Ambiguity Resolution Performance Research Articles

UPDs estimation and ambiguity resolution performance evaluation of LEO navigation system

Low-Earth orbit (LEO) satellites have fast motion and thus provide rapid geometric change relation to the ground stations in a short period of time, which are expected to improve the positioning performance. In this study, a LEO constellation of 160 LEO satellites was simulated and simulated LEO observation data at global, European, and American stations were used to estimate the uncalibrated phase delays (UPDs) and achieve static and kinematic precise point positioning (PPP) ambiguity resolution (AR). The quality of the estimated UPD products were evaluated. More than 89 % and 96 % of the wide- and narrow-lane UPDs had a posteriori residual of less than 0.15 and 0.25 cycles, respectively. In static PPP, all ambiguity fixing rates were larger than 63 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 8 %, 6 % and 7 %, respectively; the average root-mean-square errors (RMSEs) in the east, north, and up components at the global, European and American stations were decreased by (22 %, 20 %, 15 %), (36 %, 34 %, 28 %) and (44 %, 31 %, 29 %), respectively. In kinematic PPP, all ambiguity fixing rates were larger than 40 %. Compared with float solutions, the average convergence time of the fix solutions at the global, European and American stations was accelerated by 4 %, 19 % and 14 %, respectively; the average RMSEs in the east, north, and up components at the global, European and American stations were decreased by (10 %, 10 %, 7 %), (27 %, 22 %, 11 %) and (32 %, 20 %, 10 %), respectively. In both static and kinematic PPP, AR accelerated the convergence time and improved the positioning accuracy.

A novel mode of INS-aided BDS real-time high-rate and precise kinematic relative positioning between two moving platforms

ABSTRACT For kinematic relative positioning users between two moving platforms, limited communication bandwidth and computation ability usually cannot support real-time transmission of high-rate (≥10 Hz) BeiDou Navigation Satellite System (BDS) data. The performance of Ambiguity Resolution (AR) is also a major challenge in signal blocked and loss of lock environments. Based on BDS and Inertial Navigation System (INS) data, we develop a novel mode of INS-aided BDS kinematic relative positioning between two moving platforms, aiming to realize real-time, high-rate and precise positioning with low-cost communication modules in challenge environments. To achieve this goal, the INS-aided high-rate relative kinematic positioning and INS-aided BDS AR re-initialization methods are proposed. In this mode, the baseline bias caused by the different position datum is first defined and resolved. Then, high-rate INS data are assisted to obtain kinematic relative position when real-time kinematic positioning results are unavailable within 1 second. Once the BDS data are available, the predicted relative position is used as additional constraint to facilitate AR re-initialization and improve the kinematic positioning performance. The performance of these methods is discussed in a set of experiments with 1 Hz BDS data and 100 Hz INS data, and compared with the conventional method by sending raw BDS/INS measurements. The results show that the proposed methods can achieve an accuracy of about 5 cm for the INS-aided 100 Hz relative positioning in baseline components and lengths, which is equal to the conventional method, but the transmitted data have been sharply reduced by an average of nearly 80%. With the assistance of INS-predicted baseline constraint, the relative positioning performance has been further improved. The accuracy of baseline length errors is less than 4 cm, and the AR fixing rates keep larger than 95% during the experiment, while the wrongly fixed rates are reduced to less than 0.5%.

Validation and assessment of multi-GNSS phase bias products from IGS analysis centers

