Multi-frequency Global Navigation Satellite System Research Articles

Design of Universal Code Generator for Multi-Constellation Multi-Frequency GNSS Receiver

A multi-constellation, multi-frequency Global Navigation Satellite System (GNSS) receiver is capable of simultaneously receiving signals from multiple satellite constellations across various frequency bands. This allows for increased observations, thereby enhancing navigation accuracy, continuity, effectiveness, and reliability. The spread spectrum code structures used in satellite navigation signals differ among systems. Compatible code generators are employed in multi-constellation, multi-frequency GNSS receivers to support tasks such as signal acquisition and tracking. There are three main types of spread spectrum code structures: Linear Feedback Shift Register (LFSR), Legendre sequences, and Memory codes. The Indian Regional Navigation Satellite System (IRNSS) released the L1-SPS (Standard Positioning Service) signal format in August 2023, which utilizes the Interleaved Z4-linear ranging code (IZ4 code) as its spread spectrum code. Currently, there is no universal code generator design compatible with the IZ4 code. In this paper, a proposed universal code generator is based on the hardware structure of the IRNSS IZ4 code generator. It achieves compatibility with all LFSR-based spread spectrum codes and enables parallel generation of multiple sets of GNSS signal spread spectrum codes, thereby improving hardware utilization efficiency. The proposed structure is implemented and validated using FPGA design, and resource consumption is provided as part of the validation results.

Evaluation of The Effect of Spoofing on Dual-Frequency Global Navigation Satellite System (GNSS)

This paper aims to assess the impact of Global Navigation Satellite System (GNSS) spoofing on the performance of a Garmin GPSMAP 66sr dual-frequency GNSS receiver. The evaluation is conducted through field assessments under three conditions: 1) single-frequency GPS L1 coarse acquisition (C/A) only, 2) single-frequency GPS L1 C/A and Galileo E1 open service (OS), and 3) dual-frequency GPS L1 C/A and L5, as well as Galileo E1 OS and E5a. The results emphasise the critical role of multifrequency GNSS in mitigating spoofing. In the dual-frequency multi-GNSS mode, spoofing does not occur as the GPS L5 and Galileo E5a signals remain unaffected by spoofing signals in the L1 / E1 band. In the single-frequency multi-GNSS mode, the higher number of observed GNSS satellites contributes to higher minimum spoofing power levels and longer durations between position fix loss and spoofing as compared to the GPS only mode.

Occurrence of ionospheric scintillations under different solar and geomagnetic conditions over low latitude station Varanasi

In the present study, occurrences of amplitude scintillations during the ascending phase of the 25th solar cycle from November 2020 to March 2023 are studied over the equatorial anomaly region Varanasi (latitude 25.31° N, longitude 82.97° E, magnetic dip Lat. 16.2° N). Multi-frequency Global navigation satellite system (GNSS) receiver is used to study the occurrence of amplitude scintillation index S4. Diurnal, monthly, and seasonal occurrence characteristics of the S4 index are presented. The scintillation occurrence is observed during nighttime and daytime but is more probable during nighttime. It is observed that maximum scintillation occurred during the equinox season for the solar moderate period whereas the highest occurrence is in summer during the low solar activity period. The highest scintillation occurrences during the summer solstice for a period of low solar activity condition is rare and could be attributed to the gravity waves (GWs) generation due to the weather phenomena in the lower atmosphere. GWs could act as a seeding perturbation in electron density, affecting the growth of ionospheric irregularities through Rayleigh-Taylor instability. The solar flux index (F10.7) is compared with the percentage occurrence of scintillation for the low and moderate solar activity periods to observe the effect of solar activity on scintillation occurrences. Overall, the scintillation occurrence increases with increasing solar activity. To study the effect of geomagnetic storms on scintillations, we have considered seven moderate and intense geomagnetic storms grouped in three categories that occurred during solar cycle 25. It is observed that the occurrence of scintillations is enhanced for the storms with the recovery phase starting at post-midnight. The probability of occurrence of scintillation during the night hours is decreased when the geomagnetic storm occurs during the daytime.

