Search Results (398)

Real-time integrity monitoring (IM) is essential for autonomous vehicle positioning, requiring high availability and manageable computational load. This research proposes using precise point positioning real-time kinematic (PPP-RTK) as the positioning method, combined with an improved classification adaptive Kalman filter (CAKF) for processing. PPP-RTK enhances IM availability by allowing undifferenced and uncombined observations, enabling individual observation exclusion during fault detection and exclusion (FDE). The CAKF reduces FDE computational load by using a robustness test instead of traditional FDE methods, improving precision and availability in protection level estimation. Epoch-wise weighting adjustments in the robustness test create a more accurate stochastic model, aided by an adaptive unit weight variance (UWV) calculated with a sliding window, achieving a 7–28% UWV reduction. Three test scenarios with up to four simultaneous faults in code and phase observations, ranging from 1 to 200 m and 0.4 to 20 m, respectively, demonstrated successful identification and de-weighting of faults, resulting in maximum positioning errors of 6 mm (horizontal) and 11 mm (vertical). The method reduced FDE computational load by 50–99.999% compared to other approaches. Full article

Experts and scholars from various nations have proposed studying low Earth orbit (LEO) satellite signals as the space-based signals of opportunity (SOPs) for navigation and positioning. This method serves as a robust alternative in environments where global navigation satellite systems (GNSS) are unavailable or compromised, providing users with high-precision, anti-interference, secure, and dependable backup navigation solutions. The rapid evolution of LEO communication constellations has spurred the development of SOPs positioning technology using LEO satellites. However, this has also led to a substantial increase in the number of LEO satellites, thereby reintroducing the traditional challenge of satellite selection. This research thoroughly examines three critical factors affecting positioning accuracy: satellite observable time, satellite elevation, and position dilution of precision (PDOP). It introduces a strategic approach for selecting satellites in LEO SOPs navigation and positioning. Simulation outcomes confirm that this satellite selection strategy effectively identifies visible satellites, ensuring precise positioning through LEO SOPs. Full article

Unmanned aerial vehicle (UAV) systems have recently become essential for mapping, surveying, and three-dimensional (3D) modeling applications. These systems are capable of providing highly accurate products through integrated advanced technologies, including a digital camera, inertial measurement unit (IMU), and Global Navigation Satellite System (GNSS). UAVs are a cost-effective alternative to traditional aerial photogrammetry, and recent advancements demonstrate their effectiveness in many applications. In UAV-based photogrammetry, ground control points (GCPs) are utilized for georeferencing to enhance positioning precision. The distribution, number, and location of GCPs in the study area play a crucial role in determining the accuracy of photogrammetric products. This research evaluates the accuracy of positioning techniques for image acquisition for photogrammetric production and the effect of GCP distribution models. The camera position was determined using real-time kinematic (RTK), post-processed kinematic (PPK), and precise point positioning-ambiguity resolution (PPP-AR) techniques. In the criteria for determining the GCPs, six models were established within the İstanbul Technical University, Ayazaga Campus. To assess the accuracy of the points in these models, the horizontal, vertical, and 3D root mean square error (RMSE) values were calculated, holding the test points stationary in place. In the study, 2.5 cm horizontal RMSE and 3.0 cm vertical RMSE were obtained with the model containing five homogeneous GCPs by the indirect georeferencing method. The highest RMSE values of all three components in RTK, PPK, and PPP-AR methods were obtained without GCPs. For all six models, all techniques have an error value of sub-decimeter. The PPP-AR technique yields error values that are comparable to those of the other techniques. The PPP-AR appears to be an alternative to RTK and PPK, which usually require infrastructure, labor, and higher costs. Full article

