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- Snow depth retrieval using GPS signal-to-noise ratio data based on
improved complete ensemble empirical mode decomposition-
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Abstract: Abstract Snow is essential to the Earth's water source and plays a significant role in studying the climate system and hydrological cycle. Snow depth monitoring has recently become an application of Global Navigation Satellite System (GNSS) instruments. The traditional snow depth retrieval algorithm for GNSS Interferometric Reflectometry (GNSS-IR) extracts the reflected signal from the signal-to-noise ratio (SNR) data by polynomial fitting, in which high- or low-frequency noise affects the accuracy of the results. This study introduces an improved complete ensemble empirical mode decomposition (ICEEMDAN) method for use in GNSS-IR. The reflected signal is reconstructed using the correlation coefficient method, which could effectively reduce noise interference. The accuracy of the proposed algorithm is evaluated using snow depth measurements collected on GNSS footprints at 14 sites that are GNSS stations of the EarthScope Plate Boundary Observatory (PBO). The root-mean-square error (RMSE) and mean absolute error (MAE) are 10.1 cm and 8.3 cm, respectively, 21.1% and 24.5% better than the traditional algorithm's RMSE of 12.8 cm and MAE of 11.0 cm. The accuracy of the proposed algorithm in the uncertainty range is comparable to the standard algorithm. The results of the proposed algorithm for snow depth retrieval over a 262-day time series at site P351, which belongs to the PBO in the western United States, correspond well with that of the traditional algorithm and the reference snow depth. The ICEEMDAN-based algorithm for snow depth retrieval reduces the background noise of signals and increases the number of tracks with significant spectral peak amplitudes, which makes the algorithm applicable for more accurate snow depth retrieval with complex environments. Its derived Hilbert spectrum can help to visualize the variation of reflected height with elevation angle and has the potential to identify azimuth/elevation angles without reflection features.
PubDate: 2023-09-19
- Factor graph optimization-based multi-GNSS real-time kinematic system for
robust and precise positioning in urban canyons-
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Abstract: Abstract Recently, the factor graph-based global navigation satellite systems (GNSS) positioning methods have attracted much attention for more robust positioning performance in urban canyons compared with the traditional filter-based method. In the existing factor graph optimization (FGO)-based GNSS positioning methods, the pseudorange and Doppler measurements are mainly utilized to construct factors among consecutive GNSS epochs for outlier resisting and robust localization. However, the potential of high-precision positioning by using carrier phase observations is not fully explored. A factor graph optimization-based multi-GNSS real-time kinematic (FGO-RTK) framework is proposed to fill this gap, aiming to realize robust and precise positioning in urban canyons. In our method, a sliding window-based FGO estimator is designed, in which the continuously tracked double difference ambiguities are used to establish the ambiguity constraints of position states that have common-view satellites within the window. A marginalization-based carrier phase ambiguity propagation (AP) method is developed to fully use the information of carrier phase observations for achieving more reliable and continuous ambiguity resolution. Experiments in both medium urban and deep urban environments verified the effectiveness of the proposed method. Results show that FGO-RTK (with or without the AP) can achieve centimeter-level positioning accuracy in medium urban situations, showing comparable performance with the traditional extended Kalman filter (EKF)-based RTK. With the GNSS observation conditions deteriorating in deep urban environments, FGO-RTK without AP cannot outperform EKF-RTK. By contrast, the proposed FGO-RTK, considering the AP, achieves significant improvements in centimeter- to decimeter-level positioning availability, and the 3D positioning accuracy is improved by 69.6%, compared with the EKF-RTK. Furthermore, by analyzing the impact of the window size against the performance of FGO-RTK, we found that in comparison to the FGO-RTK only using the carrier phase observations inside a fixed-size window, the proposed AP method can significantly reduce the dependence on window size, and the optimal window size can be reduced from 10 to 4 epochs with more than 50% optimization time decreasing.
