. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS)-based attitude determination has been widely adopted in a wide variety of terrestrial, sea, air, and space applications. Recently, the emergence of commercial multi-GNSS common-clock receivers has brought new opportunities for high-precision GNSS-based attitude determination with single-differenced (SD) model. However, the key requirement of using this approach is the accurate estimation of the troublesome line bias (LB) in real-time. In this contribution, we propose a particle filter-based real-time phase LB estimation approach that apply to SD model with single-system single-frequency observations from common-clock receiver. We first analyzed the relationship between the integer ambiguity ratio value and the phase LB. It is proved that the accuracy of a given phase LB value can be qualified by the related ambiguity resolution ratio value, and the normalized ratio value can therefore be used to represent the likelihood function of observations. Then, we presented the particle filter-based real-time phase LB estimation procedure, and assessed its performance using GPS L1/BDS B1I observations from two datasets collected with different types of common-clock receivers in terms of the accuracy and convergence time of phase LB estimation, the computation load, and the positioning and attitude determination accuracy with respect to the double-differenced (DD) model. Experimental results demonstrated that the phase LB could be accurately estimated with short convergence time (generally within 15 epochs). Moreover, compared with the classical DD approach, the particle filter-based SD approach delivers comparable positioning root-mean-square (RMS) errors in the North and East components but significantly smaller RMS errors in the Up component. Accordingly, the achievable yaw accuracy is comparable whereas the pitch accuracy is remarkably improved. The improvements of positioning accuracy in the Up component and pitch accuracy are approximately 35.7 % to 63.7 %, and 33.3 % to 63.1 %, respectively. Additionally, the single-epoch computation time with our particle filter-based SD approach is generally 0.08 s, which is obviously larger than the DD approach but could still meet the requirements of real-time applications below 10 Hz sampling. [ABSTRACT FROM AUTHOR]

• Attitude and inertial parameter are estimated without 3D model. • Ill-posed point cloud is detected and avoided. • Combination of MEKF and pose graph reduces error of estimate. Determining the attitude and inertial parameters of a noncooperative target is essential in an on-orbit servicing mission. Various methods based on machine vision have been proposed, but most of them require the 3D model of the target. This paper proposes a model-free method through sequentially registering point clouds captured by a depth camera. Our main contributions are the avoidance of the ambiguity in registration, and the combination of the multiplicative extended Kalman filter and the pose graph optimization to reduce the effect of measurement noise and drift error. A hardware experiment was performed to generate the sequence of point clouds of a three-axis free-floating target and validate our method. The result shows that the proposed method outperforms existing methods and effectively identifies the inertial parameters, including the normalized principal moments of inertia and the orientation of principal axes. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) precise positioning can be significantly affected by severe multipath effects and outliers in harsh environments, and highly relies on quality control strategies. Previous studies mainly focus on the posterior residuals to check and exclude the outliers in GNSS observations, limited work emphasizes the combined quality control method considering both the prior and posterior knowledge simultaneously. This paper proposed a real-time combined quality control method to process the multipath effects and outliers in harsh environments simultaneously. Specifically, in the prior stage, a modified multipath processing strategy is proposed for both phase and code observations, then a modified detection, identification, and adaptation (DIA) method considering the maximum times of data snooping is studied in the posterior stage. Two dedicated experiments in real harsh environments were carried out to evaluate the performance of the proposed combined quality control method. For the static experiment, the proposed method exhibits smaller positioning errors, the best positioning accuracy, and the highest availability in this study. Specifically, the proposed method exhibits an improved percentage of 55.4 %, 56.3 %, and 59.7 % for positioning accuracy compared to those without the quality control method in the E, N, and U directions, respectively. Besides, the proposed method can further improve the performance of ambiguity resolution with an improved percentage of 32.2 %. For the kinematic experiment, the three-dimensional positioning accuracy of the proposed method is 0.577 m, which exhibits a 40.0 % improvement compared to those without the quality control method. Also, the proposed method exhibits better performance under relatively strong multipath effects. In this sense, the proposed real-time combined quality control method is highly appreciated in terms of positioning availability, accuracy, and ambiguity resolution for GNSS precise positioning, especially in harsh environments. [ABSTRACT FROM AUTHOR]

