Search Results (245)

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

The precise point positioning (PPP) method in GNSS is based on the processing of undifferenced phase observations. For long static sessions, this method provides results characterized by accuracies better than one centimeter, and has become a standard practice in the processing of geodetic permanent stations data. However, a drawback of the PPP method is its slow convergence, which results from the necessity of jointly estimating the coordinates and the initial phase ambiguities. This poses a challenge for very short sessions or kinematic applications. The introduction of new satellites in Low Earth Orbits (LEO) that provide phase observations for positioning, such as those currently provided by GNSS constellations, has the potential to radically improve this scenario. In this work, a preliminary case study is discussed. For a given day, two configurations are analyzed: the first considers only the GNSS satellites currently in operation, while the second includes a simulated constellation of LEO satellites. For both configurations, the geometric quality of a PPP solution is evaluated over different session lengths throughout the day. The adopted quality index is the trace of the cofactor matrix of the estimated coordinates, commonly referred to as the position dilution of precision (PDOP). The simulated LEO constellation demonstrates the capability to enhance positioning performance, particularly under conditions of good sky visibility, where the time needed to obtain a reliable solution decreases significantly. Furthermore, even in scenarios with limited satellite visibility, the inclusion of LEO satellites helps to reduce PDOP values and overall convergence time. Full article

The BeiDou-3 Navigation Satellite System (BDS-3) precise point positioning (PPP) service through the B2b signal (PPP-B2b) leverages precise correction data disseminated by satellites to eliminate or mitigate key error sources, including satellite orbit errors, clock biases, and ionospheric delays, thereby enabling high-precision timing and positioning. This paper investigates the disparities in time comparison and positioning capabilities associated with the PPP-B2b signals transmitted by the BDS-3 Geostationary Earth Orbit (GEO) satellites (C59 and C61). Three stations in the Asia–Pacific region were selected to establish two time comparison links. The study evaluated the time transfer accuracy of PPP-B2b signals by analyzing orbit and clock corrections from BDS-3 GEO satellites C59 and C61. Using multi-GNSS final products (GBM post-ephemeris) as a reference, the performance of PPP-B2b-based time comparison was assessed. The results indicate that while both satellites achieve comparable time transfer accuracy, C59 demonstrates superior stability and availability compared to C61. Additionally, five stations from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) were selected to assess the positioning accuracy of PPP-B2b corrections transmitted by BDS-3 GEO satellites C59 and C61. Using IGS/iGMAS weekly solution positioning results as a reference, the analysis demonstrates that PPP-B2b enables centimeter-level static positioning and decimeter-level simulated kinematic positioning. Furthermore, C59 achieves higher positioning accuracy than C61. 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

Since 2020, the BDS-3 has been providing real-time corrections via the B2b signal, enabling users in China and its neighboring regions to achieve kinematic positioning accuracy at the decimeter level. The rapid geometric changes of Low-Earth-Orbit (LEO) satellites facilitate the rapid resolution of phase ambiguities and accelerate the convergence of Precise Point Positioning (PPP). Therefore, this study proposes an LEO-enhanced BDS-3 PPP-B2b positioning model. Firstly, a novel BDS-3 PPP model accounting for satellite clock bias characteristics is proposed, and experimental validation confirms its efficacy. Subsequently, an LEO-enhanced BDS-3 PPP model is developed. Finally, the positioning performance is rigorously evaluated using combined LEO simulation observations and BDS-3 observations. The results indicate that, compared with the traditional PPP model, the new model yields an average convergence time of 25.1 min for experiments where the convergence criterion is jointly satisfied, representing a 35.6% improvement in convergence speed, while maintaining the same positioning accuracy after convergence. When augmented with LEO satellites, the convergence time of the BDS-3 PPP-B2b solution is reduced to less than 2 min. Furthermore, when more than three LEO satellites are available, the mean convergence time is shortened to within 1 min. 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 the practical application of Real-Time Precise Point Positioning (RT-PPP), the outages in receiving spatial state representation (SSR) information due to communication anomalies can result in a decrease or even divergence of the positioning accuracy of RT-PPP. To mitigate the decline in positioning accuracy, we propose a method of INS aiding RT-PPP based on an optimized stochastic model. First, the correlation between SISRE and SSR age was analyzed by using a dataset of 1800 continuous time series. A new stochastic model called clock–orbit degradation (COD) stochastic model was established to match clock–orbit time-varying statistical characteristics. Second, we introduced Inertial Navigation System (INS) enhancement information to optimize the functional model, leveraging its autonomy and high-precision short-term position constraints. Finally, the real-world static and kinematic experiments were designed to verify the proposed method. The static results showed that the RT-PPP positioning accuracy with COD stochastic model is always higher than the traditional fixed equivalent-weight stochastic model at different level SSR outages. Even with SSR interruptions, the positioning accuracy can reach 0.131 m in the horizontal direction and 0.269 m in the 3D direction, representing improvements of 23.2% and 19.0%, respectively. Furthermore, the kinematic results showed that the positioning accuracy of PPP/INS with COD stochastic model had improved by 38.7% in the horizontal direction and 69.9% in the 3D direction at half an hour of SSR age. Full article

