Multiple GNSS Research Articles

Estimation of Surface Water Level in Coal Mining Subsidence Area with GNSS RTK and GNSS-IR

Ground subsidence caused by underground coalmining result in the formation of ponding water on the ground surface. Monitoring the surface water level is crucial for studying the hydrologic cycle in mining areas. In this paper, we propose a combined technique using Global Navigation Satellite System Real-Time Kinematic (GNSS RTK) and GNSS Interferometric Reflectometry (GNSS-IR) to estimate the surface water level in areas of ground subsidence caused by underground coal mining. GNSS RTK is used to measure the geodetic height of the GNSS antenna, which is then converted into the normal height using the local height anomaly model. GNSS-IR is employed to estimate the height from the water surface to the GNSS antenna (or, the reflector height). To enhance the accuracy of the reflector height estimation, a weighted average model has been developed. This model is based on the coefficient of determination of the signal fitted by the Lomb-Scargle spectrogram and can be utilized to combine the reflector height estimations derived from multiple GNSS system and band reflection signals. By subtracting the GNSS-IR reflector height from the GNSS RTK-based normal height, the proposed method-based surface water level estimation can be obtained. In an experimental campaign, a low-cost GNSS receiver was utilized for the collection of dual-frequency observations over a period of 60 days. The collected GNSS observations were used to test the method presented in this paper. The experimental campaign demonstrates a good agreement between the surface water level estimations derived from the method presented in this paper and the reference observations.

Investigation of the Growth Random Area Based on the Multiple Techniques, Photogrammetry, GIS and GNSS

In this study, the damaging aspects of urbanisation is the stress it places on development processes of all kinds, making the proliferation of haphazard housing a problem in many nations throughout the world. While this problem has become worse in large cities and their suburbs for a variety of reasons, it has gotten increasingly concentrated in smaller towns and its environs, either in the form of haphazard housing clusters or as single-family homes interspersed throughout the urban fabric. The city of Al-Kut in the Wasit Governorate is a prototypical example of a tiny city hampered by the proliferation of this phenomena, which has substantially impeded urban development there. Al-Sawadah, Al-Wafideen, and other neighbourhoods are dispersed throughout Kut. After being divided into agricultural and military zones, the undeveloped land in between suffered from random invasion by new developments. Photogrammetry and geographic information systems from 2004 to 2021, researchers can use it to assess the pace of change and the variation between the survey area and the rest of the world.

Analysis of factors affecting the estimation of the multi-GNSS satellite differential code biases (SDCBs)

The satellite hardware differential code biases (SDCBs) are one of the important factors affecting the accuracy of GNSS-based ionospheric total electron content (TEC) estimation. The accuracy of SDCB estimates is directly influenced by the data processing methodology. To analyze the impact of various factors on multi-GNSS SDCB estimation, we conducted a comprehensive analysis of the number of contributed stations, the data sampling rate, the contributed satellite systems, and the cut-off elevation angle. Two sets of GNSS data obtained from the International GNSS Service (IGS) multi-GNSS experiment (MGEX) network, covering both high and low solar activities during the ascending phase of solar cycle 25, were processed to estimate multi-GNSS SDCBs. The results indicate that the number of contributed stations is the primary factor that influences multi-GNSS SDCB estimation. To achieve a balance between computational efficiency and accuracy, a data sampling rate of 540 s is recommended, which results in a multi-GNSS SDCB root-mean-square (RMS) error of less than 0.01 ns compared to a 60-second sampling rate. The stability of SDCBs is hardly affected by incorporating observations from multiple GNSS systems, and the differences of the standard deviations of SDCBs for quad-, triple- and dual-system solutions are below 0.002 ns. Additionally, the results indicate that the optimal cutoff elevation angle for multi-GNSS SDCB estimation is between 20° and 30°, which ensures the best stability in the estimated multi-GNSS SDCBs.