GNSS Solar Astronomy in real-time during more than one solar cycle

This work presents a summary of the continuous non-stop (hereinafter 24/7) real-time measurement and warning system for EUV solar activity, which is based on worldwide multifrequency Global Navigation Satellite Systems (GNSS) observations. The system relies on continuous tracking of the intensity of expected global patterns in the Earth’s ionosphere’s free electron distribution, which are associated with solar flares. The paper includes a discussion on the foundations of GNSS Solar Astronomy, along with details on its real-time implementation that began in 2011. Furthermore, a summary of the corresponding validation is provided, comparing it to external and direct solar EUV flux measurements obtained from SOHO-SEM. Finally, there will be a brief mention of the ongoing efforts to extend this technique to detect huge extra-solar sources.

Enhanced GNSS Reliability on High-Dynamic Platforms: A Comparative Study of Multi-Frequency, Multi-Constellation Signals in Jamming Environments

The global navigation satellite system (GNSS) signals are vulnerable to disruption sources, such as signal jamming. This, in turn, can cause severe degradation or discontinuities of the GNSS-based position, navigation, and timing services. The availability of multi-frequency signals from multi-constellation GNSS systems, such as Galileo and GLONASS, along with the modernization of GPS with multi-frequency signals, has the potential to increase the immunity of GNSS-based navigation systems to signal jamming. Despite various studies completed on the utilization of multi-frequency and multi-constellation global navigation satellite system (GNSS) signals to resist receiver jamming, there is still an urge to further investigate this concern under different circumstances. This paper presents an experimental evaluation of the advantages of the employment of multi-frequency multi-constellation GNSS signals for better GNSS receivers’ performance during signal jamming situations for high-dynamic platforms such as aircraft/drones. Additionally, the study examines the effects of both simulated and real jamming signals on all possible combinations of the GPS, Galileo, and GLONASS signal frequencies and constellations. Two airplane trajectory routes were built, and their corresponding RF signals were generated using the Spirent and Orolia GNSS signal simulators. The results indicated that the GPS multi-frequency-based solution maintains reliable positioning performance to some extent under low jamming scenarios. However, the combination of GPS, Galileo, and GLONASS signals proved its ability to provide a continuous and accurate positioning solution during both low and high jamming scenarios.

Reconstructed estimation method of the multi-frequency GNSS inter-frequency clock bias

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.

Complete Global Total Electron Content Map Dataset based on a Video Imputation Algorithm VISTA

Ionospheric total electron content (TEC) derived from multi-frequency Global Navigation Satellite System (GNSS) signals and the relevant products have become one of the most utilized parameters in the space weather and ionospheric research community. However, there are a couple of challenges in using the global TEC map data including large data gaps over oceans and the potential of losing meso-scale ionospheric structures when applying traditional reconstruction and smoothing algorithms. In this paper, we describe and release a global TEC map database, constructed and completed based on the Madrigal TEC database with a novel video imputation algorithm called VISTA (Video Imputation with SoftImpute, Temporal smoothing and Auxiliary data). The complete TEC maps reveal important large-scale TEC structures and preserve the observed meso-scale structures. Basic ideas and the pipeline of the video imputation algorithm are introduced briefly, followed by discussions on the computational costs and fine tuning of the adopted algorithm. Discussions on potential usages of the complete TEC database are given, together with a concrete example of applying this database.

Common Android Smartphones and Apps for Cost-Efficient GNSS Data Collection: An Overview

Global Navigation Satellite System (GNSS) sensors are increasingly considered as major sources of precise Position, Navigation, and Timing (PNT) information. Android-based smartphones contain inbuilt GNSS sensors, and they now contribute to a major global GNSS market segment. Various hardware and Android-based applications (App) developments are witnessed to best exploit the current multi-constellation, multi-frequency GNSS environment. Since Android version 7.0 (Nougat) and Location Application Programming Interface (API) 24, recording GNSS raw data in the smartphone became possible. This paper describes the potential of commercial Smartphones and reviews the capabilities of Android Apps for cost-efficient GNSS measurements for the geospatial community and a novel classification of the Apps based on their capabilities and usability. Results on the positioning capability of common smartphones using real-time data show the achievable modest solution precision, and these are suitable for use of the devices in geomatics applications, improved App development, and for IoT-based system and infrastructure development.