The BeiDou Navigation Satellite System (BDS) offers orbit and clock corrections through the B2b signal, enabling Precise Point Positioning (PPP) without relying on ground communication networks. This capability supports applications such as aerial and maritime mapping. However, achieving high precision during the convergence period remains challenging, particularly for missions with short observation durations. To address this, we analyze the performance of PPP over short periods using PPP-B2b products and propose using the backward smoothing method to enhance the accuracy during the convergence period. Evaluation of the accuracy of PPP-B2b products shows that the orbit and clock accuracy of the BDS surpass those of GPS. Specifically, the BDS achieves orbit accuracies of 0.059 m, 0.178 m, and 0.186 m in the radial, along-track, and cross-track components, respectively, with a clock accuracy within 0.13 ns. The hourly static PPP achieves 0.5 m and 0.1 m accuracies with convergence times of 4.5 and 25 min at a 50% proportion, respectively. Nonetheless, 7.07% to 23.79% of sessions fail to converge to 0.1 m due to the limited availability of GPS and BDS corrections at certain stations. Simulated kinematic PPP requires an additional 1–4 min to reach the same accuracy as the static PPP. Using the backward smoothing method significantly enhances accuracy, achieving 0.024 m, 0.046 m, and 0.053 m in the north, east, and up directions, respectively. For vehicle-based positioning, forward PPP can achieve a horizontal accuracy better than 0.5 m within 4 min; however, during the convergence period, positioning errors may exceed 1.5 m and 3.0 m in the east and up direction. By applying the smoothing method, horizontal accuracy can reach better than 0.2 m, while the vertical accuracy can improve to better than 0.3 m. Full article

Utilizing real-time precise point positioning (PPP) technology is an effective approach for obtaining high-precision zenith tropospheric delay (ZTD). Without relying on the terrestrial internet, Galileo high accuracy service (HAS) can provide precise orbit and precise clock products for the world. A thorough assessment of the ZTD accuracy of real-time PPP calculations based on Galileo HAS products in global regions is necessary to promote its application in the field of global navigation satellite system (GNSS) meteorology. The observation data of HAS from 1 to 7 September 2023 were selected for the experiment. Firstly, the accuracy of satellite orbit and clock products of the HAS GPS and HAS Galileo system are evaluated. Then, real-time PPP positioning accuracy within and outside the HAS service area is analyzed. Finally, 104 IGS stations in the world are selected to analyze the ZTD accuracy of real-time PPP calculations based on Galileo HAS products. The experimental results show that during the test period, the RMSE values of the satellite orbit products of the HAS GPS in the radial, along, and cross directions were 4.57 cm, 10.62 cm, and 7.56 cm, respectively. The HAS Galileo RMSE values were 2.81 cm, 8.02 cm, and 7.47 cm, respectively. The RMSE values of the clock products were 0.38 ns and 0.15 ns, respectively. At the selected stations, the real-time PPP positioning accuracies outside the HAS service area and within the service area were similar, and the correlation coefficient between HAS ZTD and IGS ZTD was above 0.90. In the global region, the average bias and RMSE values of the real-time PPP ZTD of the HAS GPS were −0.31 mm and 16.78 mm. Those of the HAS Galileo were 2.30 mm and 15.89 mm, and those of the HAS GPS/Galileo were −0.25 mm and 16.11 mm, respectively. Moreover, each system showed that the accuracy of the HAS ZTD inside the service area was better than that outside the service area. Compared with the single system, the real-time PPP ZTD continuity and stability of the dual system were better. Full article

The Global Navigation Satellite System (GNSS) has made important progress in Earth observation and applications. With the successful design of the BeiDou Navigation Satellite System (BDS), four global navigation satellite systems are available worldwide, together with Galileo, GLONASS, and GPS. These systems have been widely employed in positioning, navigation, and timing (PNT). Furthermore, GNSS refraction, reflection, and scattering signals can remotely sense the Earth’s surface and atmosphere with powerful implications for environmental remote sensing. In this paper, the recent developments and new application progress of multi-GNSS in Earth observation are presented and reviewed, including the methods of BDS/GNSS for Earth observations, GNSS navigation and positioning performance (e.g., GNSS-PPP and GNSS-NRTK), GNSS ionospheric modelling and space weather monitoring, GNSS meteorology, and GNSS-reflectometry and its applications. For instance, the static Precise Point Positioning (PPP) precision of most MGEX stations was improved by 35.1%, 18.7%, and 8.7% in the east, north, and upward directions, respectively, with PPP ambiguity resolution (AR) based on factor graph optimization. A two-layer ionospheric model was constructed using IGS station data through three-dimensional ionospheric model constraints and TEC accuracy was increased by about 20–27% with the GIM model. Ten-minute water level change with centimeter-level accuracy was estimated with ground-based multiple GNSS-R data based on a weighted iterative least-squares method. Furthermore, a cyclone and its positions were detected by utilizing the GNSS-reflectometry from the space-borne Cyclone GNSS (CYGNSS) mission. Over the years, GNSS has become a dominant technology among Earth observation with powerful applications, not only for conventional positioning, navigation and timing techniques, but also for integrated remote sensing solutions, such as monitoring typhoons, river water level changes, geological geohazard warnings, low-altitude UAV navigation, etc., due to its high performance, low cost, all time and all weather. Full article

