Search Results (86)

Ionospheric delay is a dominant error source in global navigation satellite systems (GNSSs). Conventional ionospheric estimation relies on dense networks of expensive geodetic receivers, limiting accessibility and coverage. With the widespread availability of multi-frequency, multi-constellation smartphones capable of carrier-phase tracking, this study investigates smartphone-based ionospheric estimation. Using a single-reference Precise Point Positioning Real-Time Kinematic (PPP-RTK) framework, ionospheric delays are estimated from smartphone data and evaluated using real-time correction products from BeiDou PPP-B2b and Centre National d’Études Spatiales (CNES). Quality control is performed via solution separation testing with time-differenced carrier phase and time-differenced pseudorange. Field experiments with two Google smartphones and a geodetic receiver demonstrate that the estimated slant ionospheric accuracy is comparable to geodetic receivers within the meter level under both static and kinematic scenarios. Additionally, the horizontal positioning performance demonstrates that the positioning performance of the user smartphone with ionospheric corrections broadcast from the base smartphone is significantly improved, with 74.7% and 54.9% for CNES and PPP-B2b products compared with the conventional PPP solution. Furthermore, a comparison between ionospheric corrections generated from the smartphone and those obtained from the geodetic receiver reveals that the positioning performance of the user smartphone becomes comparable after convergence. Full article

Reliable communications, accurate localization, and efficient safety monitoring remain critical bottlenecks for sustainable development in remote high-altitude regions. On the Qinghai–Tibet Plateau, harsh topography and sparse infrastructure create a persistent “digital divide” that threatens human safety and limits field governance efficiency. This study aims to design, implement, and evaluate an integrated communication and navigation security assurance platform to bridge this gap. The specific research objectives are (i) to develop a hybrid high-precision positioning model integrating PPP-B2b, RTK, and MEMS inertial constraints; (ii) to implement an adaptive multi-link communication strategy combining BeiDou-3 short message communication (SMC), 4G LTE, and VHF; (iii) to design a lightweight SM1/SM2 security-and-compression framework optimized for bandwidth-constrained satellite messaging; and (iv) to conduct a mixed-methods field evaluation of technical performance and user-level impacts. A six-month field evaluation was conducted in Qinghai Province to validate the platform. Results show that the platform achieves sub-metre positioning accuracy across representative plateau scenarios (horizontal RMSE: 0.06–0.45 m). While terrestrial cellular links in marginal-coverage areas frequently failed (<15%), the BeiDou-3 SMC maintained stable message delivery (87.5–94.7%). Sustainability-oriented indicators suggest marked improvements in disaster resilience: the 95th-percentile emergency notification time was reduced from >180 min to <2 min, and effective route coverage increased from ~15% to ~95%. User surveys (n = 112) indicate high acceptance, with 91.1% of respondents reporting improved perceived safety, though usability gaps persist among non-professional groups. Overall, this indigenous satellite-based platform functions as a practical “social safety net,” narrowing digital exclusion and supporting UN sustainable development goals (SDG 9, 10, and 11). Full article

Factor graph optimization (FGO) has emerged as a powerful alternative to Kalman filtering for high-precision GNSS positioning, particularly under challenging conditions. Its modular structure allows for the seamless integration of motion constraints, ambiguity modeling, and multi-sensor data across diverse platforms and environments. This study reviews recent FGO architectures for high-precision GNSS methodologies (PPP, RTK), comparing ambiguity management strategies, measurement factor designs, and robust optimization techniques. We compare strategies for modeling ambiguities within the graph and evaluate how they interact with measurement factor design, cycle slip detection, and integer ambiguity resolution (IAR). Trade-offs in ambiguity management and optimization techniques are discussed to guide future design choices. Full article