Application of GNSS Reflectometry in Water Level Monitoring using Low-cost GNSS Antenna: A Case Study in Tam Giang Lagoon, Thua Thien Hue Province

Extreme hydrological events become increasingly unpredictable due to climate change and sea-level rise, highlighting the importance of coastal sea level monitoring. This study aims to develop a Global Navigation Satellite System (GNSS) reflectometry technology that uses low-cost multi-frequency antennas to measure water levels. A multi-frequency GNSS antenna was installed in the Tam Giang lagoon area, Thua Thien Hue province, to collect data of GPS/GLONASS/Galileo/Beidou satellites at 1Hz from April 10 to April 29, 2022. Water level elevation is calculated from GNSS reflectometry data using Interference Pattern Technical (IPT) based on Signal-to-Noise Ratio (SNR). After filtering, the water level results are validated by data from the water level sensor located in the same location. The Root Mean Square Error between the water level from the GNSS - Reflectometry (GNSS– R) and the in situ measurement is 0,049 m and the correlation coefficient reaches 0,93 when combining different frequencies. The study results demonstrate that the multi-frequency GNSS-R station can be used as an additional method to measure water levels with an accuracy comparable to that of a standard tidal gauge. In addition, the study results also show the sensitivity of the GNSS reflected signal to weather conditions and the state of the sea surface, which is the basis for forecasting and early warning of storm surge extremes from GNSS reflectometry data.

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

A Robust Nonlinear Filter Strategy Based on Maximum Correntropy Criterion for Multi-GNSS and Dual-Frequency RTK

The multi-constellation, multi-frequency Global Navigation Satellite System (GNSS) has the potential to empower precise real-time kinematics (RTK) with higher accuracy, availability, continuity, and integrity. However, to enhance the robustness of the nonlinear filter, both the measurement quality and efficiency of parameter estimation need consideration, especially for GNSS challenging or denied environments where outliers and non-Gaussian noise exist. This study proposes a nonlinear Kalman filter with adaptive kernel bandwidth (KBW) based on the maximum correntropy criterion (AMC-KF). The proposed method excavates data features of higher order moments to enhance the robustness against noise. With the wide-lane and ionosphere-free combination, a dual frequency (DF) data-aided ambiguity resolution (AR) method is also derived to improve the measurement quality. The filtering strategy based on the DF data-aided AR method and AMC-KF is applied for multi-GNSS and DF RTK. To evaluate the proposed method, the short baseline test, long baseline test, and triangle network closure test are conducted with DF data from GPS and Galileo. For the short baseline test, the proposed filter strategy could improve the positioning accuracy by more than 30% on E and N components, and 60% on U. The superiority of the proposed adaptive KBW is validated both in efficiency and accuracy. The triangle network closure test shows that the proposed DF data-aided AR method could achieve a success rate of more than 93%. For the long baseline test, the integration of the above methods gains more than 40% positioning accuracy improvement on ENU components. This study shows that the proposed nonlinear strategy could enhance both robustness and accuracy without the assistance of external sensors and is applicable for multi-GNSS and dual-frequency RTK.

(Near) Real-Time Snow Water Equivalent Observation Using GNSS Refractometry and RTKLIB.

