Search Results (107)

High-precision satellite clock bias (SCB) prediction is essential for GNSS applications, including real-time precise point positioning (RT-PPP), Earth observation, planetary exploration, and spaceborne geodetic missions. However, during communication outages or when real-time SCB products are unavailable, RT-PPP may fail due to missing clock corrections. This underscores the necessity of reliable short-term SCB prediction in data-denied environments. To address this challenge, a hybrid model that integrates wavelet transform, a particle swarm optimization-enhanced gray model, and a first-order weighted local method is proposed for short-term SCB prediction. First, the novel model employs the db1 wavelet to perform three-level multi-resolution decomposition and single-branch reconstruction on preprocessed SCB, yielding one trend term and three detailed terms. Second, the particle swarm optimization algorithm is adopted to globally optimize the parameters of the traditional gray model to avoid falling into local optima, and the optimization-enhanced gray model is applied to predict the trend term. For the three detailed terms, the embedding dimension and time delay are calculated, and they are constructed in phase space to establish a first-order weighted local model for prediction. Third, the final SCB prediction is obtained by summing the predicted results of the trend term and the three detailed terms correspondingly. The BDS-3 SCB products from the GNSS Analysis Center of Wuhan University (WHU) are selected for experiments. Results indicate that the proposed model surpasses conventional linear polynomial (LP), quadratic polynomial (QP), gray model (GM), and Legendre (Leg.) polynomial models. The average precision and stability improvements reach (80.00, 79.16, 82.14, and 72.22) % and (36.36, 41.67, 41.67, and 61.11) % for 30 min prediction, (79.31, 78.57, 80.65, and 76.92) % and (44.44, 44.44, 47.37, and 74.36) % for 60 min prediction, and the average precision of the predicted SCB products is better than 0.20 ns and 0.21 ns for 30 min and 60 min, respectively. Furthermore, the proposed model exhibits strong robustness and is less affected by changes in clock types and the amount of modeling data. Therefore, in practical applications, the short-term SCB products predicted by the novel model are fully capable of satisfying the requirements of centimeter-level RT-PPP for clock bias precision. Full article

Space-borne gravitational wave (GW) detection is poised to significantly advance the frontiers of astrophysics, gravitation, and cosmology, which might make it possible to measure the fundamental symmetries of space-time. A critical component in GW detection is the employment of ultra-stable oscillators (USOs) on each satellite, serving as precision timing references to drive analog-to-digital converters (ADCs) for digital sampling of GW signals. Achieving the required sensitivity in GW detection hinges on highly accurate clock timing. However, the challenges posed by ADC aperture jitter and sampling clock jitter cannot be overlooked. They disrupt sampling timing, introduce clock noise, and distort the digitized signal, thus limiting the effectiveness of GW detection in space. To overcome this problem, researchers have developed pilot tone correction techniques and proposed innovative clock noise calibrated time-delay interferometry (TDI), optical comb TDI techniques, and sideband arm locking techniques that effectively suppress the effects of clock noise. This study provides an in-depth and comprehensive summary of the current status of clock noise and its suppression techniques in the space-borne GW detection. Through a systematic review and analysis, the aim is to provide theoretical and experimental technical support and optimization suggestions for the implementation of China’s space-borne GW detection mission. 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

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 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

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

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

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

The rapid expansion of BeiDou satellite navigation applications has led to a growing demand for real-time high-precision positioning services. Currently, high-precision positioning services face challenges such as a long initialization time and heavy reliance on reference station networks, thereby failing to fulfill the requirements for real-time, wide-area, and centimeter-level positioning. In this study, we consider the multi-frequency signals that are broadcast by a satellite to share a common reference clock and possess identical RF channels and propagation paths with strict temporal, spectral, and spatial coupling between signal components, resulting in strongly coherent propagation delays. Firstly, we accurately establish a multi-frequency signal model that fully exploits those coherent characteristics among the multi-frequency BDS signals. Subsequently, we propose a rapid high-precision ranging technique using the code and carrier phases of multi-frequency signals. The proposed method unitizes multi-frequency signals via a coherent joint processing unit consisting of a joint tracking state estimator and a coherent signal generator. The joint tracking state estimator simultaneously estimates the biased pseudorange and its change rate, ionospheric delay and its change rate, and ambiguities. The coherent signal generator updates the numerically controlled oscillator (NCO) to adjust the local reference signal’s code and carrier replicas of different frequencies, changing them according to the state estimated by the joint tracking state estimator. Finally, the simulation results indicate that the proposed method efficiently diminishes the estimated biased pseudorange and ionospheric delay errors to below 0.1 m. Furthermore, this method reduces the carrier phase errors by more than 60% compared with conventional single-frequency-independent tracking methods. Consequently, the proposed method can achieve rapid centimeter-level results ranging for up to 1 min without using precise atmosphere corrections and provide enhanced tracking sensitivity and robustness. Full article

The precise point positioning (PPP) service via the B2b signal (PPP-B2b) on the BeiDou Navigation Satellite System (BDS) provides high-accuracy orbit and clock data for global navigation satellite systems (GNSSs), enabling real-time atmospheric data acquisition without internet access. In this study, we assessed the quality of orbit, clock, and differential code bias (DCB) products from the PPP-B2b service, comparing them to post-processed products from various analysis centres. The zenith tropospheric delay (ZTD) and precipitable water vapour (PWV) were computed at 32 stations using the PPP technique with PPP-B2b corrections. These results were compared with post-processed ZTD with final orbit/clock products and ZTD/PWV values derived from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) and radiosonde data. For stations between 30° N and 48° N, the mean root mean square error (RMSE) of ZTD for the PPP-B2b solution was approximately 15 mm compared to ZTD from the International GNSS Service (IGS). However, accuracy declined at stations between 30° N and 38° S, with a mean RMSE of about 25 mm, performing worse than ZTD estimates using Centre National d’Études Spatiales (CNES) products. The mean RMSEs of PWV derived from PPP-B2b were 3.7 mm and 4.4 mm when compared to PWV from 11 co-located radiosonde stations and ERA5 reanalysis, respectively, and underperformed relative to CNES solutions. Seasonal variability in GNSS-derived PWV was also noted. This reduction in accuracy limits the global applicability of PPP-B2b. Despite these shortcomings, satellite-based PPP services like PPP-B2b remain viable alternatives for real-time positioning and atmospheric applications without requiring internet connectivity. Full article

The BeiDou Global Navigation Satellite System (BDS-3) provides real-time precise point positioning (PPP) service via B2b signals, offering real-time decimeter-level positioning for users in China and surrounding areas. However, common interruptions and outliers in PPP-B2b services arise due to factors such as the Geostationary Orbit (GEO) satellite “south wall effect”, Issue of Data (IOD) matching errors, and PPP-B2b signal broadcast priorities, posing challenges to continuous high-precision positioning. This study meticulously examines the completeness, continuity, and jumps in PPP-B2b orbit and clock correction using extensive observational data. Based on this analysis, a two-step method for detecting outliers in PPP-B2b orbit and clock corrections is devised, leveraging epoch differences and median absolute deviation. Subsequently, distinct prediction methods are developed for BDS-3 and GPS orbit and clock corrections. Results from simulated and real-time dynamic positioning experiments indicate that predicted corrections can maintain the same accuracy as normal correction values for up to 10 min and sustain decimeter-level positioning accuracy within 30 min. The adoption of predicted correction values significantly enhances the duration of sustaining real-time PPP during signal interruptions. Full article