Accurate and robust positioning is a critical enabler for Unmanned Aerial Vehicle (UAV) applications, ranging from mapping and inspection to emerging Urban Air Mobility (UAM). While Global Navigation Satellite Systems (GNSS) remain the backbone of absolute positioning, their performance is severely constrained by UAV platform characteristics and complex low-altitude environments. This paper presents a system-level review of GNSS-based UAV positioning. Instead of treating GNSS in isolation, we first link mission requirements and platform constraints, such as aggressive dynamics and Size, Weight, and Power (SWaP) limitations, to specific positioning challenges. We then critically evaluate the spectrum of GNSS techniques, from standalone and Satellite-Based Augmentation System (SBAS) modes to high-precision carrier-phase methods including Real-Time Kinematic (RTK), Post-Processed Kinematic (PPK), Precise Point Positioning (PPP), and PPP-RTK. Furthermore, we discuss multi-sensor fusion with inertial, visual, and Light Detection and Ranging (LiDAR) sensors to mitigate vulnerabilities in urban canyons and GNSS-denied conditions. Finally, we outline key challenges and future directions, highlighting integrity-aware architectures, Artificial Intelligence (AI)-enhanced signal processing, and multi-layer Positioning, Navigation, and Timing (PNT) concepts. The review provides a structured framework and system-level insights to guide resilient navigation for UAV operations in low-altitude airspace. Full article

This study investigates the horizontal positioning accuracy of a low-cost, multi-frequency GNSS receiver operating in static mode using a newly released PPP-RTK correction service delivering localized corrections. To the authors’ knowledge, this represents one of the first performance evaluations of this service, which optimizes correction data based on the approximate receiver location. The results are compared against those from the previous version of the service, which provided non-localized corrections. Analyses were conducted in both the time and frequency domains, employing robust statistical tools to characterize error behavior. The localized service achieved a mean horizontal error of approximately 0.020 m and a 95% Circular Error Probable (CEP95) of 0.046 m, in line with its declared performance. By contrast, the earlier non-localized service yielded a mean horizontal error of approximately 0.074 m and a CEP95 of 0.124 m under comparable static conditions, confirming the significant improvement achieved by localized corrections. Spectral and wavelet analyses revealed a dominant 33 mHz harmonic in the positioning error, corresponding to the 30 s update period of atmospheric corrections, indicating a periodic influence arising from the correction stream. Continuous wavelet analysis further identified intervals in which this harmonic was absent, during which positioning accuracy improved markedly (CEP95 reduced to 0.019 m). To properly address the non-Gaussian nature of the error distribution, bias-corrected and accelerated (BCa) bootstrap methods were applied to estimate confidence intervals. Overall, the results demonstrate the benefits of localized corrections, while emphasizing the importance of accounting for the temporal structure of correction data in PPP-RTK performance assessments. Future developments will focus on kinematic scenarios and adaptive filtering strategies to mitigate periodic errors induced by correction updates. Full article

The accurate and rapid estimation of ionospheric delays is essential for PPP-RTK positioning. While traditional spatial interpolation methods like Kriging rely solely on geographic correlations, they often fail to capture rapid temporal variations in the ionosphere. To overcome this limitation, this paper proposes a long short-term memory (LSTM)-based interpolation method for interpolating ionospheric delays between satellites. The method leverages both spatial and short-term temporal correlations to generate accurate ionospheric corrections at user locations. The model uses a sliding window approach, taking the most recent 10 min of historical data as input to predict ionospheric delays at the current epoch. Experimental validation using data from a reference network in Australia—with average and maximum baseline lengths of 280 km and 650 km, respectively—demonstrates that the proposed LSTM method achieves a centimeter-level interpolation accuracy, with RMS errors between 0.06 m and 0.07 m under both quiet and geomagnetic storm conditions, significantly outperforming the Kriging method (0.27–0.44 m). In PPP-RTK, the LSTM model achieved a 3D positioning accuracy of 8.99 cm RMS during quiet periods, representing improvements of 51.9% and 28.8% over the No Constraint and Kriging methods, respectively. Under geomagnetic storm conditions, it maintained a 3D RMS of 24.54 cm—over 44% more accurate than other methods—and reduced the average time-to-first-fix (TTFF) to just 7.0 min, a 39.1% improvement. This study provides a novel approach for ionospheric spatial interpolation, demonstrating a particular robustness even during geomagnetic storms. Full article

