Ionospheric Error Research Articles

Metrics of Astrometric Variability in the International Celestial Reference Frame. I. Statistical Analysis and Selection of the Most Variable Sources

Using very long baseline interferometry data for the sources that comprise the third International Celestial Reference Frame (ICRF3), we examine the quality of the formal source-position uncertainties of ICRF3 by determining the excess astrometric variability (unexplained variance) for each source as a function of time. We also quantify multiple qualitatively distinct aspects of astrometric variability seen in the data, using a variety of metrics. Average position offsets, statistical dispersion measures, and coherent trends over time as explored by smoothing the data are combined to characterize the most and least positionally stable ICRF3 sources. We find a notable dependence of the excess variance and statistical variability measures on decl., as is expected for unmodeled ionospheric delay errors and the Northern Hemisphere–dominated network geometries of most astrometric and geodetic observing campaigns.

Ionospheric contributions to the excess power in high-redshift 21-cm power-spectrum observations with LOFAR

ABSTRACT The turbulent ionosphere causes phase shifts to incoming radio waves on a broad range of temporal and spatial scales. When an interferometer is not sufficiently calibrated for the direction-dependent ionospheric effects, the time-varying phase shifts can cause the signal to decorrelate. The ionosphere’s influence over various spatiotemporal scales introduces a baseline-dependent effect on the interferometric array. We study the impact of baseline-dependent decorrelation on high-redshift observations with the Low Frequency Array (LOFAR). Data sets with a range of ionospheric corruptions are simulated using a thin-screen ionosphere model, and calibrated using the state-of-the-art LOFAR epoch of reionization pipeline. For the first time ever, we show the ionospheric impact on various stages of the calibration process including an analysis of the transfer of gain errors from longer to shorter baselines using realistic end-to-end simulations. We find that direction-dependent calibration for source subtraction leaves excess power of up to two orders of magnitude above the thermal noise at the largest spectral scales in the cylindrically averaged autopower spectrum under normal ionospheric conditions. However, we demonstrate that this excess power can be removed through Gaussian process regression, leaving no excess power above the 10 per cent level for a $5~$ km diffractive scale. We conclude that ionospheric errors, in the absence of interactions with other aggravating effects, do not constitute a dominant component in the excess power observed in LOFAR epoch of reionization observations of the North Celestial Pole. Future work should therefore focus on less spectrally smooth effects, such as beam modelling errors.

Testing the ionospheric model delay and uncertainty estimates with an uncombined navigation filter

In the last decade, new algorithmic positioning techniques have been developed for Global Navigation Satellite Systems (GNSS). These have brought a new focus on high accuracy applications which do not combine multiple frequencies to remove ionospheric errors (i.e. PPP-RTK, Fast-PPP). Not only do these algorithms focus on improvements in the position domain but also in acquiring the positioning solution as fast as possible. In this work, capabilities of different global ionospheric models are assessed, analyzing both the Ionospheric delay accuracy and the associated model uncertainty. Accurate model uncertainties are crucial for reducing the convergence time in uncombined filters, and to guarantee unbiased convergence in the first place. The assessment is done using an uncombined navigation filter with different ionospheric models: GPS ICA, IGS vTEC (vertical Total Electron Content) maps (IGSG, CODG and UQRG), two realizations of the ESA-UGI (Voxel and Multi-Layer), the Madrigal TEC, and the Spire Global vTEC maps. To quantify the model uncertainties without the use of a reference ionospheric model, global maps of an uncertainty inflation factor are computed to show the inflation required to produce optimal filter convergence. These maps demonstrate that some models are too optimistic in the reporting of their own uncertainty estimates, requiring an uncertainty factor up to 10 times the quoted value.

Precise point positioning (PPP) based on the machine learning-based ionospheric tomography