The objective of our research is to produce a digital elevation model (DEM) in a real-time domain. For this purpose, GNSS measurements are obtained from a kinematic trajectory in a clear location in New Aswan City, Egypt. Different real-time processing solutions are employed, including real-time precise point positioning (RT-PPP) and real-time kinematics (RTK); additionally, the widely used post-processed precise point positioning (PPP) processing scenario is used. Thereafter, the acquired positioning estimates are compared with the traditional kinematic differential GNSS solution counterparts. To achieve the RT-PPP mode, the instantaneous products from the Centre National d’Etudes Spatiales (CNES) are utilized. Our proposed models are validated for both kinematic positioning and DEM accuracies. For kinematic positioning accuracy validation, the findings indicate that the three-dimensional position is about 0.480 m, 0.101 m, and 0.628 for RT-PPP, RTK, and PPP solutions, respectively. Furthermore, the DEM accuracy investigation shows that the produced DEMs have accuracies within 0.249 m, 0.005 m, and 0.264 m for RT-PPP, RTK, and PPP solutions, respectively. Full article

With the advancement of multi-frequency and multi-constellation GNSS signals and the introduction of observable-specific bias (OSB) products, the uncombined precise point positioning (PPP) model has grown more prevalent. However, this model faces challenges due to the large number of estimated parameters, resulting in strong correlations between state parameters, such as clock errors, ionospheric delays, and hardware biases. This can slow down the convergence time and impede ambiguity resolution. We propose two methods to improve the triple-frequency uncombined PPP-AR model by integrating ambiguity constraints. The first approach makes use of the resolved ambiguities from dual-frequency ionosphere-free combined PPP-AR processing and incorporates them as constraints into triple-frequency uncombined PPP-AR processing. While this approach requires the implementation of two filters, increasing computational demands and thereby limiting its feasibility for real-time applications, it effectively reduces parameter correlations and facilitates ambiguity resolution in post-processing. The second approach incorporates fixed extra-wide-lane (EWL) and wide-lane (WL) ambiguities directly, allowing for rapid convergence, and is well suited for real-time processing. Results show that, compared to the uncombined PPP-AR model, integrating N1 and N2 constraints reduces averaged convergence time from 8.2 to 6.4 min horizontally and 13.9 to 10.7 min vertically in the float solution. On the other hand, integrating EWL and WL ambiguity constraints reduces the horizontal convergence to 5.9 min in the float solution and to 4.6 min for horizontal and 9.7 min for vertical convergence in the fixed solution. Both methods significantly enhance the ambiguity resolution in the uncombined triple-frequency PPP model, increasing the validated fixing rate from approximately 80% to 89%. Full article

Empirical tropospheric models can improve the performance of GNSS precise point positioning (PPP) by providing a priori zenith tropospheric delay (ZTD) information. However, existing models experience insufficient ZTD profile refinement, inadequate correction for systematic bias between the ZTD used in empirical modelling and the GNSS ZTD, and low time efficiency in model updating as more data become available. Therefore, a refined spatiotemporal empirical ZTD model was developed in this study on the basis of the fifth generation of European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) data and GNSS data. First, an ENM-R profile model was established by refining the modelling height of the negative exponential function model (ENM). Second, a regression kriging interpolation method was designed to model the systematic bias correction between the ERA5 ZTD and the GNSS ZTD. Last, the final refined ZTD model, ENM-RS, was established by introducing systematic bias correction into ENM-R. Experiments suggest that, compared with the ENM-R and GPT3 models, ENM-RS can effectively suppress systematic bias and improve ZTD modelling accuracy by 10~17%. To improve model update efficiency, the idea of updating an empirical model with sequential least square (SLSQ) adjustment is proposed for the first time. When ENM-RS is modelled via 12 years of ERA data, our method can reduce the time consumption to one-fifth of that of the traditional method. The benefits of our ENM-RS model are evaluated with PPP. The results show that relative to PPP solutions with ENM-R- and GPT3-derived ZTD constraints as well as no constraint, the ENM-RS ZTD constraint can decrease PPP convergence time by approximately 10~30%. Full article