PubDate: 2023-09-15
- A DIA method based on maximum a posteriori estimate for multiple outliers
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Abstract: Abstract The detection, identification, and adaptation method based on data snooping (DIA-datasnooping) is commonly used to deal with outliers in the Gauss–Markov model. However, the application of DIA-datasnooping might be limited in case of multiple outliers. In this contribution, the Maximum a posteriori (MAP) estimate is applied to the DIA framework, and a DIA method based on MAP (DIA-MAP) is proposed. Based on the prior distribution of gross errors, DIA-MAP chooses the hypothesis with the maximum posterior probability to conduct the detection and identification of outliers. To this end, a hyperparameter determination method based on supervised learning is proposed to find suitable priors for gross errors. With the priors of gross error, DIA-MAP provides a unified DIA process for both single and multiple outliers. Also, the prior can be flexibly adjusted rather than fixed to be uniform, so that the DIA method can be adapted to different application cases. Finally, a set of new evaluation indices for the DIA method with multiple outliers is defined, including True Positive Rate (TPR) which describes the detectability for outliers and True Negative Rate (TNR) which denotes the acceptance ability for inliers. Experimental results of GNSS positioning examples verified that the performance of the proposed DIA-MAP method is superior to the conventional used methods when dealing with multiple outliers.
PubDate: 2023-09-13
- A systematic approach for identifying optimal azimuth and elevation angle
masks in GNSS-IR: validation through a sea level experiment-
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Abstract: Abstract GNSS-IR is a method that enables retrieving characteristics of the reflection surface by analyzing the interference between direct and coherently reflected signals transmitted from satellites. The selection of azimuth and elevation angles is of great importance in this method. Traditional methods for determining azimuth and elevation angle masks may be insufficient due to irregularities and time-dependent changes on the reflection surface. In this study, we propose a novel empirical approach that allows determination of optimal azimuth and elevation angle masks. The approach is based on the RMSE and correlation values of estimates obtained by directly evaluating the SNR data with in situ measurements. The proposed approach was trained with four different strategies (subsequently three additional strategies) using 1-week GPS L1C SNR data of the GADA station located in the Aegean Sea and co-located with a tide gauge covering the period December 13–19, 2020. After identifying the angle masks, GNSS-IR analysis of 6-month data from the same station between January 1 and June 30, 2021 was performed using the angle masks found for each strategy combination, and then daily and sub-daily (for 12-h, 6-h, 4-h, 3-h, 2-h, and 1-h intervals) sea level estimations were obtained. Compared with tide gauge measurements, daily estimations showed a correlation of over 97% and an RMSE below 3.2 cm. For sub-daily estimations, a correlation of over 85% and an RMSE below 10 cm were obtained even for the 1-h estimation interval. The results show that the approach proposed here can be used to determine optimal azimuth and elevation angle masks in GNSS-IR analysis without requiring any data other than in situ measurements during the pre-analysis period.
PubDate: 2023-09-11
- GHASP: a Galileo HAS parser
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Abstract: Abstract Galileo High Accuracy Service (HAS) corrections are broadcast through the E6B signal using a high-parity vertical Reed-Solomon encoding scheme, which reduces message recovery time and improves transmission reliability. To recover HAS corrections, it is thus necessary to invert the encoding process and interpret the decoded bits. In order to foster HAS adoption and facilitate experimentation with HAS corrections, a Galileo HAS Parser (GHASP) has been developed. GHASP is available open-source and supports different input data types from different receiver manufacturers. Decoded corrections are provided in Comma-Separated Values files, which can be directly loaded using common data-science languages. In this way, corrections are readily available and can be used not only for Precise Point Positioning (PPP) applications but also for scientific analysis such as clock characterization using the Allan Deviation.