To address the urgent demand for high-precision positioning in power industry operations within sparse reference station areas, this paper proposes a real-time kinematic positioning method integrating BeiDou multi-antenna Precise Point Positioning–Real-Time Kinematic (PPP-RTK) with inertial measurement unit (IMU) assistance. By combining the strengths of Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) technologies, we establish a multi-antenna observation model based on State Space Representation (SSR), incorporating satellite-based augmentation signals and atmospheric correction information from sparse reference station networks. Lie group theory is employed to enhance the Extended Kalman Filter (EKF) for simultaneous estimation of position, attitude, and ambiguity parameters. The integration of IMU measurements significantly improves robustness against environmental interference in dynamic scenarios. Experimental results demonstrate average positioning errors of 3.12 cm, 3.71 cm, and 6.23 cm in the East, North, and Up (ENU) directions, respectively, with an average convergence time of 1.62 min. Compared with non-IMU-augmented single-antenna PPP-RTK solutions, the proposed method achieves accuracy improvements up to 59.6% while maintaining stability in signal-occluded environments. This approach provides centimeter-level real-time positioning support for critical power grid operations in remote areas such as desert and Gobi regions, including infrastructure inspection and precise tower assembly, thereby significantly improving the efficiency of intelligent grid operation and maintenance. Full article

The economic and strategic value of high-latitude maritime regions is increasingly significant, yet traditional Global Navigation Satellite Systems remain constrained by unfavorable geometric configurations and slow convergence speeds at high latitudes, failing to meet the growing demand for real-time centimeter-level high-precision positioning in these areas. Benefiting from their rapid motion and superior coverage over high-latitude zones, Low Earth Orbit (LEO) satellites offer an effective means to enhance positioning performance in such regions. This paper uses the real BDS data collected by an unmanned surface vessel in the high-latitude waters of the Southern Hemisphere, jointly simulates polar and medium-inclination LEO constellations, and systematically assess the enhancement effects of LEO augmentation on Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) techniques. The results demonstrate that the polar-orbiting constellation markedly improves the observation environment, increasing the number of visible satellites by 70.2% and reducing the Position Dilution of Precision from 2.4 to 1.7, whereas the medium-inclination orbit constellation offered negligible improvement due to insufficient visibility. The rapid geometric change brought by LEO constellations is the core key to achieving fast convergence. Incorporating LEO observations drastically shortened the BDS PPP convergence time from 45.3 min to under 1 min, achieving a reduction of over 97%. Simultaneously, it improved the three-dimensional Root Mean Square accuracy by 54.7%, from 0.086 m to 0.039 m. Convergence within one minute was consistently achieved when at least 5.4 LEO satellites were included in the solution. Moreover, the addition of LEO signals increased the fixed solution rate of short-baseline RTK from 96.5% to 100%, while improving horizontal and vertical accuracy by 31.5% and 12.3%, respectively. This study confirms that LEO constellations, especially those in polar orbits, can substantially enhance BDS precise positioning performance in high-latitude maritime environments, thereby providing critical technical support for related navigation applications. Full article

Developing advanced receiver autonomous integrity monitoring (ARAIM) for ground real-time precise positioning applications such as autonomous vehicles presents computational challenges, particularly in calculating real-time protection levels (PLs) that bound possible positioning errors under an acceptable integrity risk. This study proposes an enhanced method for fast PL estimation by introducing a segmentation approach to the Gershgorin circle theorem-based technique for computing standard deviation upper bounds (UBs). This method divides satellites into segments based on normalised geometry mapping coefficients, allowing multiple UBs instead of a single bound for all subsets within each fault-tolerant mode. The approach is implemented for PPP-RTK with an improved Classification Adaptive Kalman Filter (CAKF). Testing is conducted using a network of 10 continuously operating reference stations (CORSs) employing dual-frequency multi-constellation GNSS data. Results show that when monitoring single fault mode, the PL ranges from 0.05 to 0.1 m with a PL-to-PE ratio of 30:1, while dual fault modes monitoring yields PL from 1 to 10 m with a ratio of 3700:1. The segmentation method achieves 1–5% tighter PLs, i.e., better integrity monitoring (IM) availability, compared to the classical single UB approach while maintaining the same computational efficiency by reducing processed subsets from 325 to 1 for dual fault modes. While the method provides slight improvement in PL tightness, it can be more computationally efficient when having geometries with dominant off-diagonal correlation that fails the computation of a UB. Full article