Phase bias plays a crucial role in precision point positioning (PPP) with ambiguity resolution. Currently, an increasing number of analysis centers are being of releasing multi- Global Navigation Satellite System (GNSS) phase bias products. However, it remains uncertain how different phase bias products, receiver types, and GNSS systems combinations might impact user-side positioning performance and ambiguity resolution capabilities. In view of this, this contribution systematically investigates the effects on PPP with ambiguity resolution. Four types of receivers, including SEPTENTRIO POLARX5, LEICA GR50, JAVAD TRE_3 DELTA, and TRIMBLE ALLOY, are selected, and six types of GNSS system combinations, namely, GPS, Galileo, BDS3, GPS/Galileo, GPS/BDS3, GPS/Galileo/BDS3, are used, and the phase bias products from OSB (Observable-specific Bias)-CODE (Center for Orbit Determination in Europe), OSB-CNES/CLS (Centre National d’Etudes Spatiales Geodesy Team), OSB-GFZ (German Research Centre for Geosciences/Germany), OSB-WHU (Wuhan University), OSB-CNES/NAV (Centre National d’Etudes Spatiales Navigation Team), IRC (Integer Recovery Clock)-CNES/CLS, IRC-GFZ are adopted for the numerical experiment. Compared with the float-solution, the results show that the accuracy of PPP fixed-solution with single-system can be improved 1 cm–3 cm, and the convergence time is reduced 2 min–15 min. The positioning performance using the seven phase bias products for any single-system satisfies the following order from the best to the worst: OSB_WHU > OSB_CODE > OSB_CNES/CLS ≈ OSB_CNES/NAV > OSB_GFZ > IRC_CNES/CLS ≈ IRC_GFZ, but the performance of ambiguity resolution do not present certain characteristics. Meanwhile, the ambiguity-fix success-rate and Time to First Fix can keep at 80%–96% and 20 min–40 min with single-system, respectively. In the case of multi-system, although the difference in the positioning performance among the phase bias products is not significant, the multi-system outperforms the single-systemin terms of both positioning performance and ambiguity resolution. However, the difference between the dual-system and the triple-system is smaller. In addition, the positioning performance corresponding to different receiver types also shows distinction, while there is no significant difference in the ambiguity resolution performance between different receiver types.

BDS-3/Galileo multi-frequency phase-only model for long baseline with best integer equivariant estimation

Currently, long baselines generally adopt phase-code models that include both phase and pseudorange observations, such as dual-frequency ionosphere-free (PC-DFIF) and multi-frequency uncombined (PC-MFUC) models. The more significant unmodeled errors in pseudorange are likely to reduce ambiguity resolution (AR) performance, and the phase-only model with only phase observations involved is expected to avoid this problem. In view of the fact that existing phase-only research is mainly focuses on GPS/BDS-2 triple-frequency signals, a BDS-3/Galileo multi-frequency phase-only (MFPO) model is proposed in this paper. Four linearly independent extra-wide-lane (EWL) phase ranges (i.e. IR1, IR2, EWL3 and EWL4) are determined stepwise with a sliding window, among which the first two belong to ionosphere-reduced (IR) combination. In the determination of EWL3/EWL4, in addition to theoretical precision, the amplified phase multipath is also considered. The aforementioned four EWL phase ranges are then equivalently transformed to wide-lane (WL) combinations with smaller coefficients, and further incorporated with narrow-lane (NL) equation to construct MFPO model. Meanwhile, the best integer equivariant (BIE) is introduced to improve AR performance. The MFPO model is evaluated with real-tracked long baseline data. The performance of EWL phase ranges can be significantly improved after phase multipath is considered. The float solution, fixed solution and BIE solution of MFPO model all achieve centimeter-level accuracy. However, during convergence stage, incorrect fixing might exist in fixed solution, while BIE solution can improve this situation. The MFPO model is further compared with commonly used PC-DFIF and PC-MFUC models. The accuracy of the three models after convergence is basically the same, while the MFPO model has higher accuracy during convergence stage.

Improving ambiguity resolution with common-antenna-based dual-board receiver for low-cost real-time kinematic positioning

Ambiguity resolution is of critical importance to the carrier phase-based real-time kinematic (RTK) positioning method. Improving the accuracy of float ambiguities is beneficial for achieving ambiguity resolution. However, the large measurement noise from low-cost receivers will worsen the estimation accuracy of float ambiguities, which affects the ambiguity resolution performance. In this contribution, to reduce the influence of large measurement noise on ambiguity resolution for low-cost receivers, an improved RTK method for ambiguity resolution is proposed to enhance the accuracy of float ambiguities by equipping the rover receiver with common-antenna-based dual global navigation satellite system (GNSS) boards instead of only one GNSS board. First, the dual-board design can increase the measurement redundancy of the same frequency to suppress the measurement noise. Second, because the common-antenna design can form a moving zero-baseline between the dual GNSS boards, the ambiguities between them can be easily fixed. Known fixed ambiguities can be used as constraints to strengthen the positioning model. Simulation and real-world static and kinematic experiments were conducted to test the proposed method. The results demonstrate that the proposed method can improve the accuracy of float ambiguities by increasing the redundancy of the measurements and introducing the constraints of the ambiguities, and the improved accuracy is about 20%. Compared with the traditional single-board RTK method, better ambiguity resolution performance can be achieved by taking advantage of the proposed common-antenna-based RTK method.

Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time.