PubDate: 2023-09-05
- Can we measure sea surface wind speed with a smartphone'
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Abstract: Abstract We aim to explore the feasibility of using a smartphone in-built GNSS sensor to measure sea surface wind speed. For this purpose, a proof-of-concept campaign is conducted. Two observables that may be sensitive to wind speed, namely, the reflected-to-direct ratio (RTR) and texture correlation time (TCT), are defined, and a smartphone and geodetic receiver are equipped in the experiment. The results show that the carrier-to-noise ratio (CNR) of the smartphone in-built GNSS sensor presents some sensitive to wind speed. As the elevation angle and wind speed increase, the RTR and TCT both gradually decrease. A rational function is used to develop the empirical geographic model functions (GMFs) between the defined observables and wind speed. The multipath signals from the surrounding buildings have an important influence on the measured wind speed. After a simple data quality control, the retrieved wind speed has an RMSE of 2.06 m/s.
PubDate: 2023-09-03
- Hong Kong–Zhuhai–Macao Bridge deformation monitoring using PPP-RTK
with multipath correction method-
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Abstract: Abstract The present study provides a suitable GNSS positioning model for long-span bridge deformation monitoring and further improves the GNSS positioning performance using the multipath mitigation technique. An ambiguity-fixed ionosphere-weighted PPP-RTK model is constructed to provide real-time high-accuracy positioning service for long-span bridge deformation monitoring. In addition, a multipath model is established for GPS and BDS (GEO/IGSO/MEO) in the space domain for multipath mitigation. Elevation and azimuth of each satellite is recorded to compute multipath correction when the satellite appears in the same location. The results show that PPP-RTK can be well used for long-span bridge deformation monitoring. The multi-constellation multipath model can significantly improve performance. With the multipath mitigation method, PPP-RTK has obviously gained in the convergence time to reliably fix the ambiguities, as well as in the positioning accuracy and normal distribution characteristics of the observation residuals. We show bridge deformation monitoring results of the Hong Kong–Zhuhai–Macao Bridge for five consecutive days, where the PPP-RTK performance with multipath mitigation shows high positioning accuracy with fast convergence time. Moreover, our model is capable of identifying the high-frequency vibration and low-frequency displacement of the bridge. The natural frequency of 0.373 Hz in the vertical direction of the bridge under the typhoon Chaba excitation has been detected.
PubDate: 2023-09-02
- In memory of Prof. Ivan I. Mueller (1930–2023)
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PubDate: 2023-08-31
- Multipath mitigation in GNSS precise point positioning using multipath
hierarchy for changing environments-
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Abstract: Abstract Global navigation satellite system precise point positioning (PPP) technology can be significantly affected by multipath errors of code and phase observations. Previous studies using multipath hemispherical map (MHM) to mitigate multipath highly rely on stable surrounding environments, and limited work emphasizes multipath mitigation in changing environments (i.e., the surrounding environments are variable but the user maybe static). We propose a new multipath mitigation method using multipath hierarchy (MH) derived from the C/N0 discrepancy in azimuth and elevation grid in changing environments. The main processing procedures using MH in GNSS PPP are given. Two dedicated static datasets are collected to analyze the multipath discrepancy of normal MHM and further conduct the C/N0-based MH. The performance using MH is carefully analyzed in terms of positioning accuracy and residual reduction. Specifically, the normal MHM exhibits multipath discrepancy in changing environments; thus, the C/N0-based MH is of great necessity to further mitigate multipath. Compared to the normal MHM, the MH-corrected positioning errors are improved, especially at the initial epochs. By calculating the three-dimensional positioning accuracy of all epochs, the MH-corrected positioning accuracy can be improved by approximately 6 and 3 cm compared to the uncorrected and MHM-corrected results in centimeter-level PPP, respectively. Also, the standard deviations of MH-corrected code and phase residuals are smaller than MHM-corrected results for each satellite. In this sense, the proposed multipath mitigation method using MH is highly appreciated for the performance of positioning accuracy and residual reduction in changing environments.