With the availability of multi-frequency, multi-constellation global navigation satellite system (GNSS) modules, precise transportation applications have become attainable. For transportation applications, GNSS geodetic-grade receivers can achieve an accuracy of a few centimeters to a few decimeters through differential, precise point positioning (PPP), real-time kinematic (RTK), and PPP-RTK solutions in both post-processing and real-time modes; however, these receivers are costly. Therefore, this research aims to assess the accuracy of a cost-effective multi-GNSS real-time PPP solution for transportation applications. For this purpose, the U-blox ZED-F9P module is utilized to collect dual-frequency multi-GNSS observations through a moving vehicle in a suburban area in New Aswan City, Egypt; thereafter, datasets involving different multi-GNSS combination scenarios are processed, including GPS, GPS/GLONASS, GPS/Galileo, and GPS/GLONASS/Galileo, using both RT-PPP and RTK solutions. For the RT-PPP solution, the satellite clock and orbit correction products from Bundesamt für Kartographie und Geodäsie (BKG), Centre National d’Etudes Spatiales (CNES), and the GNSS research center of Wuhan University (WHU) are applied to account for the real-time mode. Moreover, GNSS datasets from two geodetic-grade Trimble R4s receivers are collected; hence, the datasets are processed using the traditional kinematic differential solution to provide a reference solution. The results indicate that this cost-effective multi-GNSS RT-PPP solution can attain positioning accuracy within 1–3 dm, and is thus suitable for a variety of transportation applications, including intelligent transportation system (ITS), self-driving cars, and automobile navigation applications. Full article

Precise point positioning–real-time kinematic (PPP-RTK) enables users to achieve rapid centimeter-level absolute positioning accuracy within a few epochs. The interpolation of ionospheric delay corrections at the user end, extracted from reference stations, constitutes a key aspect of the process, which depends not solely on the precision of the interpolation model. This study investigates the recommended number of selected reference stations and proposes a method to mitigate the potential loss of observations due to missing ionospheric corrections. According to the experimental results, the number of reference stations should be determined based on the reference network size. Under normal conditions (terrain is relatively flat and the atmospheric conditions are inactive) where reference stations are approximately evenly distributed in all directions, and using low-order surface interpolation model, for networks with 50 km spacing, four or five reference stations are recommended, while for 100 km networks, six or seven stations are enough to calculate precise corrections. Adding more stations beyond these thresholds provides limited improvement in interpolation accuracy and increases the communication load. In addition, an interpolation basis recovery algorithm is proposed to preserve otherwise excluded satellite observations through intelligent handling of correction data gaps at individual reference stations. Experimental validation demonstrates that the recovered ionospheric delay corrections obtained through the algorithm deviate from the ground-truth interpolated values of no more than ±1 cm, an accuracy level deemed adequate for PPP-RTK applications. Furthermore, approximately 3% of the observations, which would otherwise have been discarded due to the missing corrections from a specific reference station, are retained by the algorithm. Full article

Ensuring Global Navigation Satellite System (GNSS) integrity, which provides operational reliability via fault detection, is important for safety-critical applications using high-precision techniques like Precise Point Positioning (PPP) and Real-Time Kinematic (RTK). Ionospheric errors, from atmospheric free electrons, challenge this integrity by introducing variable uncertainties into positioning solutions. This study investigates how ionospheric error modeling spatial resolution impacts protection level (PL) calculations, a metric defining positioning error bounds with high confidence. A comparative evaluation was conducted in low-latitude (Guangdong) and mid-latitude (Shandong) regions, contrasting large-scale with small-scale grid-based ionospheric models from regional GNSS networks. Experimental results show small-scale grids improve characterization of localized ionospheric variability, reducing ionospheric residual standard deviation by approximately 30% and enhancing PL precision. Large-scale grids show limitations, especially in active low-latitude conditions, leading to conservative PLs that reduce system availability and increase missed fault detection risks. A user-side PL computation framework incorporating this high-resolution ionospheric residual uncertainty improved system availability to 94.7% and lowered misleading and hazardous outcomes by over 80%. This research indicates that refined, high-resolution ionospheric modeling improves operational reliability and safety for high-integrity GNSS applications, particularly under diverse and challenging ionospheric conditions. Full article