Global navigation satellite system (GNSS) refractometry enables automated and continuous in situ snow water equivalent (SWE) observations. Such accurate and reliable in situ data are needed for calibration and validation of remote sensing data and could enhance snow hydrological monitoring and modeling. In contrast to previous studies which relied on post-processing with the highly sophisticated Bernese GNSS processing software, the feasibility of in situ SWE determination in post-processing and (near) real time using the open-source GNSS processing software RTKLIB and GNSS refractometry based on the biased coordinate Up component is investigated here. Available GNSS observations from a fixed, high-end GNSS refractometry snow monitoring setup in the Swiss Alps are reprocessed for the season 2016/17 to investigate the applicability of RTKLIB in post-processing. A fixed, low-cost setup provides continuous SWE estimates in near real time at a low cost for the complete 2021/22 season. Additionally, a mobile, (near) real-time and low-cost setup was designed and evaluated in March 2020. The fixed and mobile multi-frequency GNSS setups demonstrate the feasibility of (near) real-time SWE estimation using GNSS refractometry. Compared to state-of-the-art manual SWE observations, a mean relative bias below 5% is achieved for (near) real-time and post-processed SWE estimation using RTKLIB.

Modeling and analysis of an ionospheric mapping function considering azimuth angle: A preliminary result

Generally, dual- and multi-frequency global navigation satellite system (GNSS) users can use dual- or multi-frequency combinations to eliminate the ionospheric delay. However, different vertical ionospheric models are applied for single-frequency GNSS users, which need an ionospheric mapping function for conversion. Although many mapping functions can be employed, the influence of latitude, azimuth, solar flux, and other factors are not taken into account. Thus, we proposed a mapping function, named SGG-MF, considering the influence of azimuth. The conversional results of single-layer model mapping function (SLM-MF), Klobuchar mapping function (Klobuchar-MF), modified single layer model mapping function (MSLM-MF) and SGG-MF are evaluated by using coinciding pierce point (CPP) technique as well as single-frequency precise point positioning (SF-PPP) in static mode. For the CPP technique, it is found that the mean absolute errors (MAE) of SLM-MF, Klobuchar-MF, and, MSLM-MF range from 1.5 to 2.1 TECU (total electron content unit), while SGG-MF ranges from 1.5 to 1.7 TECU. The standard deviation (STD) of SGG-MF improved by about 13.6%, 14.9%, and 13.6% compared with that of SLM-MF, Klobuchar-MF, and MSLM-MF, respectively. For the SF-PPP test, the positioning error of SGG-MF was reduced by about 6.0%, 22.9%, and 11.9% compared with that of SLM-MF, Klobuchar-MF, and MSLM-MF, respectively.

Modeling and performance assessment of precise point positioning with multi-frequency GNSS signals

The development of global navigation satellite system (GNSS), especially BeiDou-3 Navigation Satellite System (BDS-3) and Galileo system, promotes the progress of the precise point positioning (PPP) technology. Considering deep integration and full utilization of GNSS signals, this study dedicates to developing three triple-frequency PPP models apply to multi-constellation including BDS-3. Besides, some biases such as differential code bias (DCB), inter-frequency bias (IFB) and inter-system bias (ISB) are also addressed. Through the ten-day datasets collected from 160 stations, the multi-frequency PPP models for single- and multi-constellation solutions are analyzed and compared from static positioning performance, Zenith Tropospheric Delay (ZTD) estimates, ISB estimates, and IFB estimates. The results indicate that the triple-frequency PPP models, especially two dual-frequency ionosphere-free (IF) model namely TIF with triple-constellation which can provide the positioning accuracy of 4.89, 7.31, 12.1 mm after the convergence time of 10.75 min in east, north and up directions, perform better than the dual-frequency model, apart from the a single IF model with GPS. Interestingly, the positioning performance is not effectively improved with the addition of GLONASS constellation. But the performance of GAL/BDS combined constellation is comparable to GPS single constellation in TIF model.