The full operational capability of the Chinese BeiDou Satellite Navigation System (BDS) has injected additional energy into the GNSS field. Along with the visibility of more BDS satellites, as well as the precise products generated by analysis centers, ambguity float and fixed Precise Point Positioning (PPP) performance with the complete BDS constellation are evaluated in this study. Inter-system biases (ISBs) between BDS-2 and BDS-3 are first evaluated, and Fractional Cycle Bias (FCB) with and without consideration of ISBs are assessed. Results show that when considering ISBs, the standard deviations of ambiguity residuals are smaller, thus the ISB parameter should be taken into consideration in BDS PPP. BDS-3 FCBs are more stable than those of BDS-2, at the same time, the ambiguity residuals are smaller for BDS-3 satellites. In terms of PPP performance, BDS-3 outperforms BDS-2 in positioning accuracy, convergence time and time to first fix. For the test data, the convergence time of BDS-2 static solution is 48.8 min, while for BDS-2 + 3 it is 19.7 min, representing an improvement of 59.6% when BDS-3 satellites are included. The positioning accuracy of static BDS-2, BDS-3 and BDS-2 + 3 PPP can reach the same millimeter-level after a long time of convergence, while kinematic solution with BDS-2 + 3 has the highest accuracy compared to BDS-2 and BDS-3, which could reach 1.7, 1.3 and 4.3 cm in East, North and Up components, respectively, in fixed solution. The performance of BDS PPP with the whole constellation is comparable with that of GPS and Galileo, and the PPP performance is promising with receiver updates for MGEX stations in the near future. [ABSTRACT FROM AUTHOR]

Multi-GNSS multi-frequency observations improve the accuracy, availability and reliability of the single-site RTK positioning but also simultaneously raise the communication bandwidth needed for the transmission of differential corrections. A RTK positioning algorithm is proposed that transmit the phase-only differential corrections to achieve the ambiguity-fixed RTK positioning, significantly reducing the communication bandwidth requirements. The essence of the presented method is that the code differential positioning solution implied in the conventional RTK positioning procedure can be replaced by the single point positioning solution of the rover receiver to realize RTK positioning. For typical application scenarios, the transmitted bits in a single epoch can be reduced by more than 25% when the corrections are sent with the RTCM protocol. The experiments by the GPS dual-frequency data over the 10 km and 180 km baselines shown that the performance of the presented RTK algorithm are comparable to that of the conventional RTK positioning, which verifies its feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

With the development of commercial services in the European Union, the advanced designs of Galileo E6 signals can be freely offered to Global Navigation Satellite System (GNSS) users. However, only a few studies have analyzed the benefit of Galileo E6 signals, and their application in the real-time instantaneous precise point positioning (PPP) with ambiguity resolution (AR) has not been investigated. In this study, based on the triple-frequency ionosphere-free combination, the positioning performance of instantaneous decimeter-level PPP AR was assessed with real-time orbit, clock and phase biases provided by the Centre National d'Études Spatiales Navigation Team (CNES/NAV). Experimenting on the GPS/Galileo observations from the 42 globally distributed stations, the wide-lane (WL) ambiguity residuals within ± 0.25 cycle for GPS L1/L2/L5, Galileo E1/E5a/E5b and E1/E5a/E6 frequency combinations were 92.54%, 90.72% and 96.48% with single-epoch data, respectively. When the WL ambiguities are fixed instantaneously, owing to the low combination noise of Galileo E1/E5a/E6, the positioning performance of instantaneous PPP AR with GPS/Galileo (E1/E5a/E6 used) outperforms that of GPS/Galileo (E1/E5a/E5b used). If the position dilution of precision is <1.5, the Root Mean Square (RMS) of GPS/Galileo (E1/E5a/E6 used) for east, north and up components are 0.13 m, 0.13 m and 0.57 m, respectively, while those of GPS/Galileo (E1/E5a/E5b used) are 0.17 m, 0.19 m and 0.62 m, respectively. Moreover, the WL ambiguity fixing rate of GPS/Galileo (E1/E5a/E6 used) is higher than that of GPS/Galileo (E1/E5a/E5b used), which shows an improvement of approximately 9% in the relatively low satellite elevation angles (20°< elevation angle < 40°). The results indicate that the Galileo E6 signal can bring a significant improvement in real-time instantaneous decimeter-level PPP AR. [ABSTRACT FROM AUTHOR]