Multi-Sensor and Analytical Constraints Tightly Augmented BDS-3 RTK for Vehicle-Borne Positioning

The third generation BeiDou Navigation Satellite System (BDS-3) can provide high-accuracy service for vehicle-borne positioning and navigation. The performance of BDS-3 in terms of accuracy, continuity, and reliability, however, are significantly degraded in environments with weak satellite observability. To improve the positioning performance of BDS-3 around the partial and complete signal-blocked areas, this paper presents a multi-sensor and analytical constraints tightly augmented BDS-3 Real-time Kinematic (RTK). The Non-holonomic Constraint (NHC), vehicle-odometer, and dual-antenna-based attitude constraints applied to restrain the drift of the position estimate from Inertial Measurement Units (IMU). Compared to previous work, it’s the first time to reveal that the Ambiguity Resolution (AR) performance of RTK can be augmented by integrating these measurements. To validate the performance of this proposed method, the drifts of position and attitude during the poor satellite observability and the impacts of those sensors and constraints on ambiguity fixing are analyzed based on an urban vehicle-borne test. The test results illustrate that the presented model brought 52.73%, 55.56%, and 49.44% positioning accuracy improvements in the north, east, and vertical components compared to the RTK mode. Meanwhile, 10.87% and 57.20% attitude accuracy enhancements in roll and heading were obtained compared to the traditional RTK/IMU tight integration mode. In addition, this presented model can retain the accuracy of position and attitude during the partial and complete satellite signal outage periods, and can also improve the ambiguity resolution performance significantly.

Performance Assessment of Multi-GNSS PPP Ambiguity Resolution with LEO-Augmentation

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from January 1 to January 3 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to redu ce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate.

BDS-3 new signals observable-specific phase biases estimation and PPP ambiguity resolution

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.

Tightly Coupled Integration of BDS-3 B2b RTK, IMU, Odometer, and Dual-Antenna Attitude

Real Time Kinematic (RTK) based on single-frequency observation is still widely used in many fields due to the characteristics of low-cost and low-power consumption. However, the positioning performance of single-frequency RTK in terms of accuracy, stability, and continuity would be significantly degraded during the harsh satellite environments. To improve the performance, this contribution presented a model of multi-sensor and analytical observations augmented the single frequency RTK tightly based on a modified Psi-angle state model. In such a model, the single frequency observations of the new signal of BDS-3 B2b are tightly integrated with inertial measurements, odometer data, dual-antenna attitude, and non-holonomic constraint. To evaluate the presented model, the typical navigation performance and the ambiguity resolution performance are analyzed based on a set of vehicle-borne data. Results illustrated that the Inertial Navigation System (INS) would bring about 13.5%, 16.2%, and 12.3% position enhancements to the BDS-3 B2b RTK mode. Such improvements could be up to 15.9%, 16.2%, and 25.2% while adding the non-holonomic constraint and odometer data. Besides, non-holonomic constraint and odometer also upgrade the attitude accuracy visibly in pitch and heading directions, with enhancements of about 16.9% and 62.9%. In contrast, augmentations from the dual-antenna attitude are mainly presented in terms of heading angle with about 29.5% compared to the RTK/INS/Odometer/NHC tight integration mode. Besides, the convergence time of yaw angle is visibly enhanced while using the odometer/NHC, the dual-antenna heading, or the two together. Moreover, the ambiguity resolution performance could also be improved while using the presented model. Due to the enhancements in position and attitude brought by different sensors, the ADOP performance would be improved to varying degrees. Besides, the fixed rate and reliability of ambiguity resolution could also be enhanced.

Tight integration of BDS-3/BDS-2/GPS/Galileo observations considering the new overlapping DISBs and its application in obstructed environments

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.

BDS-2/BDS-3 uncalibrated phase delay estimation considering the intra-system bias

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.

Assessment of Galileo FOC + IOV Signals and Geometry-Based Single-Epoch Resolution of Quad-Frequency Carrier Ambiguities