Undifferenced and Uncombined Precise Point Positioning (UPPP) currently stands as a prominent research area, where the integration of high-precision ionospheric products holds the potential to substantially enhance accuracy and convergence performance in UPPP. Presently, the majority of external ionospheric constraints for UPPP rely on Global Ionospheric Maps (GIM). However, the accuracy and resolution of GIM fall short, imposing significant limitations on the positioning performance of UPPP. Consequently, this paper introduces the application of Computerized Ionospheric Tomography based on Machine Learning (CIT-ML) to enhance UPPP performance (PPP-CIT-ML). In this approach, we convert the three-dimensional electron density of CIT-ML into vertical total electron content (VTEC), and then it is compiled into ionospheric grid files essential for UPPP. Simultaneously, the traditional ionospheric tomography methods based on the improved algebraic reconstruction technique (IART) is also employed for UPPP (PPP-CIT-IART), alongside the ionospheric grid files broadcasted by the Center for Orbit Determination in Europe (CODE) for UPPP (PPP-CODE), where PPP-CIT-IART and PPP-CODE are used as the reference methods to test the performance of PPP-CIT-ML. In Static and Kinematic UPPP, compared to PPP-CODE, PPP-CIT-IART demonstrated average improvements in positioning accuracy and convergence performance by over 10% and 7%, respectively. PPP-CIT-ML showed average improvements in positioning accuracy and convergence performance by over 26% and 28%, respectively. The extrapolated ionospheric electron density (IED) applied to UPPP (ECIT-ML-PPP) and compared with PPP-CODE displayed average improvements in positioning accuracy by over 21% and convergence performance by over 26%. Compared with PPP-CIT-IART, ECIT-ML-PPP displayed average improvements in positioning accuracy and convergence performance by over 6% and 21%, respectively. These findings highlight that ionospheric error correction information obtained through ionospheric tomography significantly enhances the positioning accuracy and convergence performance of UPPP. Moreover, the performance enhancement achieved through machine learning-based ionospheric tomography is more pronounced. This study provides preliminary validation for the feasibility of applying machine learning-based ionospheric tomography results to navigation positioning.

Understanding Ionospheric and Geomagnetic Effects on Residual Biases in Radio Occultation Data for Stratospheric Climate Monitoring

AbstractHigher‐order residual ionospheric errors in Global Navigation Satellite System (GNSS) radio occultation (RO) data can induce a systematic residual ionospheric bias (RIB) in RO bending angles, which can impact stratospheric climate monitoring. The main RIB causes are the ray path splitting of dual‐frequency GNSS signals, the electron density distribution along the ray path and at the RO receiver location, and the geomagnetic field. In this study, we investigate the ionospheric and geomagnetic effects on RO‐retrieved stratospheric bending angle and temperature profiles by inspecting the kappa and bi‐local RIB correction methods, the current state‐of‐the‐art methods, using multiple RO satellite mission data in different ionospheric and geomagnetic conditions. We find that, globally, the layer mean/median RIBs of the kappa and bi‐local correction methods exhibit similar behaviors for different RO missions: the estimated bending angle RIBs reach about −0.025/−0.01 and −0.024/−0.008 μrad in the upper (40–45 km) and lower (30–35 km) stratosphere, respectively, while the temperature RIBs reach about −1.0/−0.3 and −0.2/−0.1 K in these layers. However, in the equatorial day time region, the RIB statistics of the mission results diverge. Both the kappa and bi‐local RIBs increase in magnitude with increasing ionization and geomagnetic field strength but show no increase with an increasing degree of ionospheric asymmetry. Overall, the more refined bi‐local method has higher capacity than the comparatively simple kappa method to represent the variability of the ionospheric and geomagnetic conditions that affect RO events. This is important for regional‐scale studies, where the geomagnetic term can be of key relevance.

Fusion of Land-Based and Satellite-Based Localization Using Constrained Weighted Least Squares.

Combining multiple devices for localization has important applications in the military field. This paper exploits the land-based short-wave platforms and satellites for fusion localization. The ionospheric reflection height error and satellite position errors have a great impact on the short-wave localization and satellite localization accuracy, respectively. In this paper, an iterative constrained weighted least squares (ICWLS) algorithm is proposed for these two kinds of errors. The algorithm converts the nonconvex equation constraints to linear constraints using the results of the previous iteration, thus ensuring convergence to the globally optimal solution. Simulation results show that the localization accuracy of the algorithm can reach the corresponding Constrained Cramér-Rao Lower Bound (CCRLB). Finally, the localization results of the two methods are fused using Kalman filtering. Simulations show that the fused localization accuracy is improved compared to the single-means localization.

