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GNSS phase observable-specific signal bias (OSB) corrections are essential for widespread application of precise point positioning with ambiguity resolution (PPP-AR) or PPP-RTK. However, subject to the orbital error effects, conventional undifferenced (UD) model-derived BeiDou System (BDS) real-time (RT) OSB products are usually unsatisfactory. In this study, a novel OSB-generating method assisted by the double-differenced (DD) model is proposed. The reliable integer UD ambiguities are obtained by converting DD ambiguities with given ambiguity datums, by which the RT orbit error effects on ambiguity fixing can be reduced during the OSB extraction and PPP-AR process. Validated using data from two regional sparse GNSS reference networks in Shaanxi, China, and Europe, results show that the proposed method-derived OSB products can improve RT PPP-AR performance effectively. In the Shaanxi network, the narrow-lane ambiguity residuals for BDS-3 within ± 0.25 cycles are improved by 23.1% and 33.2% compared to those using the UD model and Centre National d’Etudes Spatiales (CNES)-derived OSB products, respectively, and the corresponding values are 15.2% and 43.1% in the European network. A centimeter- or even millimeter-level positioning accuracy can be achieved for BDS PPP using the poposed OSB products in both networks. In the kinematic PPP-AR test within the Shanxi network, the mean RMS of the BDS-2/3 fixed solutions in the east, north, and up directions is 0.9, 0.7, and 2.3 cm, with a decrease of 57.1%, 53.3%, and 46.5% compared to that using OSB derived by UD model. The median Time-To-First-Fix (TTFF) is also shortened from 23.8 to 7.5 min. [ABSTRACT FROM AUTHOR]

The observation data is the basis for the global navigation satellite system (GNSS) to provide positioning, navigation and timing (PNT) service, and the observation quality directly determines the performance level of the PNT service. At present, the analysis of GNSS observations quality is partial and can only be based on a single index assessment. GNSS observation quality is difficult to analyze comprehensively by fusing multiple indicators. To solve the above problem, the supervised and unsupervised machine learning algorithms are applied, and a new comprehensive and classification method of GNSS observations quality based on the k-means clustering algorithm (k-means) and K-nearest neighbor algorithm (KNN) was proposed. The four core index features of GNSS observations, including data integrity rate, carrier-to-noise-density ratio (CNR), pseudorange multipath and the number of observations per slip, were selected to construct the sample dataset. The sample set was unsupervised clustered based on the k-means algorithm, and the classification label of GNSS observations quality was obtained. Then KNN algorithm was used to construct a comprehensive classification and evaluation model for GNSS observations quality. The data from 30 MGEX stations in the Asia–Pacific region in 2019 were selected for modeling analysis. The experiment results show that: (1) a strong correlation has been revealed between pseudorange multipath, CNR and the number of observations per slip. (2) The average classification correctness rate of the new model was over 90% by n -fold cross-validation. (3) The new model can effectively realize the automatic evaluation and classification of GNSS observations quality and easily distinguish the superiority and inferiority of the station observations. The relevant results provide a new idea for the automatic classification and assessment of GNSS observation quality. [ABSTRACT FROM AUTHOR]

The Real-Time Kinematic (RTK) positioning method of the Global Navigation Satellite System (GNSS) has been widely used for landslide monitoring. The stability of its reference station is crucial to obtain accurate and reliable monitoring results. Unstable reference stations due to the geological environment and human activities are difficult to detect and in practical applications often ignored. As a result, it affects the positioning solutions and subsequently the interpretation and detection of landslide motions, which must be addressed in GNSS landslide monitoring. To solve this problem, we propose using the Precise Point Positioning (PPP) technique to analyze the stability of the reference station by verifying its position. The deformations of the monitoring stations are then compensated. First, the reference station coordinates are obtained by the PPP technique and tectonic motion is considered in data processing. The change or breakout of the reference station position is then determined using a cumulative sum control chart method. Finally, each monitoring station's displacements are compensated according to the displacements of the reference station. According to the results of the Tengqing landslide experiment, the PPP technique can be used in GNSS landslide monitoring to analyze the stability of reference stations. With PPP, millimeter-level accuracy for the coordinates of reference stations is achieved. Compared to the traditional deformation series, the compensated displacement series more reliably reflects the landslide motions. This study will increase the reliability of monitoring results and contribute to implementing GNSS in monitoring landslides. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) positioning technology is widely used in landslide monitoring due to its unique real-time and high-precision advantages. However, in complex landslide environments with severe occlusion, multipath error becomes one of the main error sources affecting GNSS real-time kinematic high-precision positioning, as it cannot be eliminated by differential correction. Traditional sidereal filtering methods cannot retain deformation information, which affects the accuracy of landslide early warning. To mitigate multipath error and preserve landslide deformation information, an improved sidereal filtering method based on mutation points and landslide evolution stage recognition is proposed. The method considers the landslide evolution stage, establishes a dataset for sidereal filtering, matches the multi-day correlation data with the sliding section-related data, and constructs a multipath model using averaging. Experimental results show that, compared with the traditional sidereal filtering and conventional segmentation methods, the proposed method reduces the coordinate deviation (QE) in the 3D direction by 25.02% and 22.13% and reduces the fitting deviation (QR) by 4.01% and 36.21% during the stabilization stage. During the critical sliding stage, QE decreases by 48.54% and 23.8%, and QR decreases by 60.12% and 42.54%, respectively. The proposed method has the best smoothness and power spectral density indicators in both stages. It has also been successfully applied to the Heifangtai landslide in Gansu Province, providing more stable and reliable data than traditional methods, avoiding delayed and false alarms, and issuing a red warning 3 h before the landslide failure, demonstrating its practical value. [ABSTRACT FROM AUTHOR]