Principle and performance of multi-frequency and multi-GNSS PPP-RTK

PPP-RTK which takes full advantages of both Real-Time Kinematic (RTK) and Precise Point Positioning (PPP), is able to provide centimeter-level positioning accuracy with rapid integer Ambiguity Resolution (AR). In recent years, with the development of BeiDou Navigation Satellite System (BDS) and Galileo navigation satellite system (Galileo) as well as the modernization of Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS), more than 140 Global Navigation Satellite System (GNSS) satellites are available. Particularly, the new-generation GNSS satellites are capable of transmitting signals on three or more frequencies. Multi-GNSS and multi-frequency observations become available and can be used to enhance the performance of PPP-RTK. In this contribution, we develop a multi-GNSS and multi-frequency PPP-RTK model, which uses all the available GNSS observations, and comprehensively evaluate its performance in urban environments from the perspectives of positioning accuracy, convergence and fixing percentage. In this method, the precise atmospheric corrections are derived from the multi-frequency and multi-GNSS observations of a regional network, and then disseminated to users to achieve PPP rapid AR. Furthermore, a cascade ambiguity fixing strategy using Extra‐Wide‐Lane (EWL), Wide-Lane (WL) and L1 ambiguities is employed to improve the performance of ambiguity fixing in the urban environments. Vehicle experiments in different scenarios such as suburbs, overpasses, and tunnels are conducted to validate the proposed method. In suburbs, an accuracy of within 2 cm in the horizontal direction and 4 cm in the vertical direction, with the fixing percentage of 93.7% can be achieved. Compared to the GPS-only solution, the positioning accuracy is improved by 87.6%. In urban environments where signals are interrupted frequently, a fast ambiguity re-fixing can be achieved within 5 s. Moreover, multi-frequency GNSS signals can further improve the positioning performance of PPP-RTK, particularly in the case of small amount of observations. These results demonstrate that the multi-frequency and multi-GNSS PPP-RTK is a promising tool for supporting precise vehicle navigation.

PPP\u2013RTK functional models formulated with undifferenced and uncombined GNSS observations

Technique PPP–RTK combines the advantages of both the Precise Point Positioning (PPP) and the Real-Time Kinematic (RTK) positioning. With the emergence of multi-frequency Global Navigation Satellite System (GNSS) observations, it is preferable to formulate PPP–RTK functional models based on original (undifferenced and uncombined) observations. While there exist many variants of the undifferenced and uncombined PPP–RTK models, a unified theoretical framework needs developing to link these variants. In this contribution, we formulate a class of undifferenced and uncombined PPP–RTK functional models in a systematic way and cast them in a unified framework. This framework classifies the models into a code-plus-phase category and a phase-only category. Each category covers a variety of measurement scenarios on the network side, ranging from small-, medium- to large-scale networks. For each scenario, special care has been taken of the distinct ionospheric constraints and the difference between Code Division Multiple Access (CDMA) and Frequency Division Multiple Access (FDMA) signals. The key to systematically formulating these models lies in how to deal with the rank deficiency problems encountered. We opt for the Singularity-basis (S-basis) theory, giving rise to the full-rank observation equations in which the estimable parameters turn out to be the functions of original parameters and those selected as the S-basis. In the sequel, it becomes straightforward to derive for each scenario the user model as it, more or less, amounts to the single-receiver network model. Benefiting from the presented theoretical framework, the relationships and differences between various undifferenced and uncombined PPP–RTK models become clear, which can lead to the better use of these models in a specific situation.

Variation Characteristics of Multi-Channel Differential Code Biases from New BDS-3 Signal Observations

A multi-frequency Global Navigation Satellite System (GNSS) provides greater opportunities for positioning and navigation applications, particularly the BeiDou Global Navigation Satellite System (BDS-3) satellites. However, multi-frequency signals import more pseudorange channels, which introduce more multi-channel Differential Code Biases (DCBs). The satellite and receiver DCBs from the new BDS-3 signals are not clear. In this study, 9 DCB types of the new BDS-3 signals from 30-days Multi-GNSS Experiment (MGEX) observations are estimated and investigated. Compared with the DCB values provided by the Chinese Academy of Science (CAS) products, the mean bias and root mean squares (RMS) error of new BDS-3 satellite DCBs are within ±0.20 and 0.30 ns, respectively. The satellite DCBs are mostly within ±0.40 ns with respect to the product of the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The four sets of constructed closure errors and their mean values are within ±0.30 ns and ±0.15 ns, respectively. The mean standard deviation (STD) of the estimated satellite DCBs is less than 0.10 ns. In particular, our estimated satellite DCBs are more stable than DCB products provided by CAS and DLR. Unlike satellite DCBs, the receiver DCBs have poor compliance and show an obvious relationship with the geographic latitude when compared to the CAS products. The STDs of our estimated receiver DCBs are less than 1.00 ns. According to different types of receiver DCBs, the distribution of STDs indicates that the coefficient of the ionospheric correction has an influence on the stability of the receiver DCBs under the ionosphere with the same accuracy level. In addition, the type of receiver shows no regular effects on the stability of receiver DCBs.