Accurate kinematic calibration of subreflector actuators is essential for pointing precision of large radio telescopes, particularly at high frequencies. Conventional least-squares methods are vulnerable to noise and outliers, and their accuracy may degrade when limited pose diversity leads to poor parameter excitation. To address these challenges, this paper proposes a novel robust self-calibration framework that integrates Huber loss and $L_2$ regularization into the Levenberg–Marquardt (LM) algorithm—yielding a hybrid optimization approach that combines residual robustness, numerical stability, and convergence reliability. A comprehensive simulation study was conducted under varying workspace sizes and sensor noise levels. The proposed method maintained stable performance even under reduced excitation and high-noise conditions, where traditional LM methods typically degrade, confirming its robustness and applicability to realistic calibration scenarios. The framework was further validated using a structured-light 6-DOF pose measurement system, the proposed method achieved over 90% improvement in both position and orientation accuracy compared to the traditional LM approach. These findings confirm the method’s effectiveness for high-precision 6-DOF calibration in parallel mechanisms, and its suitability for real-world applications in radio telescope subreflector alignment. Full article

GNSS Precise Point Positioning (PPP) technology has been extensively applied to post-processing international comparisons between UTC/TAI times and real-time time transfer, predominantly in static configurations. However, with the swift advancement of intelligent and unmanned systems, there is an urgent need for research into kinematic time transfer. This paper introduces a kinematic model Galileo/GPS integrated PPP time transfer approach leveraging the Galileo High Accuracy Service (HAS). The study utilized observational data from seven stations spanning 22 days. The findings indicate that under static conditions, GPS, Galileo, and Galileo/GPS PPP, when supported by the Galileo HAS, can achieve time transfer with sub-nanosecond precision. In kinematic scenarios, the accuracy of single-system PPP time transfer is comparatively lower, with frequent re-convergence events leading to significant accuracy degradation (exceeding 1 ns). However, in cases where re-convergence is infrequent due to a limited number of satellites, sub-nanosecond time transfer is still attainable. The Galileo/GPS integrated PPP time transfer effectively mitigates the issue of re-convergence, ensuring sub-nanosecond accuracy across all links (0.48 ns). Consequently, it is recommended to employ a multi-system integration approach for kinematic PPP time transfer, particularly when utilizing the Galileo HAS. In terms of frequency stability, GPS, Galileo, and Galileo/GPS PPP demonstrate short-term stability (over 960 s) of (5.29 × 10⁻¹³, 3.34 × 10⁻¹³, and 1.60 × 10⁻¹³), respectively, and long-term stability (over 15,360 s) of (1.49 × 10⁻¹³, 1.02 × 10⁻¹³, and 4.06 × 10⁻¹⁴), respectively. 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