Galileo can independently provide navigation and positioning services globally. Galileo satellites transmit quad-frequency E1, E5a, E5b, and E5 signals, which can benefit the integer ambiguity rapid resolution. Firstly, the qualities of Galileo signals from Carrier-to-Noise (C/N0), Multipath Combination (MPC), and pseudo-range and phase noise using the ultra-short baseline were evaluated. The experimental results indicated that the Galileo E5 signal has the highest C/N0, while the C/N0 of other signals is lower and almost equal. In terms of MPC, the Galileo E1 was the most severe followed by E5a and E5b, and the MPC of E5 is less severe. As for the precision of un-differenced observations, the carrier phase and pseudo-range observations of Galileo E5 had higher accuracy than those of Galileo E5a, E5b, and E1. Secondly, the quad-frequency observations allowed for various linear combinations of different frequencies, which provides some feasibility for improving the performance of ambiguity resolution. Assuming that the phase noise σ∇ΔΦ = 0.01 m and the first-order ionosphere σ∇ΔI1 = 1 m, the total noise of the Extra-Wide-Lane (EWL) combination observation ((0, 0, 1, −1) and (0, −1, 1, 0)) and Very-Wide-Lane (VWL) combination observation ((0, −2, 1, 1), (0, −3, 2, 1)) are still less than 0.5 cycles. Finally, a geometry-based quad-frequency carrier ambiguities (GB-QCAR) method was developed, and all different options of linear combinations were investigated systematically from the ambiguity-fixed rate with two baselines. Experimental results demonstrated that, the ambiguity fixed rate of combination observation (0, −1, 1, 0), (0, −3, 5, −2), (1, −1, 0, 0) and (0, 0, 0, 1) is the highest and the positioning accuracy of VWL combination observation (0, −3, 5, −2) is equivalent to that of the EWL combination observation (0, −1, 1, 0). The positioning accuracies of WL combination observation (1, −1, 0, 0) are preferable to 3 cm and 10 cm in the horizontal and vertical, respectively. The positioning accuracy of NL combination observation E5 in the horizontal direction is about 1 cm, and is better than 4 cm in the vertical direction. Therefore, we can use Galileo observations to realize high-precise navigation services utilizing the proposed GB-QCAR method.

Centimeter-level positioning by instantaneous lidar-aided GNSS ambiguity resolution

High-precision vehicle positioning is key to the implementation of modern driving systems in urban environments. Global Navigation Satellite System (GNSS) carrier phase measurements can provide millimeter- to centimeter-level positioning, provided that the integer ambiguities are correctly resolved. Abundant code measurements are often used to facilitate integer ambiguity resolution (IAR); however, they suffer from signal blockage and multipath effects in urban canyons. In this contribution, a light detection and ranging (lidar)-aided instantaneous ambiguity resolution method is proposed. Lidar measurements, in the form of 3D keypoints, are generated by a learning-based point cloud registration method using a pre-built high-definition map and integrated with GNSS observations in a mixed measurement model to produce precise float solutions, which in turn increase the ambiguity success rate. Closed-form expressions of the ambiguity variance matrix and the associated Ambiguity Dilution of Precision (ADOP) are developed to provide a priori evaluation of such lidar-aided ambiguity resolution performance. Both analytical and experimental results show that the proposed method enables successful instantaneous IAR with limited GNSS satellites and frequencies, leading to centimeter-level vehicle positioning.

A real-time combined quality control method for GNSS precise positioning in harsh environments

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.

Multi-GNSS-Weighted Interpolated Tropospheric Delay to Improve Long-Baseline RTK Positioning.

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

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

The correct ambiguity resolution of real-time kinematic precise point positioning (PPP-RTK) plays an essential role in achieving fast, reliable, and high-precision positioning. However, the ambiguity of incorrect fixing will cause poor PPP-RTK positioning performance. Hence, it is essential to optimize the selected strategy of the ambiguity subset to obtain a more reliable ambiguity resolution performance for PPP-RTK. For this reason, a partial ambiguity resolution (PAR) method combining quality control and Schmidt orthogonalization (Gram–Schmidt) is proposed in this study. To investigate the performance of global positioning system (GPS) dual- and three-frequency PPP-RTK comprehensively, the PAR method based on the Gram–Schmidt method was analyzed and compared with the highest elevation angle method, which considered the satellite with the highest elevation angle as the reference satellite. The performance of ambiguity fixing, atmospheric corrections, and positioning were evaluated using five stations in Belgium and its surrounding area. The results showed average epoch fixing rates of 81.01%, 95.92%, 82.05%, and 97.93% in the dual-frequency highest elevation angle (F2-MAX), dual-frequency Gram–Schmidt (F2-ALT), three-frequency highest elevation angle (F3-MAX), and three–frequency Gram–Schmidt (F3-ALT), respectively. In terms of the time to first fix (TTFF), 89.02%, 94.25%, 90.24%, and 95.69% of the single-differenced (SD) narrow lane (NL) ambiguity fell within 3 min in F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. As far as the ionospheric corrections are concerned, the proportion of SD ionospheric residuals within ±0.25 total electron content units (TECU) were 95.08%, 95.93%, 95.68%, and 96.98% for the F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. The centimeter-level accuracy of both the horizontal and vertical positioning errors can be achieved almost instantaneously in F3-ALT. This is attributed to the accurate and reliable SD NL ambiguity fixing based on the Gram–Schmidt approach.