Signal distortion bias (SDB) in Global Navigation Satellite System (GNSS) data processing, defined as the time difference between the distorted chip and the ideal rectangular chip, leads to systematic biases in pseudoranges, affecting satellite and receiver differential code biases (DCBs). The stability of SDBs, allowing them to be treated as constant values, highlights the importance of investigating both their stability and estimation accuracy. Two different methods are used to estimate SDBs: (1) the hybrid method and (2) the geometry-free method. Data from approximately 430 stations, spanning the entire year of 2021, were analyzed to evaluate the estimation accuracy and the short-term and long-term stability of GPS SDBs. The analysis focused on two code signals: C1C (L1 Coarse/Acquisition) and C2W (L2 P(Y)). The results show that the short-term and long-term stability of GPS C1C and C2W SDBs is comparable for both methods, with only minor variations between them. Additionally, one month of data were used to validate the accuracy of estimated SDBs across different receiver groups. The results demonstrate that geometry-free SDBs provide stable satellite DCB estimates with an average bias below 0.15 ns and minimal residual biases, while hybrid SDBs provide satellite DCB estimates with an average bias below 0.20 ns. Overall, the comparison underscores the superior performance of geometry-free SDBs in achieving consistent satellite DCB estimates. Full article

The legacy Global Navigation Satellite System (GNSS) satellite clock offsets obtained by the dual-frequency undifferenced (UD) ionospheric-free (IF) model absorb the code and phase time-variant hardware delays, which leads to the inconsistency of the precise satellite clock estimated by different frequencies. The dissimilarity of the satellite clock offsets generated by different frequencies is called the inter-frequency clock bias (IFCB). Estimates of the IFCB typically employ epoch-differenced (ED) geometry-free ionosphere-free (GFIF) observations from global networks. However, this method has certain theoretical flaws by ignoring the receiver time-variant biases. We proposed a new undifferenced model coupled with satellite clock offsets, and further converted the IFCB into the code and phase time-variant mixed observable-specific signal bias (OSB) to overcome the defects of the traditional model and simplify the bias correction process of multi-frequency precise point positioning (PPP). The new model not only improves the mixed OSB performance, but also avoids the negative impact of the receiver time-variant biases on the satellite mixed OSB estimation. The STD and RMS of the original OSB can be improved by 7.5–60.9% and 9.4–66.1%, and that of ED OSB (it can reflect noise levels) can be improved by 50.0–87.5% and 60.0–88.9%, respectively. Similarly, the corresponding PPP performance for using new mixed OSB is better than that of using the traditional IFCB products. Thus, the proposed pseudorange and phase time-variant mixed OSB concept and the new undifferenced model coupled with satellite clock offsets are reliable, applicable, and effective in multi-frequency PPP. Full article

Uncrewed aircraft systems (UASs) and structure-from-motion/multi-view stereo (SfM/MVS) photogrammetry are efficient methods for mapping terrain at local geographic scales. Traditionally, indirect georeferencing using ground control points (GCPs) is used to georeference the UAS image locations before further processing in SfM software. However, this is a tedious practice and unsuitable for surveying remote or inaccessible areas. Direct georeferencing is a plausible alternative that requires no GCPs. It relies on global navigation satellite system (GNSS) technology to georeference the UAS image locations. This research combined field experiments and simulation to investigate GNSS-based post-processed kinematic (PPK) as a means to eliminate or reduce reliance on GCPs for shoreline mapping and charting. The study also conducted a brief comparison of real-time network (RTN) and precise point positioning (PPP) performances for the same purpose. Ancillary experiments evaluated the effects of PPK base station distance and GNSS sample rate on the accuracy of derived 3D point clouds and digital elevation models (DEMs). Vertical root mean square errors (RMSE_z), scaled to the 95% confidence interval using an assumption of normally-distributed errors, were desired to be within 0.5 m to satisfy National Oceanic and Atmospheric Administration (NOAA) requirements for nautical charting. Simulations used a Monte Carlo approach and empirical tests to examine the influence of GNSS performance on the quality of derived 3D point clouds. RTN and PPK results consistently yielded RMSE_z values within 10 cm, thus satisfying NOAA requirements for nautical charting. PPP did not meet the accuracy requirements but showed promising results that prompt further investigation. PPK experiments using higher GNSS sample rates did not always provide the best accuracies. GNSS performance and model accuracies were enhanced when using base stations located within 30 km of the survey site. Results without using GCPs observed a direct relationship between point cloud accuracy and GNSS performance, with R2 values reaching up to 0.97. Full article