Multi-sensor Attitude Estimation using Quaternion Constrained GNSS Ambiguity Resolution and Dynamics-Based Observation Synchronization

Recently, high accuracy and low-cost navigation hardware is becoming increasingly available that can be efficiently used for the control of autonomous vehicles. We present a sensor fusion method providing tightly coupled integration of pseudorange, carrier phase, and Doppler satellite measurements taken at multiple vehicle-mounted GNSS antennas with onboard inertial sensor observations. The key of accurate GNSS position and orientation estimation is the successful integer ambiguity resolution. We propose a method that uses the quaternion states as constraints to improve ambiguity resolution and to increase the accuracy of the GNSS based attitude determination. Generally, the low-cost hardware neither allows a hardware-level time synchronization between the GNSS receivers due to a lack of a common external oscillator nor provides the clock steering function available in geodetic GNSS receivers. The lack of observation synchronization causes several degrees of error in attitude estimation. To eliminate this effect, a dynamics-based solution is presented that synchronizes the observations by taking the dynamics of the moving platform into account. Compared to common external oscillator based sensor setups, our solution allows to increase both the number of rover receivers on the platform and the baselines between them easily, thus it opens up new possibilities in the attitude determination of large vehicles. We validate our approach against a tactical grade inertial navigation system. The results show that our approach using low-cost sensors provides the ambiguity success rate of 100% for the moving baselines, and the positioning and attitude error reached the centimeter and half a degree level, respectively.

Precise and Robust IMU-Centric Vehicle Navigation via Tightly Integrating Multiple Homogeneous GNSS Terminals

Precise and Robust IMU-Centric Vehicle Navigation via Tightly Integrating Multiple Homogeneous GNSS Terminals

Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations

Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution.

Structure and variations of global planetary boundary layer top from 2008-2022 multiple GNSS RO observations

The structural changes at the planetary boundary layer (PBL) top are very complex and closely related to climate and environmental changes. With the development of Global Navigation Satellite System Radio Occultation (GNSS RO), it provides a good opportunity to estimate and study PBL variations. In this paper, long-term variations and structures of planetary boundary layer height (PBLH) from 2008 to 2022 are investigated by the Wavelet Covariance Transform (WCT) method based on refractivity profiles from Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) and Korea Multi-purpose Satellite-5 (KOMPSAT-5). Furthermore, the temperature and pressure of PBL top are detected using the temperature and pressure profiles from COSMIC and KOMPSAT-5 occultation data. The results demonstrate the latitudinal distribution of the PBL top height, temperature, and pressure, with the more apparent temperature's latitudinal characteristics. The pressure is more strongly correlated with PBL height than temperature. The PBL height in most land and oceans is high in summer and low in winter, and the PBL pressure is low in summer and high in winter, according to seasonal variation characteristics. The global PBL temperature is high in summer and low in winter, which is more obvious in high latitude region. A positive correlation between latitude and the magnitude of seasonal variation in PBL temperature is observed worldwide. Seasonal variation is less pronounced in the Southern Hemisphere (SH) than in the Northern Hemisphere (NH) due to sea-land differences. The annual average value of the global PBL height, temperature, and pressure do not change significantly over the long term, and also there is no a discernible upward or downward trend.

Research on Soil Moisture Inversion Method for Canal Slope of the Middle Route Project of the South to North Water Transfer Based on GNSS-R and Deep Learning

The soil moisture from the South-to-North Water Diversion Middle Route Project is assessed in this study. Complex and variable geological conditions complicate the prediction of soil moisture in the study area. To achieve this aim, we carried out research on soil moisture inversion methods for channel slopes in the study area using massive monitoring data from multiple GNSS observatories on channel slopes, incorporating GNSS-R techniques and deep learning algorithms. To address the issue of low accuracy in linear inversion when using a single satellite, this study proposes a multi-satellite and multi-frequency data fusion technique. Furthermore, three soil moisture inversion models, namely, the linear model, BP neural network model, and GA-BP neural network model, are established by incorporating deep learning techniques. In comparison with single-satellite data inversion, with the data fusion technique proposed in this study, the correlation is improved by 12.7%, the root mean square error is reduced by 0.217, the mean square error is decreased by 0.884, and the mean absolute error is decreased by 0.243 with the linear model. With the BP neural network model, the correlation is increased by 15.4%, the root mean square error is decreased by 0.395, the mean square error is decreased by 0.465, and the mean absolute error is reduced by 0.353. Moreover, with the GA-BP neural network model, the correlation is improved by 6.3%, the root mean square error is decreased by 1.207, the mean square error is decreased by 0.196, and the mean absolute error is reduced by 0.155. The results indicate that performing data fusion by using multiple satellites and multi-frequency bands is a feasible approach for improving the accuracy of soil moisture inversion. These research findings provide new technical means for the risk analysis of deformation disasters in the expansive soil channel slopes of the South-to-North Water Diversion Middle Route Project.