Tight Integration of GNSS and Static Level for High Accuracy Dilapidated House Deformation Monitoring

Global Navigation Satellite System (GNSS) can provide high-precision three-dimensional real-time or quasi-real-time changes of monitoring points automatically in house monitoring applications. However, due to the signal sheltering problem, large observation noise and multipath effects in urban observing environment with dense buildings, ambiguity resolution would be hard, and GNSS accuracy cannot always achieve millimeter level to satisfy the requirement of house monitoring. Static level is a precision instrument for measuring elevation difference and its variations, with a precision up to sub-millimeter level. It could be integrated with GNSS to improve the positioning accuracy in height direction. However, the existing integration of GNSS and static level is mostly on a respective results level. In this study, we proposed a method of integrating GNSS and static level observations tightly to enhance the GNSS positioning performance. The hardware design and integration mathematic model in data processing were introduced, and a group of experiments were carried out to verify the performance in positioning with and without the static level observation constraints. It found that the vertical monitoring measurement results of static level can achieve less than 1 mm. The GNSS ambiguity resolution performance can be improved by incorporating the measurement of static level into GNSS positioning equation as external constraints, and the precision of GNSS float solutions was significantly improved. Finally, the static level constraint can further improve the accuracy of the fixed solution from about 2 cm to better than 2 mm in vertical direction, which is even better than the accuracy in horizontal directions with about 3–6 mm with the static level constraint. The tight combination data processing algorithm can significantly improve the working efficiency, accuracy, and reliability of the application of dangerous house monitoring.

OPTIMAL LINEAR COMBINATIONS SELECTION BASED ON FUZZY CLUSTERING ANALYSIS FOR MULTI-FREQUENCY GNSS

Abstract. Currently, satellite navigation and positioning systems, such as BDS, GPS, and Galileo, can broadcast 3 or more navigation signals. In theory, multi-frequency signals can form more high-quality carrier-phase linear combinations, which is conducive to improving the performance of multi-frequency carrier ambiguity resolution (MCAR). In this paper, focusing on the selection of the optimal combinations in the multi-frequency GNSS carrier phase ambiguity resolution, according to the long wavelength of the combinations, the influence of weak ionospheric delay, and low noise, the fuzzy clustering analysis method is used to realize objective selection of multi-frequency optimal linear combinations (e.g., GPS, BDS-2, BDS-3, Galileo) and introduced the total noise level (TNL) for the analysis of the combinations characteristics under different baseline length scenarios. In order to verify the ambiguity resolution performance of the extra-wide lane combinations selected by the fuzzy clustering analysis method, the GF_MCAR model was used to solve the BDS-2, BDS-3 triple-frequency combination ambiguities and the BDS-3 five-frequency combination ambiguities of the baseline JNFG and WUH2. The results manifest that the number of high-quality linear combinations of multi-frequency GNSS increases sharply with the increase of the frequencies number, which is conducive to the formation of combinations with a lower total noise level, and the experiments show that the difference between adjacent epochs of the combination ambiguities of the extra-wide lane obtained by GF_MCAR is basically less than ±0.5 cycles, and the single epoch rounding can be used to directly fix the ambiguity of the extra-wide lane.

A Novel Clock Parameterization and Its Implications for Precise Point Positioning and Ionosphere Estimation.

By convention, IGS precise clock products are computed using the ionosphere-free linear combination. Due to the broad use of IGS products, this convention is exploited in PPP-RTK models not using such a linear combination. So, in different carrier phase combinations, the code hardware biases are contained in different combinations, thus making the problem of separating biases from integer ambiguities more complicated. In this paper, we proposed a novel clock parameterization which allows facilitating this problem. Based on the proposed parameterization, we derived a dual-frequency PPP-RTK model for the undifferenced measurements and assessed this model for the static positioning case in terms of positioning accuracy, convergence, and ambiguity resolution performance. The results showed that a cm-level accuracy level is achievable with the derived models with nearly instant convergence and almost 100% successfully resolved ambiguities. We demonstrated the use of this parameterization for slant ionosphere estimation. We derived the analog of the equation linking the wide-lane, geometry-free, and ionosphere-free biases from the Fast-PPP system and used it to retrieve slant ionosphere information. Our TEC estimates showed some evidence of capability to reach an agreement of 1–2 TECU and the standard deviation of 3–4 TECU with GIM TEC values.