Integrated water vapor (IWV) is a crucial parameter for tropospheric sounding and weather prediction applications. IWV is essentially calculated using observations from global navigation satellite systems (GNSS). Presently, the Galileo satellite system is further developed, including more visible satellites that transmit multi-frequency signals. This study aims to evaluate the accuracy of real-time IWV estimated from a triple-frequency Galileo-only precise point positioning (PPP) processing model utilizing E₁, E_5a, E_5b, and E₅ observations, which is not addressed by the previous studies. For this purpose, Galileo datasets from 10 global reference stations spanning various 4-week periods in the winter, spring, summer, and fall seasons are acquired. To process the acquired datasets, dual- and triple-frequency ionosphere-free PPP solutions are used, including E₁E_5a PPP, E₁E_5aE_5b PPP, and E₁E₅E_5b PPP solutions. The publicly available real-time products from the Centre National d’Etudes Spatiales (CNES) are utilized. The real-time IWV values are computed and then validated with the European Centre for Medium-Range Weather Forecasting (ECMWF) reanalysis products (ERA5) counterparts. The findings demonstrate that the root mean square error (RMSE) of the estimated IWV is less than 3.15 kg/m² with respect to the ECMWF ERA5 counterparts. Furthermore, the E₁E_5aE_5b PPP and E₁E₅E_5b PPP models enhance the IWV’s accuracy by about 11% and 16%, respectively, compared with the E₁E_5a PPP model. Full article

The Galileo High Accuracy Service (HAS) is a free of charge Global Navigation Satellite System (GNSS) augmentation service provided by the European Union. It is designed to enable real-time Precise Point Positioning (PPP) with a target accuracy (at the 95% confidence level) of 20 cm and 40 cm in the horizontal and vertical components, respectively, to be achieved within 300 s. The performance of the service has been confirmed with geodetic-grade receivers. However, mass market applications require low-cost GNSS receivers connected to low-cost antennae. This paper focuses on the performance of the real-time static and kinematic positioning achieved with Galileo HAS and low-cost GNSS receivers. The study is limited to GPS + Galileo dual-frequency positioning, thus exploiting the full potential of Galileo HAS SL1. We demonstrate that the target accuracy of Galileo HAS SL1 is reached with both geodetic-grade and low-cost receivers in dual-frequency static and kinematic applications in open-sky conditions. Precision of a few centimeters is reached for static positioning, while kinematic positioning results in subdecimeter precision. Vertical accuracy is limited by missing phase center offset models for low-cost antennas. In general, the performance of low-cost hardware using Galileo HAS for real-time PPP is comparable to that of geodetic-grade hardware. Therefore, combining low-cost GNSS receivers with Galileo HAS is feasible and justified. Full article

The availability of raw Global Navigation Satellites System (GNSS) measurements in Android smartphones fosters advancements in high-precision positioning for mass-market devices. However, challenges like inconsistent pseudo-range and carrier phase observations, limited dual-frequency data integrity, and unidentified hardware biases on the receiver side prevent the ambiguity resolution of smartphone GNSS. Consequently, relying solely on GNSS for high-precision positioning may result in frequent cycle slips in complex conditions such as deep urban canyons, underpasses, forests, and indoor areas due to non-line-of-sight (NLOS) and multipath conditions. Inertial/GNSS fusion is the traditional common solution to tackle these challenges because of their complementary capabilities. For pedestrians and smartphones with low-cost inertial sensors, the usual architecture is Pedestrian Dead Reckoning (PDR)+ GNSS. In addition to this, different GNSS processing techniques like Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) have also been integrated with INS. However, integration with PDR has been limited and only with Kalman Filter (KF) and its variants being the main fusion techniques. Recently, Factor Graph Optimization (FGO) has started to be used as a fusion technique due to its superior accuracy. To the best of our knowledge, on the one hand, no work has tested the fusion of GNSS Post-Processed Kinematics (PPK) and PDR on smartphones. And, on the other hand, the works that have evaluated the fusion of GNSS and PDR employing FGO have always performed it using the GNSS Single-Point Positioning (SPP) technique. Therefore, this work aims to combine the use of the GNSS PPK technique and the FGO fusion technique to evaluate the improvement in accuracy that can be obtained on a smartphone compared with the usual GNSS SPP and KF fusion strategies. We improved the Google Pixel 4 smartphone GNSS using Post-Processed Kinematics (PPK) with the open-source RTKLIB 2.4.3 software, then fused it with PDR via KF and FGO for comparison in offline mode. Our findings indicate that FGO-based PDR+GNSS–PPK improves accuracy by 22.5% compared with FGO-based PDR+GNSS–SPP, which shows smartphones obtain high-precision positioning with the implementation of GNSS–PPK via FGO. Full article