An Improved VMD-LSTM Model for Time-Varying GNSS Time Series Prediction with Temporally Correlated Noise

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and the maintenance of the global coordinate framework. Long short-term memory (LSTM) is a deep learning model that has been widely applied in the field of high-precision time series prediction and is often combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 were used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that, compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86% and the average MAE is reduced by 9.44%; moreover, the average R2 increased by 17.97%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average velocity accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby demonstrating the reliability of the predicted results.

Feasibility and performance evaluation of low-cost GNSS devices for sea level measurement based on GNSS-IR

The low-cost GNSS devices are more convenient, flexible, and can be used as the low-cost Global Navigation Satellite System interferometric reflectometry (GNSS-IR) sensors. In this study, the feasibility and performance of low-cost GNSS devices for the temporary sea level measurement are assessed, by jointly utilizing signal-to-noise ratio (SNR) data from an Android smartphone Redmi Note 9 Pro and a low-cost antenna BT560 connected to a CHCNAV P5 GNSS receiver, while another identical receiver equipped with a standard geodetic-quality antenna and a pressure tide gauge (TG) were placed nearby for comparison. 80-hours of SNR data from multiple GNSS constellations were collected and processed. First, the SNR data from the three devices are compared and analyzed. In most cases, the SNR data of low-cost antennas have longer and clearer oscillations. But they are maybe more vulnerable due to the manufacturing of antennas or positioning modules. Second, quality control and height rate correction are crucial to stable sea level measurement of low-cost GNSS devices. Finally, the performance of sea level measurement of multiple GNSS constellations, dual-frequency, and dual-antenna was also assessed. It is found that the low-cost GNSS devices could yield stable sea level measurements, and have a root-mean-square error (RMSE) of about 16 cm, of which the performance is equivalent to or even slightly better than standard geodetic-quality devices, making it a promising solution for the temporary TGs.

Assessing the influence of differential code bias and satellite geometry on GNSS ambiguity resolution through MANS-PPP software package

Abstract Ambiguity resolution (AR) is essential for quick and accurate Global Navigation Satellite System GNSS location and navigation. In addition to location parameters, there are various additional GNSS characteristics that are relevant for a wide range of applications such as instrumental calibrations, atmospheric sounding, and time transfer. We offer differential code bias and satellite geometry for the GNSS estimable parameters using MANS-PPP software backage. In this research, we used the MANS-PPP software package to execute the processing method and generate the PPP GNSS solution. We demonstrated how differential code bias and satellite geometry can effectively enhance initial time and positioning error for multi-GNSS satellites. PPP Processing observation data in static mode was used by the different DCB files the Chinese Academy of Sciences (CAS), the German Aerospace Centre (DLR), and the Centre for Orbit Determination in Europe (CODE), for the 12 stations from IGS, and we analyzed the impact of errors from the satellite geometry. The results illustration that the correction of DCB significantly improves the PPP ambiguity resolution success rate and quality, which have higher DCB values. The satellite geometry also has a substantial influence on the PPP ambiguity resolution, with a better geometry leading to a higher success rate and quality. Furthermore, the use of multiple GNSS constellations and the optimization of the satellite selection and weighting algorithms can further improve the PPP ambiguity resolution and the resulting positioning accuracy.

Accuracy assessment of RTK/PPK UAV-photogrammetry projects using differential corrections from multiple GNSS fixed base stations

Unmanned aerial vehicles (UAVs) equipped with global navigation satellite system-real-time kinematic (GNSS RTK) receivers allow direct georeferencing of the photogrammetric project without using ground control points (GCPs). However, it is necessary to establish the correct methodologies to reduce the errors inherent in these systems, i.e. to reduce the systematic error of the elevation data. For this purpose, multiple GNSS fixed base stations have been used simultaneously. The results showed how the fact of using different bases and averaging their corrections allows to obtain results that improve the altimetric accuracy without the need to use GCPs or oblique photographs. For flight altitudes of 50 m, improvements in altimetric accuracy of 14% were obtained, while for flight altitudes of 70 and 90 m, the improvements in altimetric accuracy reached 35%. Regarding planimetric accuracy, no significant improvements have been found. However, the total errors are similar to those obtained with various combinations of GCPs and closed to the ground sampling distance (GSD) of the photogrammetric project.