Non-holonomic constraint (NHC) is a commonly used enhancement technology for GNSS/SINS vehicle positioning. Due to the vehicle's inevitable side slip, bounce, and other special movements during driving and the non-ignorable IMU installation angle, the traditional NHC can no longer satisfy the zero-value assumption for vehicle lateral and vertical velocity. The latest research demonstrates that machine learning (ML) can establish a mapping relationship between IMU output and NHC pseudo-measurements and directly predict the NHC value in the observation domain, which can improve the NHC performance. However, the existing ML-based NHC prediction and corresponding stochastic model are not sufficiently accurate and robust, especially for complex vehicle movements, such as turning. Moreover, the current studies mainly focus on IMU-only dead reckon (DR) positioning and lack feasible verification of NHC-assisted GNSS/SINS integrated positioning performance during the complete travel. Thus, we study a convolutional neural network based on a vehicle motion state classification (VMSC) for NHC prediction and an adaptive stochastic model in the variance domain using the NHC innovation residuals. Additionally, we propose an “end-to-end” framework for adaptive NHC-assisted GNSS/SINS vehicle positioning during the whole traveling, and then, the validation experiment is conducted with the vehicle GNSS/SINS tightly coupled real-time kinematic positioning in the urban environment. Numerical results show that the average predicted accuracy of VMSC-based NHC-Nets can reach approximately 2 cm/s, and by using the new NHC, the positioning error is reduced by around 91.4% compared with the IMU-only DR during a 60-s GNSS outage; for the whole traveling, the GNSS/SINS positioning accuracy achieved a significant improvement, especially in the heavily limited GNSS observation environment. Due to a relatively high DR accuracy, the GNSS ambiguity fixed rate and satellite availability can also be promoted to a certain extent. [ABSTRACT FROM AUTHOR]

Due to the multipath and signal shading effects, there exist biases in the carrier phase measurements, which degrades the reliability of ambiguity resolution in real-time kinematic (RTK) positioning and, subsequently, the positioning accuracy. Integrity monitoring is an effective way to measure, improve, and guarantee the correctness of the RTK positioning solutions, but most integrity monitoring has focused only on the pseudorange faults and further the traditional ambiguity validation methods cannot monitor faulty ambiguity resolution separately. To provide high accuracy and high reliability for safety–critical applications, this study proposes a solution separation (SS)-based method for integrity monitoring of RTK precise positioning, in which the SS failure mode and test statistics are used to monitor the reliability of fixed ambiguity solutions by detecting faulty ambiguity fixes and bound positioning errors in the position domain using protection level (PL). The vehicular test with a low-cost receiver shows that the SS method can effectively detect and exclude fault ambiguity resolutions by 98.35%, and the double-difference residuals of SS are reduced from 6.89 cm to 2.56 cm. The positioning accuracy with the SS method has gained an 83.64% improvement compared with the traditional methods. The horizontal PL and the vertical PL can also effectively bound the positioning errors, with average values of 4.49 cm and 12.25 cm, respectively. The SS PL can achieve 99.17% and 96.14% in the horizontal and vertical directions to provide normal integrity service, respectively. [ABSTRACT FROM AUTHOR]

