Search Results (225)

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

Onboard Vehicle-to-Everything (V2X) communication technology is being widely implemented in domains such as intelligent driving, vehicle–road cooperation, and smart transportation. Nevertheless, time synchronization in V2X systems suffers from instability due to the random loss of Global Navigation Satellite System (GNSS) Pulse-Per-Second (PPS) signals. To address this challenge, a model-driven local clock correction approach is proposed. Leveraging probability theory and mathematical statistics, models for the randomly lost GNSS PPS signals are developed. High-order polynomials are used to model local clocks. An optimized Kalman-filter-based time compensation algorithm is then devised to compensate for time errors during PPS signal loss. A software-based task-scheduling solution for precision-time synchronization is developed. An experimental testbed was then built to measure both terminal clocks and PPS signals. The proposed algorithm was integrated into the V2X terminals. Results show that the full-value PPS signals follow an exponential distribution. The onboard clock correction algorithm operates stably across three V2X terminals and accurately predicts clock variations. Furthermore, the virtual clocks achieve an average absolute error of 1.1 μs and a standard deviation of 16 μs, meeting the time synchronization requirements for V2X communication in intelligent connected vehicles. Full article

This research examines the performance of the affordable Xiaomi 11T smartphone in static positioning mode. Static Global Navigation Satellite System (GNSS) measurements are acquired over a two-hour period with a known reference point, spanning three consecutive days. The acquired data are processed, employing both real-time and post-processing Precise Point Positioning (PPP) solutions using GPS-only, Galileo-only, and the combined GPS/Galileo datasets. To correct the satellite and clock errors, the instantaneous Centre National d’Études Spatiales (CNES), the final Le Groupe de Recherche de Géodésie Spatiale (GRG), GeoForschungsZentrum (GFZ), and Wuhan University (WUM) products were applied. The results demonstrate that sub-30 cm positioning accuracy is achieved in the horizontal direction using real-time and final products. Additionally, sub-50 cm positioning accuracy is attained in the vertical direction for the real-time and post-processed solutions. Furthermore, the real-time products achieved three-dimensional (3D) position accuracies of 40 cm, 29 cm, and 20 cm using GPS-only, Galileo-only, and the combined GPS/Galileo observations, respectively. The final products achieved 3D position accuracies of 24 cm, 26 cm, and 28 cm using GPS-only, Galileo-only, and the combined GPS/Galileo measurements, respectively. The attained positioning accuracy can be used in some land use and urban planning applications. 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

Compared to high-cost hardware-based Global Navigation Satellite System (GNSS) positioning techniques, smartphone-based precise positioning technology plays an important role in applications such as the Internet of Things (IoT). Since Google released the Nougat version of Android in 2016, this has provided a new method for achieving high-accuracy positioning solutions with a smartphone. However, two factors are limiting smartphone-based high-accuracy applications, namely, real-time precise orbit/clock products without the internet and the quality-adaptive precise point positioning (PPP) model. To overcome these two factors, we introduce BDS PPP-B2b orbit/clock corrections and a hybrid weight function (based on C/N₀ and satellite elevation) into smartphone real-time PPP. To validate the performance of such a method, two sets of field tests were arranged to collect the smartphone’s GNSS measurements and PPP-B2b orbit/clock corrections. The results illustrated that the hybrid weight function led to 5.13%, 18.00%, and 15.15% positioning improvements compared to the results of the C/N₀-dependent model in the east, north, and vertical components, and it exhibited improvements of 71.10%, 72.53%, and 53.93% compared to the results of the satellite-elevation-angle-dependent model. Moreover, the mixed-frequency measurement PPP model could also provide positioning improvements of about 14.63%, 19.99%, and 9.21%. On average, the presented smartphone PPP model can bring about 76.64% and 59.84% positioning enhancements in the horizontal and vertical components. 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