MADOCA: Japanese precise orbit and clock determination tool for GNSS

The Japan Aerospace Exploration Agency (JAXA) has developed Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA). This tool estimates orbits and clock offsets of multiple GNSS systems (Multi-GNSS), namely GPS, GLONASS, QZSS, Galileo, and BeiDou. The orbit and clock offsets are estimated in both post-processing with iterative weighted least squares and real-time processing with extended Kalman filter (EKF) using observation data collected from the International GNSS Service (IGS) network and our monitoring station network (MGM-net). Since we began the development in 2011, we have improved the MADOCA’s performance by adopting the precise force and measurement models, the original empirical solar radiation pressure (SRP) model, and processing algorithms for stability and reduction of processing time. In the latest annual evaluation of MADOCA products in 2021, the orbit comparison with the IGS final product for the GPS and GLONASS were 2.8 and 8.0 cm (median value of daily 3D-root mean square (RMS)), respectively, and the results of satellite laser ranging (SLR) residual evaluation for the BeiDou and Galileo were 14.6 and 4.9 cm (RMS), respectively, a performance comparable to the products of the IGS Analysis Centers (ACs). QZSS products, in particular, have achieved the world’s highest level of accuracy as 6.4, 10.1, 9.0, and 10.5 cm (RMS) for the QZS-1, -2, -3, and -4 respectively in the SLR residual evaluation. This was achieved by improving and fine-tuning for the original empirical SRP models. Consequently, the position difference in those products’ static precise point positioning (PPP) reached 1.2 cm (3D-RMS). JAXA has made post-processing and real-time MADOCA products publicly available to users and is promoting experiments using MADOCA products in Japan and abroad.

Ionosphere Delay Extraction in GNSS using DSP Algorithm

With multiple GNSS availability and wider applications, many positioning modes like SPS, DGNSS, RTK and PPP have been developed to cover these flexible employments. Currently, some intricate influences such as ionosphere delays and environmental interference have caused obvious impacts to accurate positioning, and they are therefore formed highlighted research points for worldwide researchers and scholars. To deal with the ionosphere delay, this submission has proposed an intrinsic approach to identify and extract the ionospheric disturbance from GNSS observations in which Digital Signal Process (DSP) is employed to form an adaptive band pass filter for combined observations in the form of either code minus phase (CMP) or double differential (DD) carrier phase. Related mechanism for identification and extraction of the ionosphere delay using DSP are introduced and analyzed. We have also discussed the separation of ionosphere delay with multipath caused by signal reflections from nearby surroundings when deformation monitoring is conducted on some restricted environments. Effects achieved by DSP have been verified combining with typical SPS and carrier based relative positioning conducted in Guangzhou metro construction sites. Results exhibit that the suggested standalone approach to extract ionosphere delays is an innovative technical frame to achieve accurate positioning regardless of assistant messages from base stations or satellite navigation broadcast.

Theoretical Analysis and Design Optimization for Multi-GNSS Direct Radio Frequency Sampling Receiver

Abstract: Recently, a considerable amount of research has been conducted on multiple GNSS receivers using the Direct RF sampling concept. This approach greatly reduces the hardware requirements of the traditional receiver by placing the analog-todigital converter as close as possible to the antenna, eliminating the mixer stages. Furthermore, directly sampling the RF signal using the ADC allows for a more efficient design. In this paper, a Multi-GNSS Direct Radio Frequency Sampling Method is designed, optimized, and its performance is presented for several GNSS signals, including GPS L1, GPS L2, and GPS L5. The implemented method is used to find the ranges of valid sampling frequencies in single and multiple band RF signal cases. The algorithm presented results in an easier way to find valid sampling frequencies and a straightforward implementation without the need for complicated mathematical calculations. We consider aliasing issues and computational problems, providing a full theoretical and practical analysis compared to previously presented algorithms in the literature. This paper also examines the relationship between the sampling frequency, noise folding, and its effect on the signal-to-noise ratio (SNR), thus allowing for the selection of the optimal sampling frequency.