Currently, Global Navigation Satellite System (GNSS) Real-Time Kinematic positioning (RTK) and Precise Point Positioning (PPP) techniques are widely employed for real-time monitoring of landslides. However, both RTK and PPP monitoring techniques have their limitations, such as limited service coverage or long convergence times. PPP-RTK technique which integrates RTK and PPP is a novel approach for monitoring landslides with the advantages of rapid convergence, high-precision, and a wide service area. This study summarizes the limitations of RTK, PPP, and PPP-RTK monitoring techniques and suggests some improved strategies. Their performances are compared and analyzed using real monitoring data. The experiment results demonstrate that RTK is the best option for small-scale (the baseline distance < 15 km) and real-time landslide monitoring without considering the cost. PPP technique converges to centimeter-level accuracy in tens of minutes, only suitable for the stability analysis of reference stations. Over a large area (the baseline distance < 100 km), PPP-RTK can provide excellent horizontal accuracy and adapt the service range in response to the demand for monitoring accuracy, as the vertical accuracy is significantly impacted by the service range and elevation difference. Finally, the characteristics of three techniques are integrated to form a comprehensive landslide monitoring technique that considers intelligence, robustness, and real-time. [ABSTRACT FROM AUTHOR]

Real-time satellite clock offsets are key in realizing real-time precise point positioning (PPP). Typically, tens of minutes are required for re-convergence because many tropospheric and ambiguity parameters are estimated in the clock offset estimation when the interruption of observation data occasionally occurs. This contribution proposes a rapid re-convergence method for multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation. In case of a few seconds of interruption, the dual-thread integer ambiguity resolution method is proposed. The float clock offset, uncalibrated phase delay, fixed and float ambiguities, clock offset with IAR, zenith wet delay (ZWD) and inter-system bias (ISB) are generated in a slow thread, in which the fixed and float ambiguities, ZWD and ISB are used in a quick thread to achieve rapid re-convergence. Observations from 60 globally distributed stations were processed using the proposed method. The experimental results show that rapid re-convergence, fast estimation and high-precision clock offsets can be achieved. The re-convergence time of clock offset estimation was 0.14, 0.15, 0.74, 0.36 and 2.48 min for the GPS, Galileo, BDS-2, BDS-3 and GLONASS, respectively. Most satellite clock offsets can realize instantaneous re-convergence. The clock offset standard deviations are 0.028, 0.024, 0.069, 0.043 and 0.125 ns, respectively. The computation times were 21.4 and 1.7 s for the slow and quick threads, respectively. Compared to the float PPP solutions, the positioning accuracy of the PPP-AR was improved by 53.9, 29.9 and 18.2% from 1.80 to 0.83 cm, 1.57 to 1.10 cm and 3.63 to 2.97 cm for the east, north and up components, respectively. In case of interruptions lasting from a few minutes to tens of minutes, the ZWD, ambiguities and ISB information before interruption are used in the clock offset estimation, and a strong constraint is imposed on the normal equation, i.e., a large value (e.g., 105) is used instead of the diagonal value of the normal equation matrix corresponding to each estimated parameter. Experimental results show that rapid re-convergence can be achieved for GPS and Galileo with an interruption of 10 min, whereas the rapid re-convergence cannot be achieved for BDS-2, BDS-3 and GLONASS because of the impact of satellite orbit accuracy, error model, and neglection of the inter-frequency bias, respectively. [ABSTRACT FROM AUTHOR]

The service areas of the BeiDou Navigation Satellite System (BDS) are China, the Asia–Pacific, and the world via three stages of development. The BDS constellation is designed to maintain a geostationary Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO). These orbital maneuvers yield certain difficulties for data processing, especially for the BeiDou satellites, such as a decrease in the real-time service performance, which causes a missing precise orbit product from the maneuvered satellites. The frequencies of the orbital maneuvers for the GEO and IGSO satellites are higher than those for the MEO satellites. The maneuvering time and strategy cannot be obtained by common users due to secrecy, which can yield a decline in the service performance of the BDS. Thus, in this study, we analyzed the variation in the orbital semimajor axis for the satellites. The long-term variation in the orbital semimajor axis changes linearly. The short-term variation in the orbital semimajor axis also has periodicity, which can be described by the sum of sine functions. According to the long-term variation in the orbital semimajor axis for the satellites, we propose a detection method for in-plane orbital maneuvering of the GEO, IGSO, and MEO satellites. We then propose a detection method for out-of-plane maneuvering of the GEO satellites. BDS and Global Positioning System (GPS) data from the broadcast ephemeris were analyzed to verify the proposed methods. The experimental results from 2013 to 2019 show that the frequency of orbital maneuvering is approximately once a month for the GEO satellites, once every six months for the IGSO satellites, and once every 1.4 years for the MEO satellites. [ABSTRACT FROM AUTHOR]