In wireless communication systems, traditional frequency synchronization methods struggle to effectively track carrier frequency in low signal-to-noise ratio (SNR) environments, leading to degraded demodulation performance and severely impacting the stability and reliability of communication systems. To address this challenge, an innovative frequency synchronization framework is introduced, enhancing frequency synchronization accuracy and robustness in low-SNR environments through bit synchronization techniques. Specifically, the approach constructs a “bit synchronization-frequency synchronization” joint correction mechanism, where clock offset information extracted during the bit synchronization process is utilized to estimate frequency offset. This method enables an indirect measurement and compensation of carrier frequency offset, forming a hierarchical error compensation system. Furthermore, to overcome the limited convergence speed of the classical Gardner algorithm under significant phase offset conditions, an improved error feedback structure is proposed, accelerating bit synchronization convergence and reducing timing synchronization errors, thereby enhancing overall system performance. The effectiveness of the proposed method is validated through theoretical analysis and simulation experiments. Simulation results demonstrate that, compared to conventional frequency synchronization schemes, the proposed method achieves higher frequency correction accuracy in low-SNR scenarios, thereby improving the robustness and anti-interference capability of wireless communication systems in complex environments. 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

This paper explores effective methods for taming rubidium atomic clocks with longwave timing signals. In an in-depth analysis of the time-difference data between the 1PPS timing signal output from the ground-wave signal received by a long-wave receiver and the 1PPS signal from UTC, we observe that the time-difference data has significant short-term jitter and long-term periodicity effects. To meet this challenge, we adopt several innovative strategies. First, we use the Fourier transform algorithm to analyse the time-frequency characteristics of the time-difference data in detail and accordingly propose a de-jittering correction algorithm for the long-wave timing data, which is aimed at improving the stability of the long-wave timing signals. Secondly, the time difference model of the rubidium clock is innovatively modified, and a quadratic polynomial superimposed with a periodic fluctuation term is constructed, which can accurately solve and eliminate the periodic components and obtain smoother time difference data. Finally, the parameters of the rubidium clock are accurately estimated by the least-squares method using the corrected smoother time difference data, and the output frequency of the rubidium clock is adjusted accordingly so that the rubidium clock is tamed effectively by the long-wave timing signal successfully. The experimental results show that the long-term stability of the tamed rubidium clock is significantly improved to 3.52 × 10⁻¹³/100,000 s; meanwhile, the phase deviation of the output 1PPS from the UTC of the tamed rubidium clock after entering the stabilisation period is kept within 25 ns. Full article

This research investigates the positioning performance of the L-band Digital Aeronautical Communications System (LDACS) and presents a system architecture based on carrier-smoothed ground-to-air pseudoranges (PRs), along with clock corrections derived from asymmetric two-way time and frequency transfer (A-TWTFT) filters. The objective is to achieve required positioning accuracy and integrity for aviation operations, addressing the complexities associated with utilizing a terrestrial communications system for complementary positioning, navigation, and timing (CPNT). Through error covariance analysis, this study assesses the steady-state value, convergence time, and bounding performances of the filters. The positioning performance highlights the benefits provided by the proposed architecture. Full article

Time-to-Digital Converters (TDCs) are increasingly vital in modern measurement systems, with Field-Programmable Gate Arrays (FPGAs) offering a cost-effective platform despite challenges in asynchronous circuit design. Among various solutions, Tapped Delay-Line (TDL)-TDCs stand out for balancing precision, speed, and resource efficiency. However, a primary concern in FPGA-based TDL-TDCs are the Bubble Errors (BEs), i.e., spurious zeros introduced in the information code in the TDL that put the measurement precision at severe risk. The main goal of this contribution is to investigate the distribution of BEs, utilizing the Clock Region Crossing (CRC) within the FPGA as a case study, in order to demonstrate theoretically and experimentally that if BEs are manipulated properly, they create an interpolation effect that reduces the quantization error of the TDL-TDC. The analysis is carried out on a 256-tap fully integrated TDL-TDC implemented in a 28 nm Xilinx Artix 100T FPGA. The outcome confirms the potential to use CRC-BEs instead of suppressing them with precision increasing up to 0.17 ps r.m.s., or by almost 2% while also supporting the correctness of the model. Full article