PubDate: 2023-08-28
- Evaluation of real-time kinematic positioning performance of the BDS‑3
PPP service on B2b signal-
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Abstract: Abstract The BeiDou global navigation satellite system (GNSS) of China (BDS-3) had full operation capacity on July 31, 2020, and started providing free precise point positioning (PPP) service on B2b signals. Although GNSS community has conducted many evaluations on the PPP-B2b products and its user performance, comprehensive evaluations of real-time PPP solutions using the BDS-3 PPP service at kinematic and highly kinematic platforms are still absent. We present a general evaluation of a real-time PPP performance exploiting the PPP-B2b corrections in various user situations represented with static stations, a car, an offshore vessel and an aircraft. We found that errors of the PPP-B2b corrections are less stable and higher approximately by a factor of two for GPS compared to BDS-3 medium earth orbit (MEO) satellites. An average convergence time of 28.5 and 12.9 min can be achieved with a standalone BDS-3 and BDS-3 + GPS solution for a low-speed object, such as a permanent station, a car, and a ship, in real time when using the PPP-B2b corrections. For a high-kinematic airborne platform, the convergence time is much longer, reaching 48.9 min. The 95% positioning errors after convergence are less than 20 and 35 cm in horizontal and vertical directions for all the experiments. We conclude that the PPP-B2b service offered by the BDS-3 is prospective for real-time kinematic positioning applications.
PubDate: 2023-08-25
- Performance assessment of the signal-in-space ranging errors of BDS-3:
statistical characterization and integrity standard-
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Abstract: Abstract The orbit errors, clock errors, and signal-in-space ranging errors (SISREs) of the third generation of BeiDou navigation satellite system (BDS-3) are analyzed by comparing broadcast ephemeris with precise products from January 1, 2019, to June 2, 2021. The average availability of signal-in-space (SIS) over all BDS-3 satellites is 98.41%, and those with the medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites are 98.74% and 96.86%, respectively. Due to the inter-satellite link of BDS-3, the percentages of ages of data, ephemeris and ages of data, clock less than one hour increase to 97.34% and 96.85%, respectively. The root-mean-square (RMS) of the three-dimensional (3D) orbit errors of a BDS-3 satellite is 0.57 m. The eclipses and maneuvers of the IGSO satellites have a greater impact on orbit accuracy than those of the MEO satellites. The clock errors of different satellites are remarkably positively correlated. The orbit-only, global-average, and the RMS values of worst-case SISREs of BDS-3 are 0.12 m, 0.59 m and 1.10 m, respectively, and the actual URA of 2.0 m in the navigation message might be conservative for integrity since it can overbound the 95th percentile of global-average SISRE for most satellites and RMS of the daily worst-case SISRE for all satellites. A super-Gaussian distribution can describe the BDS-3 orbit errors and clock errors, although a heavier tail exists for clock errors. Since the empirical distribution of worst-case SISRE is neither symmetric nor unimodal, the two-step Gaussian overbounding method is introduced and based on the overbounding distribution parameters the integrity standards for different integrity risk levels are proposed.
PubDate: 2023-08-24
- Accurate analytical non-gravitational force model for precise orbit
determination of QZS-1, 2, and 4-
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Abstract: Abstract We propose an accurate analytical non-gravitational force model of QZS-1, 2, and 4 for a precise orbit determination of these satellites. To construct an accurate disturbance model, we used a high-fidelity satellite geometry model and the thermal information provided by the satellite developer. They are the most detailed design information to be used to construct the analytical solar radiation pressure and thermal radiation pressure models ever for QZSS satellites. We applied the pre-computed geometry tensor method for solar radiation pressure modeling and constructed a simple box-wing-hat thermal radiation pressure model. In particular, this thermal radiation pressure is the first model constructed with realistic temperature information. Based on the analytical model, we also proposed a hybrid model combined with the empirical approach. The accurate force models were implemented on a precise orbit determination tool called MADOCA, and orbit determination experiments were performed for QZS-1, 2, and 4. The results show that the proposed analytical model has better accuracy in orbit determination than the currently published orbit products obtained by empirical disturbance models.