The atomic clock is the core of the Global Navigation Satellite System (GNSS), which plays an important role in Positioning, Navigation and Timing (PNT) services. However, the long-term characteristics of the global BeiDou navigation system (BeiDou-3) and comparison of satellite clocks performance for the five GNSSs have not yet been revealed. We evaluated and analysed the performance of atomic clocks for BeiDou-3 and other GNSSs using satellite clock offset data. The important contributions are summarised as follows. (1) The phase and frequency sequences of Passive Hydrogen Maser (PHM) and rubidium (Rb) atomic clocks for BeiDou-3 are more stable and continuous than those of the regional BeiDou navigation system (BeiDou-2). The clock offset model precision and average frequency stability at 10,000, 1000, and 100 s for the BeiDou-3 satellite clock offsets are 0.15 ns and 6.8 × 10–14, respectively, exhibiting significant improvements compared with those for BeiDou-2. (2) The performance of cesium (Cs) atomic clocks installed on Global Positioning System (GPS) Block IIF are more inferior than Global Navigation Satellite System (GLONASS), which may be due to the poor level of Cs atomic clock manufacturing technology or obvious noise characteristics. Thus, more attention should be paid to these two satellite clocks. (3) A comparison of various indicators revealed that the satellite clocks for Galileo are the best, followed by BeiDou-3, GPS Block IIF satellites with Rb atomic clocks, Quasi-Zenith Satellite System (QZSS), BeiDou-2, GLONASS, GPS Block IIR, and Block IIR-M. The GPS Block IIF satellites equipped with a Cs atomic clock shows the poorest performance. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) with wide-lane ambiguity resolution (PPP-WAR) can quickly achieve decimeter-level positioning accuracy, which is an essential improvement for real-time PPP in terms of reliability and accuracy. However, current implementations of PPP-WAR are based only on the standard Kalman filter (KF) under the assumption of uncorrelated measurements. As Global Navigation Satellite System measurements are often contaminated by colored noises, a KF considering the time-correlation of measurements (CKF) has the potential to improve the performance of PPP-WAR. In this paper, we proposed a real-time cascading PPP-WAR technique based on the CKF model. A real-time kinematic vehicle experiment is conducted to assess the performance of the proposed real-time PPP-WAR method. On the one hand, we analyze and compare the efficiency of CKF-based cascading PPP-WAR with that of KF-based PPP-WAR. The filter output analysis shows that the proposed CKF method is, overall more efficient than the standard KF method in terms of performance indicators, such as wide-lane ambiguity fix-rate, time-to-first-fix, ambiguity residual statistics and correctness of the filter’s stochastic model. On the other hand, we evaluate the convergence time and positioning accuracy of CKF-based PPP-WAR by comparing it with KF-based PPP-WAR. The results show that the fix-rate of the CKF method increased by 26% compared with the KF-based WAR method. Moreover, the CKF-PPP-WAR can achieve 0.5 m (sub-meter) level with 1–4 s faster, 0.2 m level with 2–20 s faster, 0.1 m level with 5–60 s faster compared with float PPP. On average, CKF-PPP-WAR can achieve decimeter-level accuracy by reducing the convergence time 20% than KF-PPP-WAR, and 25% than float PPP. After convergence, the average positioning accuracy of CKF-PPP-WAR is 2–6 cm better with 25% improvement over float PPP and 1–4 cm better with a 23% improvement over KF-PPP-WAR. [ABSTRACT FROM AUTHOR]

Apart from positioning accuracy, the reliability of a navigation system is also significant, especially for safety–critical applications, such as intelligent vehicle navigation. Generally, the Global Navigation Satellite System (GNSS) positioning algorithm assumed that measurement noise is uncorrelated white noise. However, the appearance of colored noise, which comes from various noise sources, does not follow the Gaussian white noise assumption in the Kalman filter and would degrade both the accuracy and reliability of positioning. To deal with this problem, we propose a linear Kalman filter-based integrity monitoring method, which is based on a linear colored Kalman filter (CKF) considering measurement time correlation colored noise by a first-order Gauss–Markov model. Both simulated and real dynamic experiments were conducted to test the proposed algorithm. The results proved that CKF is capable of modeling time correlation with a realistic filter covariance in both simulated static and in-field dynamic tests. Furthermore, the performance of an integrity monitoring system with a protection level based on the CKF has proved to be more feasible and effective to bound position errors. Besides, the simulated results demonstrate that it can typically reduce false alarm by 24.81% in the horizontal direction and 39.47% in the vertical direction in a simulated experiment. The dynamic test shows that the proposed method can reduce the false alarm rate by 22.11% and 15.62% in the horizontal and vertical directions, respectively. [ABSTRACT FROM AUTHOR]