Tight integration of BDS-3/BDS-2/GPS/Galileo observations considering the new overlapping DISBs and its application in obstructed environments

Tight integration can enhance the model strength and positioning performance by considering the characteristic of differential inter-system bias (DISB), especially in obstructed environments. However, limited work emphasizes the comprehensive analysis of five-frequency DISBs between BDS-3 and other systems considering the receiver type, receiver configuration, and antenna type. In addition, the overlapping DISBs between BDS-3 and BDS-2 are also in great demand for further investigation since they are often regarded as one system. In this study, one DISB-float model is introduced to estimate the DISBs, and one DISB-fixed model and one DISB-free model are formulated to enhance the model strength of tight integration. Four dedicated datasets were collected to estimate the DISBs, which are also comprehensively analyzed considering the receiver type, receiver configuration, and antenna type. The results show that the DISBs between BDS-3 and other systems are rather stable over a certain period and are related to the receiver type and receiver configuration, whereas are not related to the antenna type. More interestingly, the B1I code DISB between BDS-3 and BDS-2 exhibits significant magnitude with a mean value of −1.44 m for the baseline composed of two different receivers. In this case, the B1I code DISB must be considered and the tight integration between BDS-3 and BDS-2 considering its calibration can improve the positioning performance. Besides, the tight integration of the DISB-fixed model can significantly improve the positioning accuracy between multiple GNSS. Compared to the loose integration, the improvement of 60.6 %, 56.6 %, and 61.2 % can be obtained in the E, N, and U directions, when only two satellites are available for each system. In real obstructed environments, the tight integration of the DISB-free model can also improve the positioning performance in terms of positioning availability and accuracy, as well as the ambiguity resolution performance.

Two-epoch centimeter-level PPP-RTK without external atmospheric corrections using best integer-equivariant estimation

Ambiguity resolution enabled precise point positioning (PPP-AR or PPP-RTK) without atmospheric corrections requires the user to estimate tropospheric and ionospheric delay parameters. The presence of the unconstrained ionosphere parameters impedes fast and reliable ambiguity resolution, so a time-to-first-fix of around 30 min for GPS-only solutions is generally reported, which can, to some extent, be reduced when combining multiple GNSS. In this contribution, we investigate the capabilities of almost instantaneous PPP-RTK, using only a few observation epochs at a sampling interval of 30 s, with the ionosphere-float model. The considered key elements are (a) the MSE-optimal best integer-equivariant estimator, (b) a combination of dual-frequency GPS, Galileo, BDS, and QZSS, (c) an area with good visibility of BDS and QZSS, and (d) a proper weighting of the PPP-RTK corrections. We provide a formal and simulation-based analysis of kinematic and static PPP-RTK with perfect, i.e., deterministic, clock and bias corrections as well as corrections computed from only a single reference station. The results indicate that, on average, one can expect centimeter-level positioning results with just slightly more than two epochs already with single-station corrections. This is confirmed with real four-system GNSS data, for which the availability of two-epoch centimeter-level horizontal positioning results is 99.7% during an exemplary day.

Determination of tropical belt widening using multiple GNSS radio occultation measurements