PubDate: 2023-08-24
- A grid-based ionospheric weighted method for PPP-RTK with diverse network
scales and ionospheric activity levels-
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Abstract: Abstract The performance of precise point positioning real-time kinematic (PPP-RTK) is closely tied to the accuracy of atmospheric corrections, with the ionospheric delay, including its uncertainty, being of particular importance. In this study, a grid-based slant ionospheric weighted method is proposed to enhance PPP-RTK performance across diverse network scales and ionospheric activity levels. First, the receiver-specific hardware delays are precisely calibrated for the maximum utilization of ionospheric corrections retrieved in PPP-RTK networks. Then, a grid-based polynomial fitting and residual interpolation model is developed with a stochastic model considering the distribution of reference stations, the elevation of satellites, and rate of total electron content index (ROTI). Three networks situated in different latitudes with the max inter-station distance of 26.7 km, 134.2 km, and 247.9 km, respectively, were employed to verify the enhancement to PPP-RTK. The proposed method presents a significant improvement in reducing the convergence time of PPP-RTK in all three networks, with the horizontal convergence time decreased from 5 to 14 s to less than 1 s in the small- and medium-scale networks, 44–25 s in the large-scale network compared to the modified linear combination method (MLCM). Besides, a vehicular experiment on an urban loop was conducted for further validation. The positioning accuracy of the PPP-RTK vehicular solutions with the newly proposed method is 2.74, 2.28 and 5.54 cm in the east, north and up components, respectively, with an improvement of 10, 11 and 40% over MLCM. The proportion of 3D positioning accuracy less than 5 cm also increased from 50.1 to 87.8%. Moreover, during the ionospheric active period, the average positioning accuracy is increased from decimeter- to centimeter-level horizontally, and the fixing rate can be increased from 80.6 to 90.0%.
PubDate: 2023-08-24
- Multipath hemispherical map model with geographic cut-off elevation
constraints for real-time GNSS monitoring in complex environments-
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Abstract: Abstract Global Navigation Satellite System (GNSS) is an important technical tool for building deformation monitoring, but in complex environments such as urban canyons, the GNSS signals received by monitoring stations are susceptible to severe multipath errors, resulting in a significant decrease in positioning precision. The multipath hemispherical map (MHM) model is a common method to mitigate multipath errors in GNSS, but its performance can be compromised by high-frequency multipath errors, outliers, and non-line-of-sight signals caused by nearby obstructions. In this study, an MHM model with geographic cut-off elevation constraints is proposed, which considers signal quality and terrain topography surrounding the station to mask those unsatisfactory signals, and leverages the advantages of the MHM model for mitigating low-frequency multipath. To validate the effectiveness of the proposed method, a GNSS deformation monitoring experiment was carried out in an urban environment. The results show that the root mean square (RMS) values of horizontal and vertical positioning errors for the ambiguity-fixed solution using the proposed method are 0.40 and 0.68 cm, respectively, showing improvements of 65.9% and 63.4% compared to the solution without multipath correction (M0), 43.8% and 37.0% to the solution using traditional MHM model (M1), and 63.2% and 50.0% to the solution using geographic cut-off elevation model (M2), respectively. Correspondingly, the ambiguity fixing rate increased from 84.95%, 95.31% and 98.97% of M0, M1 and M2 solutions to 99.95%. The proposed MHM model with geographic cut-off elevation constraints can improve the positioning precision, and thus would be helpful for GNSS deformation monitoring in complex environments.
PubDate: 2023-08-18
- POSGO: an open-source software for GNSS pseudorange positioning based on
graph optimization-
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Abstract: Abstract Graph optimization (GO) can correlate more historical information to increase the resistance against the GNSS outliers. Therefore, GO has the potential to obtain a higher accuracy and robust position in urban canyon. Here, we develop POSGO (POSition based on Graph Optimization), an open-source software designed for single-point positioning and relative positioning with multi-GNSS pseudorange in a GO framework. It is coded in C/C+ + language and recommended to run in the Linux environment. It can be easily extended to process the carrier phase and fuse the data from multiple sensors by adding corresponding graph factors. To assess the performance of the current version, data from a kinematic vehicle experiment in urban area are processed. The results indicate GO has better accuracy and robustness than classic least squares or Kalman filters, particularly in areas with severe occlusions.