Improvement of Multi-GNSS Precision and Success Rate Using Realistic Stochastic Model of Observations

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open problem. Weighting among different GNSS systems requires a realistic stochastic model for all observations to achieve the best linear unbiased estimation (BLUE) of unknown parameters in multi-GNSS data processing mode. In addition, the correct integer ambiguity resolution (IAR) becomes crucial in shortening the Time-To-Fix (TTF) in RTK, especially in challenging environmental conditions. In general, it is required to estimate various variances for observation types, consider the correlation between different observables, and compensate for the satellite elevation dependence of the observable precision. Quality control of GNSS signals, such as GPS, GLONASS, Galileo, and BeiDou can be performed by processing a zero or short baseline double difference pseudorange and carrier phase observations using the least-squares variance component estimation (LS-VCE). The efficacy of this method is investigated using real multi-GNSS data sets collected by the Trimble NETR9, SEPT POLARX5, and LEICA GR30 receivers. The results show that the standard deviation of observations depends on the system and the observable type in which a particular receiver could have the best performance. We also note that the estimated variances and correlations among different observations are also dependent on the receiver type. It is because the approaches utilized for the recovery techniques differ from one type of receiver to another kind. The reliability of IAR will improve if a realistic stochastic model is applied in single or multi-GNSS data processing. According to the results, for the data sets considered, a realistic stochastic model can increase the computed empirical success rate to 100% in multi-GNSS as well as a single system. As mentioned previously, the realistic precision of the solution can be achieved with a realistic stochastic model. However, using the estimated stochastic model, in fact, leads to better precision and accuracy for the estimated baseline components, up to 39% in multi-GNSS.

Single Epoch Ambiguity Resolution of Small-Scale CORS with Multi-Frequency GNSS

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises.

New results of ionospheric total electron content measurements from a low-cost global navigation satellite system receiver and comparisons with other data sources

New results of ionospheric Total Electron Content (TEC) measurements obtained from a newly installed low-cost multi-frequency Global Navigation Satellite System (GNSS) U-BLOX receiver at Abuja-Nigeria (Geographic: 8.99° N, 7.38° E; Geomagnetic: 1.6° S) is presented. The paper motivates the use of the U-BLOX receiver for TEC studies in the African equatorial region. Data obtained for the periods of July-August and November-December 2020 are used. TEC data from the U-BLOX are compared with TEC obtained from a nearby high-cost GNSS receiver, and with COSMIC – RO (Constellation Observing System for Meteorology Ionosphere and Climate – Radio Occultation) TEC measurements. Corresponding TEC values from the AfriTEC and NeQuick ionospheric models are also presented. The results show an excellent level of agreement between the U-BLOX and high-cost GNSS receiver measurements. The COSMIC values were typically less than the U-BLOX and high-cost receiver values, and this is mainly attributed to the difference in TEC integration heights used for the two systems. The correlation coefficients between the U-BLOX values and values from the other four datasets are mostly greater than 0.9. The root-mean-square differences (RMSDs) between the U-BLOX and high-cost receiver values are about 2 TECU and less. The RMSDs between the U-BLOX values and values from each of the AfriTEC and NeQuick models are less than 5 TECU. The values are comparable and even lower than values computed in previous research that used TEC from high-cost receivers. There is also consistent and significant agreement between 30-second ROT values computed from both the low-cost and high-cost receivers. These results summarily indicate that the U-BLOX is a good candidate for TEC studies in the region, just like the high-cost receivers.