The integrated navigation of single-frequency global navigation satellite system (GNSS) and inertial navigation system (INS) has broad application prospects with the development of multi-constellation GNSS. However, GNSS signals are susceptible to interference from a complex environment, which results in low-quality observations. The combination of frequencies cannot be applied for a single-frequency signal, so it is difficult to fix the ambiguity and process cycle slip. Therefore, the method of ambiguity resolution and cycle slip processing with INS aiding is proposed in this paper. When full ambiguities cannot be completely fixed, a subset of ambiguity is determined based on the elevation angle and posteriori residuals. The satellite is firstly eliminated one by one if the absolute value of posteriori residual is over the set threshold. And if the ambiguities still cannot be fixed, the satellite with the minimum elevation angle is eliminated each one. The short-term and high-accuracy position predicted by the INS was used as the constraint equation of the cycle slip detection. The unit weight mean square error of the cycle slip detection equation was used to identify the epoch where the cycle slip occurs, and the residual calculated by robust estimation was used to detect and repair the cycle slip. A set of data collected by a vehicle was used to analyze the proposed method. The experimental results showed that the proposed partial ambiguity resolution can obtain the optimal ambiguity fixing rate and positioning performance compared with the full ambiguity resolution and partial ambiguity resolution based on the elevation angle. The proposed algorithm can effectively detect and accurately repair the cycle slip for the simulated small and large cycle slips, and the cycle slips can still be detected when the global positioning system (GPS), global navigation satellite system of Russia (GLONASS), and BeiDou navigation satellite system (BDS) were outage for 10 s, 5 s, and 10 s without sufficient visible satellites. [ABSTRACT FROM AUTHOR]

The ionospheric delay is one of the major error sources in GNSS precise data processing. In most scenarios, only the first-order ionosphere delay was fully considered, which contributes to about 99% of the total ionosphere delay. Recent research reveals that the higher-order ionospheric (HOI) delay can also introduce up to 2 cm biases for the GPS L1 observations. This bias is generally not considered in the underlying function model and consequently, it introduces unintentional biases, which may degrade the reliability of the ambiguity estimation in long-baseline RTK. This study examined the impact of the HOI on the observations and the ambiguity estimation procedure. We considered the HOI bias in the underlying model to evaluate the unintentional HOI bias on the success rate (SR) of ambiguity estimation. The numerical results showed that the double-differenced HOI effect reaches about 7 mm in the ionospheric active period, and can affect the ambiguity estimation success rate by up to 30% in the GNSS data processing and the HOI impact is more significant when a new satellite arose. The presence of the HOI biases may change about 0.3% ambiguity fixing results. In addition, the HOI bias can also introduce several millimeters biases in positioning solutions. [ABSTRACT FROM AUTHOR]

AR (Ambiguity Resolution) is one of the critical issues in high-accuracy GNSS (Global Navigation Satellite System) applications. Commonly, the double-difference AR technique is employed in GNSS network data processing. With the demand of high-accuracy, low-latency and high-integrity GNSS orbit, the orbit estimation in sequential mode becomes a candidate of that in batch mode. Unlike orbit estimation with double-difference AR in either batch or sequential mode, researches on real-time orbit estimation with undifferenced AR in sequential mode is still limited. In this study, real-time orbit determination with epoch-independent undifferenced AR in sequential mode is assessed. With one-week observation data from about 100 global distributed IGS (International GNSS Service) network stations, simulated real-time Galileo orbit determination are conducted with GFZ post-processed solution as reference for validation. Numerical results indicate that, first, the 3D error RMS (Root Mean Square) of fixed orbit is about 30% smaller than that of float orbit; second, the Galileo orbit error RMS reach 3.66, 3.60 and 3.09 cm for the radial, tangential and normal directions respectively for the fixed solution; third, small jumps exist in the real-time orbit and may be attributed to the temporal variations of UPD (Uncalibrated Phase Delay) and wrongly fixed ambiguities. In summary, the orbit quality is comparable to that of IGS real-time solutions, and further improvements may be achieved with improved AR constraint strategy and background orbit model. [ABSTRACT FROM AUTHOR]