Armillary spheres were developed in the East and the West for a long time. They independently developed various functions for astronomy. In this article, we discuss the differences in mechanical structures, appearance, and functions between the armillary spheres in ancient China and Europe. The earliest armillary sphere in ancient China was invented by Luo Xia Hong (落下閎) between 156 BC and 87 BC. Then, the armillary sphere in ancient China improved with the historical development of astronomy. The famous armillary sphere was built in an astronomical clock tower (水運儀象台) by Su Song (蘇頌) in the Song (宋) dynasty. This armillary sphere was an astronomical apparatus for the observation of celestial phenomena and the correction of time standards. However, the armillary sphere in Europe had different applications, even though the structures were similar. The armillary spheres in Europe simulated the sun’s trajectory in one day to predict the sunrise and sunset positions. They adjusted the tilting angle of the celestial sphere with the altitude of observation to observe the path of the stars around the ecliptic. Through this review, the armillary spheres in ancient China and Europe are defined clearly. Full article

In 2020, BDS-3 began broadcasting high-precision positioning correction products through B2b signals, effectively addressing the limitations of ground-based augmentation. However, challenges such as the “south wall effect” from geostationary orbit (GEO) satellites, issues of data (IOD) mismatch, and signal priority conflicts often result in interruptions and anomalies during real-time positioning with the B2b service. This paper proposes a continuous B2b-PPP (B2b signal-based Precise Point Positioning) model that incorporates signal-in-space range error (SISRE) residuals and predictions for B2b orbits and clock corrections to achieve seamless, high-precision continuous positioning. In our experiments, we first analyze the characteristics of B2b SISRE for both BDS-3 and GPS. We then evaluate the positioning accuracy of several models, B2b-PPP, EB2b-PPP, PB2b-PPP, EB2bS-PPP, and PB2bS-PPP, through simulated and real dynamic experiments. Here, ‘E’ indicates the direct utilization of the previous observation corrections from B2b before the signal interruption, ‘P’ represents B2b prediction products, and ‘S’ signifies the incorporation of the SISRE residuals. The results show that EB2b-PPP exhibits significant deviations as early as 10 min into a B2b signal interruption. Both PB2b-PPP and EB2bS-PPP demonstrate comparable performances, with PB2bS-PPP emerging as the most effective method. Notably, in real dynamic experiments, PB2bS-PPP maintains positioning accuracy in the E/N directions like B2b-PPP, even after 40 min of signal interruption, ensuring continuous and stable positioning upon signal restoration. This achievement significantly enhances the capability for high-precision continuous positioning based on B2b signals. Full article

Wireless surface electromyography (sEMG) sensors are very practical in that they can be worn freely, but the radio link between them and the receiver might cause unpredictable latencies that hinder the accurate synchronization of time between multiple sensors, which is an important aspect to study, e.g., the correlation between signals sampled at different sites. Moreover, to minimize power consumption, it can be useful to design a sensor with multiple clock domains so that each subsystem only runs at the minimum frequency for correct operation, thus saving energy. This paper presents the design, implementation, and test results of an sEMG sensor that uses Bluetooth Low Energy (BLE) communication and operates in three different clock domains to save power. In particular, this work focuses on the synchronization problem that arises from these design choices. It was solved through a detailed study of the timings experimentally observed over the BLE connection, and through the use of a dual-stage filtering mechanism to remove timestamp measurement noise. Time synchronization through three different clock domains (receiver, microcontroller, and ADC) was thus achieved, with a resulting total jitter of just 47 µs RMS for a 1.25 ms sampling period, while the dedicated ADC clock domain saved between 10% to 50% of power, depending on the selected data rate. Full article