PubDate: 2023-08-17
- A precipitation forecast model with a neural network and improved GPT3
model for Japan-
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Abstract: Abstract Accurate monitoring of atmospheric water vapor content is essential for the early warning of extreme weather events. As known, GNSS zenith troposphere delay (GNSS_ZTD) is an indispensable data source for retrieving precipitable water vapor (PWV). However, the newest GPT3 empirical model is not accurate enough to perform the ZTD (GPT3_ZTD) and PWV (GPT3_PWV) estimation in some regions, such as Japan. Thus, here, we introduce a radial basis function (RBF) neural network to establish ZTD forecast models based on the GPT3 model and use the predicted ZTD to retrieve PWV and adopt the retrieved PWV in forecasting precipitation. To thoroughly verify the accuracy of forecast results in 2021, we selected three external validation data: GNSS, radiosonde, and meteorological data. The GNSS_ZTD validation results show that the error compensation model of GPT3 based on RBF is superior to the GPT3 model and the model using a single RBF and back propagation (BP) neural network. The average RMSE of all GNSS stations is 50.7 mm, 53.7 mm, and 37.8 mm for GPT3_ZTD, RBF_BP_ZTD, and RBF_GPT3_ZTD, respectively. The GNSS_PWV and RO_PWV validation results show that the retrieved PWV with compensation of RBF_GPT3_ZTD is better than the uncompensated GPT3_ZTD, the average accuracy of RBF_GPT3_PWV of GNSS stations and radiosonde stations is improved by 40.4% and 25.8% against that of GPT3_PWV. For the precipitation forecast model results, the average forecast accuracy of all GNSS stations and radiosonde stations is 63.1% and 61.4%, according to the ERA5 precipitation. The average forecast accuracy is 66.3%, validated by meteorological precipitation records. The proposed model not only improves the GPT3 model but also forecasts the PWV value, which can improve the precipitation forecast in Japan, and is expected to expand to other regions.
PubDate: 2023-08-16
- Low-computation GNSS post-correlation signal parameter estimation method
based on the complex signal phase in a high-dynamic environment-
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Abstract: Abstract To estimate global navigation satellite system (GNSS) post-correlation signal parameters in a highly dynamic environment with low complexity, we propose a GNSS acquisition method based on the complex signal phase (CSP). The proposed method is based on the idea that compared with the fast Fourier transform (FFT)-based method, the single-frequency signal estimation method based on CSP can achieve high-precision frequency estimation with a small number of signal points at a high signal-to-noise ratio (SNR). Compared to the FFT-based method, which uses a search process to estimate frequency parameters, the proposed method directly uses the CSP of the received signal to estimate frequency parameters. However, there are some problems for the method based on this idea. In detail, due to the influence of bit signs and noise on peak detection, adjacent differential processing, coherent integration and coarse initial frequency search processing procedures are adopted to address the detection peak reduction problem. Moreover, the detection performance of the proposed method is analyzed. The simulation results show that the proposed method can achieve the same estimation accuracy with low complexity at a moderate signal-to-noise ratio (SNR) compared with block accumulating semicoherent integration of correlations (BASIC). In particular, when the post-correlation signal SNR is higher than 8 dB, the proposed method can achieve the same chirping rate and initial frequency estimation accuracy as BASIC.