Global navigation satellite systems provide important data sets that can be used to study the influence of various space weather factors. We analyzed the effects of the main phase of the May 2024 extreme geomagnetic storm on the ionosphere and GPS kinematic precise point positioning (PPP). ROTI and global ionospheric maps showed the ionospheric dynamics. The auroral oval expanded up to low latitudes: up to 30°N in the American sector and up to 45°N in the European–Asian sector during the main phase of the geomagnetic storm. The ROTI peaked at 2 TECU/min, which is four times as much against the background. The equatorial anomaly crest intensified considerably (up to 200 TECU) and shifted poleward in the American sector. The counter-propagation finally caused the equatorial anomaly to cross the auroral oval boundary. The ROTI correlated with errors in the kinematic PPP. Positioning errors increased 1.5–5 times at the boundary of the auroral oval. Increased positioning errors propagated according to the shift of the auroral oval boundary. The geomagnetic storm significantly affected the positioning and the ionosphere, threatening various applications based on navigation and communication. Full article

In addressing the optimal motion planning issue for multi-arm rock drilling robots, this paper introduces a high-precision motion planning method based on Multi-Strategy Sampling RRT* (MSS-RRT*). A dual Jacobi iterative inverse solution method, coupled with a forward kinematics error compensation model, is introduced to dynamically correct target positions, improving end-effector positioning accuracy. A multi-strategy sampling mechanism is constructed by integrating DRL position sphere sampling, spatial random sampling, and goal-oriented sampling. This mechanism flexibly applies three sampling methods at different stages of path planning, significantly improving the adaptability and search efficiency of the RRT* algorithm. In particular, DRL position sphere sampling is prioritized during the initial phase, effectively reducing the number of invalid sampling points. For training a three-arm DRL model with the twin delayed deep deterministic policy gradient algorithm (TD3), the Hindsight Experience Replay-Obstacle Arm Transfer (HER-OAT) method is used for data replay. The cylindrical bounding box method effectively prevents collisions between arms. The experimental results show that the proposed method improves motion planning accuracy by 94.15% compared to a single Jacobi iteration. MSS-RRT* can plan a superior path in a shorter duration, with the planning time under optimal path conditions being only 20.71% of that required by Informed-RRT*, and with the path length reduced by 21.58% compared to Quick-RRT* under the same time constraints. Full article

Background: Laparoscopic pancreatic surgery demands high precision and minimal invasiveness, yet conventional robotic systems often face challenges due to complex anatomical environments and uncertainties inherent in surgical procedures. Optimizing key design parameters such as the Remote Center of Motion (RCM) and robotic link lengths is critical for enhancing workspace accessibility and instrument maneuverability. Methods: An integrated optimization framework combining genetic algorithms (GA) with fuzzy logic was developed to determine the optimal RCM position and the ideal lengths of crucial robotic links in a 3-DOF parallel robotic system. The GA explored a large design space based on 6951 tracking points recorded during manual instrument manipulation, while the fuzzy logic system refined fitness evaluations by incorporating expert-defined membership functions and heuristic rules to manage uncertainties and ensure robust performance. Results: Simulation studies demonstrated that the optimized RCM position shifted from an initial [100, 0, 300] to [119.003337, −146.610801, 269.07376], yielding improved workspace coverage and enhanced instrument maneuverability. The GA further determined optimal link lengths of approximately 213.5 mm, 248.5 mm, and 48.6 mm for the primary, tertiary, and minimum secondary links, respectively, which were rounded to practical values of 215 mm, 250 mm, and 50 mm. The optimized design exhibited significant improvements in workspace reachability, precision, and operational stability, as validated by detailed 3D workspace plots and time history diagrams of the instrument tip and joint trajectories. Conclusions: The integrated GA–fuzzy optimization approach effectively enhances the design of a 3-DOF parallel robot for laparoscopic pancreatic surgery by achieving superior kinematic performance. The optimized parameters contribute to improved surgical precision and workspace accessibility, indicating strong potential for clinical application and further experimental validation. Full article