Real-time satellite orbit and clock product is a key prerequisite for real-time precise positioning service based on precise point positioning (PPP). With the rapid development of the multiple global navigation satellite systems (Multi-GNSS), about 120 satellites will be processed for Multi-GNSS real-time clock estimation. Unfortunately, the computation is very time-consuming, especially for quality control since problematic observations are inevitable. Taking advantage of computer technology, sequential least square adjustment with an adapted online quality control procedure is developed to rapidly estimate Multi-GNSS real-time clocks, although various filtering estimators are commonly used now. A globally distributed network including 70 stations tracking mostly satellites of GPS, GLONASS, BDS, and Galileo is employed for experimental validation. The results show that the computation time per epoch is less than 3 s in average and can meet the 5 s update rate of the IGS real-time clock product. Compared to the GeoForschungsZentrum MGEX (GBM) final clock product, the averaged STD values of the estimated clocks of the four GNSS systems are 0.089 ns and 0.153 ns, respectively, for the clock solutions with and without the online quality control, which also confirms the importance of the quality control procedure. The Multi-GNSS kinematic PPP experiment using the estimated clocks with quality control shows that the positioning RMS is about 4 cm and generally 2 cm in vertical and horizontal components, respectively, and the corresponding convergence time is about 15 min. [ABSTRACT FROM AUTHOR]

In order to estimate the satellite clock offset in a real-time mode, a new algorithm of adaptively robust Kalman filter with classified adaptive factors for clock offset estimation is proposed. Compared with standard Kalman filter clock offset model, the new method can detect and control outliers and clock jumps automatically in real-time. Moreover, the clock model parameters, which contain the clock offset, clock speed and clock shift, are classified to decide the adaptive factors in the new model. Thus, clock jumps with different characteristics can be distinguished more effectively. Meanwhile, the dynamic noise characteristics of clock offset series are used for stochastic modeling. An actual numerical example is presented, which shows that the proposed filter can give a better performance than other commonly used filters. [ABSTRACT FROM AUTHOR]

Precise and reliable fractional cycle bias (FCB) products are critical for ambiguity resolution of precise point positioning (PPP). Three PPP models are usually adopted to generate the FCB products, i.e., the traditional ionospheric-free combined PPP (IF-PPP) model, the uncombined and unconstrained PPP model (UU-PPP) as well as the ionospheric-constrained PPP (IC-PPP) model. Considering that different observation models and ionospheric delay constraints are used, the applicability and interoperability of the obtained FCB products are assessed. We presented the equivalent conversion formulas of different FCB products obtained with different PPP models, which are then converted and compared. The root mean square (RMS) of the wide-lane (WL) FCB differences for IF-UU, IF-IC and UU-IC is 0.021, 0.024 and 0.010 cycles, while the RMS of the narrow-lane FCB differences is 0.028, 0.018 and 0.021 cycles. The precision of the WL FCBs based on the uncombined PPP models is higher than that based on the IF-PPP model since the new WL ambiguities derived from the uncombined ambiguities are free of the pseudorange noise. The equivalence of the FCB products estimated from the three different PPP models is confirmed in theory and by experiment results. To further evaluate the performance of the three PPP models, the positioning accuracy, the convergence time and the ambiguity fixing success rate are calculated using IGS data. The maximum positioning difference is less than 0.9 mm among the three PPP models. Compared to the float solutions of the IF-PPP, UU-PPP, IC-PPP with GIM model or with re-injected ionospheric delay corrections, the convergence time is shortened by 38.5%, 46.2%, 50.0% and 87.8% and the positioning accuracy improved by 27.1%, 38.9%, 41.1% and 25.7%, respectively. The ambiguity fixing success rate of the uncombined PPP models is slightly higher than that of the combined model, and fast ambiguity-fixed solution can proceed with high-precise ionospheric delay corrections. [ABSTRACT FROM AUTHOR]