Abstract. In the last decades, several studies reported the tropics' expansion, but the rates of expansion are widely different. In this paper, data of 12 global navigation satellite systems radio occultation (GNSS-RO) missions from June 2001 to November 2020 with high resolution were used to investigate the possible widening of the tropical belt along with the probable drivers and impacts in both hemispheres. Applying both lapse rate tropopause (LRT) and cold point tropopause (CPT) definitions, the global tropopause height shows an increase of approximately 36 and 60 m per decade, respectively. The tropical edge latitudes (TELs) are estimated based on two tropopause height metrics, subjective and objective methods. Applying both metrics, the determined TELs using GNSS have expansive behavior in the Northern Hemisphere (NH), while in the Southern Hemisphere (SH) there are no significant trends. In the case of ECMWF Reanalysis v5 (ERA5) there are no considerable trends in both hemispheres. For the Atmospheric Infrared Sounder (AIRS), there is expansion in the NH and observed contraction in the SH. The variability of tropopause parameters (temperature and height) is maximum around the TEL locations in both hemispheres. Moreover, the spatial and temporal patterns of total column ozone (TCO) have good agreement with the TEL positions estimated using GNSS LRT height. Carbon dioxide (CO2) and methane (CH4), the most important greenhouse gases (GHGs) and the main drivers of global warming, have spatial modes in the NH that are located more poleward than that in the SH. Both surface temperature and precipitation have strong correlation with GNSS LRT height. The surface temperature spatial pattern broadly agrees with the GNSS TEL positions. In contrast, the standardized precipitation evapotranspiration index (SPEI) has no direct connection with the TEL behavior. The results illustrate that the tropics' widening rates are different from one dataset to another and from one metric to another. In addition, TEL behavior in the NH is different from that in the SH. Furthermore, the variability of meteorological parameters agrees with GNSS TEL results more than with that of other datasets.

FY3E GNOS II GNSS Reflectometry: Mission Review and First Results

FengYun-3E (FY3E), launched on 5 July 2021, is one of China’s polar-orbiting meteorological satellite series. The GNOS II onboard FY3E is an operational GNSS remote sensor that for the first time combines GNSS radio occultation (GNSS RO) and GNSS reflectometry (GNSS-R). It has eight reflection channels that can track eight specular points at the same time, receiving reflected signals from multiple GNSS systems, including GPS, BeiDou and Galileo. The basic GNSS-R output generated by GNOS II is a 122 × 20 non-uniform delay-Doppler map whose high resolution portion captures more information near the specular point. This paper introduces the GNSS-R aspect of the FengYun-3E GNOS II, including the instrument, power calibration and wind speed retrieval algorithm. Preliminary validation results for its first four months of data are also presented. After preliminary quality control, the overall wind speed error is less than 2 m/s at wind speeds below 20 m/s for data from both GPS satellites and BeiDou satellites when compared to the ECMWF reanalysis winds.

Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass

Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex 3.04 navigation file for multiple GNSS and the corresponding SP3 precise orbits computed by CNES (Centre National d’Etudes Spatiales) for GPS, Glonass, Galileo and CODE (Center for Orbit Determination in Europe) for Beidou, and compute broadcast ECEF coordinates and clocks. The pre-fit discrepancies are converted by least squares to corrections to the broadcast ephemeris parameters in two-hour consecutive arcs (for GPS, Galileo and Beidou) and to a set of seven Helmert parameters for the entire day, to align in origin, orientation and scale to the common GNSS IGS14 Reference Frame. The test cases suggest that the Broadcast Ephemeris Message, complemented with Reference Frame information, can reproduce the precise ephemeris and clocks with centimetric accuracy for intervals at least equal to the respective validity times, typically 2 h. The broadcast ephemeris of Glonass consists of three initial positions and velocities at epoch, three constant Lunisolar accelerations for the satellite position, and of three polynomial coefficients for the satellite clock. The 9D vector of state is numerically integrated to generate position and velocity data within the validity time (0.5 h) of the message. To test the capability of this model to reproduce the corresponding values of a precise ephemeris, the 9D vector of state and clock polynomials are adjusted until the rms (root mean squared spread) of the post-fit residuals relative to a precise orbit (CNES’s in our case) is minimum. We show in one example (one satellite for one day) that the Glonass type of message can reproduce a precise ephemeris and clock with a rms spread of 0.025 m over one-hour arcs. Volume computations on one month of data with all available satellites confirm the test results. For GPS, Glonass, Galileo and Beidou, the best fitting clock values predicted by our second order polynomials, based on a 15 min sampling, are shown to fit the corresponding high rate clocks (30 s sampling) of MGEX with zero bias and a rms spread of 0.062 ns (GPS G01), 0.023 ns (Galileo E01), 0.43 ns (Glonass R01), 0.086 ns (Beidou C07) and 0.086 ns (Beidou C12). Modifications to the GPS-like message structure and Glonass algorithm are proposed to increase the validity time by including the effect of the 3rd zonal harmonic of the Earth’s gravity field. The potential of the RTCM messages for broadcasting the improved navigation message is reviewed.