PubDate: 2023-08-14
- Exploring the role of PPP–RTK network configuration: a balance of server
budget and user performance-
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Abstract: Abstract With atmospheric corrections generated from the server, precise point positioning real-time kinematic (PPP–RTK) can achieve high-precision solutions in a fast convergence. PPP–RTK users are concerned about how to use the corrections and the level of performance that can be achieved; thus, our research has focused on correction methods, a priori stochastic modeling, and positioning performance evaluation. Conversely, it is crucial for the server to improve the precision of corrections provided and to consider the balance between cost, computation burden and user performance, especially for commercial applications. We use different scales of the national GPS network of France to generate ionospheric and tropospheric corrections, and corresponding uncertainty information is generated by establishing error functions with respect to an inter-station distance. The quality of corrections and corresponding user performance are analyzed with inter-station distances varying from 22 to 251 km. The results show that the precision of atmospheric corrections can be improved with an increasing number of stations in the network, but the improvement is not significant when the inter-station distances are smaller than 50 km. Regarding user performance, compared to conventional PPP solutions with ambiguity resolution, the convergence time can be reduced by a maximum of 93% and 85% in the horizontal and vertical components, respectively, when the inter-station distance is about 23 km. However, a station spacing within 100 km can still support a 3-min convergence; thus, a balance of server budget and user performance should be considered instead of a dense network.
PubDate: 2023-08-12
- Adapting empirical solar radiation pressure model for BDS-3 medium Earth
orbit satellites-
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Abstract: Abstract For the precise orbit determination (POD) of global navigation satellite systems (GNSS) constellation, it is very difficult to precisely model the solar radiation pressure (SRP) force acting on GNSS satellites. For GPS satellites, the ECOM model developed by the Center for Orbit Determination in Europe has been utilized by most of International GNSS Service (IGS) analysis centers. However, it should be adapted and optimized to the characteristics of satellites of each GNSS system or even individual satellites. It was extended to the ECOM2 model for GLONASS satellites and then for Galileo satellites by employing a box–wing model. Since November 2020, the third generation of the BeiDou satellite system (BDS-3) has been in its full operation and there are about 200 globally distributed IGS ground stations tracking BDS-3 signals, which creates a great potential to evaluate and optimize its SRP modeling. From the POD processing carried out in this study, we found significant fluctuations of up to 20 cm in overlapping orbit differences for satellites over eclipses in the radial direction and of about 20 and 50 cm in the cross and along directions for ECOM2 and ECOM models. Then, based on numerical analyses we demonstrate that the fourth- and sixth-order sine terms in the Sun direction can significantly reduce the overlapping orbit differences of ECOM. Therefore, an adapted SRP model by adding the fourth- and sixth-order sine periodical terms in the Sun direction to the ECOM model is presented. The adapted model is then validated for BDS-3 POD and orbit prediction. Results show that fluctuations in the amplitude of overlapping estimated orbits using ECOM models are reduced from 20 to < 10 cm in the radial-track component and satellite laser ranging residuals are reduced to half by the adapted SRP model. For the predicted BDS-3 satellite orbits, the RMS values over deep eclipses can be improved from about 7, 14 and 26 cm to about 3, 5 and 12 cm, in the radial, cross and along directions, respectively, compared to the ECOM model.
PubDate: 2023-08-12
- A GNSS interference source tracking method using the continuous-discrete
Gaussian kernel quadrature Kalman filter-
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Abstract: Abstract Global Navigation Satellite Systems (GNSSs) are vulnerable to interference due to low satellite signal transmission power, and thus the problem of tracking GNSS interference sources has attracted much attention. A new nonlinear filtering algorithm called the continuous-discrete Gaussian kernel quadrature Kalman filter (CD-GKQKF) is proposed for tracking such interference sources. Continuous-discrete filtering framework considers the process model as being in the continuous-time domain and subsequently constructs the univariate Gaussian kernel quadrature (GKQ) rule based on scaled Gaussian Hermite quadrature rule. On that basis, it is extended to the multivariate space with tensor product rule. Finally, the multivariate GKQ rule is introduced into the continuous-discrete filtering framework and the CD-GKQKF algorithm is obtained. The proposed algorithm has been applied to the Van der Pol Oscillator and the GNSS interference source tracking application, respectively. The results show that the proposed CD-GKQKF algorithm with appropriate Gaussian kernel bandwidth provides better accuracy than the traditional continuous-discrete filtering algorithms.
PubDate: 2023-08-07
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