In this study, we introduce a decentralized architecture aimed at enhancing the efficiency of precise point positioning real-time kinematics (PPP-RTK) in large-scale networks with a common pivot station. Initially, we partition the extensive network into multiple smaller subnetworks (SNs), each with a common pivot station. The augmentation parameters for each SN are then computed using the precise orbit corrections and ionosphere-weighted constraints. However, directly applying the estimated augmentation parameters to users across subnetworks poses challenges due to inter-subnetwork discontinuities. These discontinuities arise from variations in the network configurations and the time correlation of the Kalman filters, despite the use of the same pivot station. To address this, common augmentation parameters, such as the satellite clocks and phase biases from each SN, are integrated into a unified set of parameters and broadcast to users. The aligned common augmentation parameters are then fed back into each SN, and the Kalman filter is re-updated to mitigate the inter-subnetwork discontinuities. The proposed architecture offers a reduced computational burden compared to the centralized PPP-RTK architecture, which handles a full-scale network simultaneously. Unlike previous research on decentralized PPP-RTK, the use of a common pivot station ensures a consistent basis for the common augmentation parameters. This approach enables seamless user positioning during transitions between SNs, eliminating the need to reset the user navigation filter during handover operations and simplifying the integration process. To evaluate the effectiveness of our proposed architecture, we gather dual-frequency global positioning system (GPS) observation data from over 40 continuously observed reference stations (CORSs) in Korea. These data are then partitioned into four SNs, each sharing a common pivot station. Subsequently, we compare the static positioning error and processing time of our proposed architecture with those of the centralized architecture. Additionally, the mitigation performance of the inter-network discontinuities is shown. Full article

Tropospheric delay products play a critical role in achieving high-precision positioning in Precise Point Positioning Real-Time Kinematic (PPP-RTK) applications. The short-term prediction of these products remains a significant challenge that warrants further exploration. This study proposes a novel short-term prediction method for tropospheric delay products in PPP-RTK applications, leveraging a multi-scale sliding window and Long Short-Term Memory (LSTM) network. The multi-scale sliding window approach effectively captures data features across different temporal scales, while LSTM, a well-established and robust time series forecasting technique, ensures the accurate modeling of temporal dependencies. The integration of these two methods significantly enhances the precision of short-term tropospheric delay predictions. Experimental analysis utilizing one week of data from the Hong Kong Continuously Operating Reference Stations (CORS) network demonstrates that the proposed method achieves a maximum prediction error of less than 1.5 cm. Furthermore, compared to the standard LSTM approach, the Root Mean Square Error (RMSE) values are improved by 18.9% and 36.6% for different reference values, respectively. PPP-RTK positioning experiments reveal that the predicted products generated by this method exhibit notable improvements in Root Mean Square (RMS) values for the east, north, and up directions, with enhancements of 10.7%, 19.1%, and 4.1%, respectively, over those obtained using the conventional LSTM method. These results comprehensively validate the effectiveness and superiority of the proposed approach. Full article

Precise Point Positioning with real-time kinematic (PPP-RTK) technology, which relies on Global Navigation Satellite Systems (GNSS), encounters difficulties in achieving high-precision and rapid convergence during ionospheric active conditions such as those occurring in thunderstorms. Most existing research on PPP-RTK has primarily focused on calm ionospheric conditions, with limited analysis of its performance under ionospheric anomalies. This study analyzes 13-day data collected from 305 Australian stations, encompassing both ionospheric anomalies (from 10 to 13 May 2024) and calm periods. We evaluated the residuals of uncalibrated phase delay (UPD), the accuracy of atmospheric modeling, as well as the positioning accuracy and convergence time of PPP-RTK. The results reveal that during ionospheric anomalies, compared to calm conditions, the accuracy of wide-lane and narrow-lane UPDs decreases by 2.4% and 1.4%, respectively. Meanwhile, the accuracy of estimated ionospheric and tropospheric delays deteriorates by 167.1% and 17.3%, respectively. In terms of PPP-RTK services, for the horizontal component, the convergence times increase by 25.0%, 44.4%, and 55.6% for the GPS-only, GPS + Galileo, and GPS + Galileo + BDS solutions, respectively. For the vertical component, the increases are 56.9%, 81.6%, and 87.2%, respectively. Regarding the positioning accuracies, for the horizontal component, they decline by 5.5%, 7.4%, and 10.4% for the GPS-only, GPS + Galileo, and GPS + Galileo + BDS solutions, respectively. For the vertical component, the declines are 11.8%, 13.0%, and 18.5%, respectively. This indicates that ionospheric anomalies significantly disrupt PPP-RTK services, mainly due to the degradation of ionospheric delay estimates, which directly affects positioning results. Although the ionosphere can lead to significant degradation in positioning performance, the positioning performance can still be substantially improved with an increase in the number of satellites. This study thus offers new insights into the performance of PPP-RTK during ionospheric active conditions. Full article