A novel stop-and-go kinematic positioning method for PPP–RTK

ABSTRACT The technology of precise point positioning – real time kinematic (PPP – RTK) can realize regional accurate positioning. However, poor quality atmospheric corrections can greatly impact the integer ambiguity resolution. The low reliability of interpolated corrections may arise from blocked transmission of the updated corrections, atmospheric disturbance, and when the user is located outside the service area. Therefore, to maintain a continuous ambiguity-fixed state in an inaccurate correction observation environment, we propose a novel stop-and-go (SAG) kinematic positioning method. Integer ambiguities inherited from the last epoch are used to estimate the ionospheric errors of the current epoch using an inversion calculation method. Unmodeled errors contained in the ionospheric corrections are also considered. We then experimentally compare the proposed method and traditional PPP – RTK and SAG methods with the results of the PPP-ambiguity resolution calculation using geomagnetic storm-influenced data. All indicators, including the number of fixed ambiguities, errors of corrections, successful fix rate, and correct fix rate, confirm the superiority of the proposed method. The proposed method achieves a horizontal correct fix rate of 98% and maintains the vertical correct fix rate above 96% throughout the day. It is proved that for most of the time the novel method can provide continuous ambiguity-fixed solutions for users in an inaccurate correction observation environment.

Characterization of the Ionospheric Vertical Error Correlation Lengths Based on Global Ionosonde Observations

AbstractData assimilation is one of the most important approaches to monitoring the variations of ionospheric electron densities. The construction of the background error covariance matrix is an important component of ionospheric data assimilations. To construct the background error covariance matrix, the information about the spatial ionospheric correlations is required. We present a statistical analysis on the ionospheric vertical error correlation length (VCL) based on a global network of ionosondes and the Neustrelitz Electron Density Model. We show that the locally derived VCL is well‐defined and the VCL does not show a considerable dependency on the geographical seasons while local time dependencies of the VCL are shown to be present. A novel VCL model is also established based on the ionospheric scale heights. We show that the ionospheric VCL can be characterized by the variance ratio between the ionosphere model and ionospheric measurements. The altitudinal variations of VCLs are controlled by the interactions between the inherent VCLs of the ionosphere model and the measurements. Two experiments are conducted at two different latitudes based on the proposed model. The results show that the proposed model is stable and well‐correlated with the observed VCLs, which implies a potential to be generalized for a global correlation model. The proposed model can be used in the temporal evolution of error covariance matrices in the ionospheric 4D‐Variational (4D‐Var) assimilations, which may overcome the main drawbacks of the static error covariance specifications in the ionospheric 4D‐Var assimilations.

Characteristic analysis of the differences between total electron content (TEC) values in global ionosphere map (GIM) grids

Abstract. Using total electron content (TEC) from a global ionosphere map (GIM) for ionospheric delay correction is a common method of eliminating ionospheric errors in satellite navigation and positioning. On this basis, the TEC of a puncture point can be obtained by GIM grid TEC interpolation. However, in terms of grid, only few studies have analyzed the TEC value size characteristics of its four grid points, that is, the TEC difference characteristics among them. In view of this, by utilizing the GIM data from high solar-activity years (2014) and low solar-activity years (2021) provided by CODE (Center for Orbit Determination in Europe), this paper proposes the grid TEC difference as a way of analyzing TEC variation characteristics within the grid, which is conducive to exploring and analyzing the variation characteristics of the ionosphere TEC in the single-station area. The value is larger in high solar-activity years and generally small in low solar-activity years, and the value of high-latitude areas is always smaller than that of low-latitude areas. Specifically, in high solar-activity years, most of the GIM grid TEC internal differences are within 4 TECu (1 TECu = 1016 electrons m−2) in high-latitude and midlatitude regions, while only 78.17 % are in low-latitude regions. In low solar-activity years, the TEC difference values within a GIM grid are mostly less than 2 TECu, and most of them in the high and middle latitudes are within 1 TECu. The main finding of this analysis is that the grid TEC differences are small for most GIM grids, especially in the midlatitudes to high latitudes of low solar years. This means that relevant extraction methods and processes can be simplified when TEC within these GIM grids is needed.

A novel ionospheric TEC mapping function with azimuth parameters and its application to the Chinese region

The ionospheric mapping function (MF) for Global Navigation Satellite System (GNSS), a mutual projection method for the slant total electron content (STEC) and vertical total electron content, is one of the significant factors affecting the performance of ionospheric models. The commonly used MF assumes isotropic TEC variations and takes into account only the satellite elevation angle, which may result in significant ionospheric projection errors, especially at low elevation angles. Based on the single-layer model, we propose an additional azimuth parameter mapping function (APMF). The APMF was estimated and evaluated by the NeQuick model during the periods of January 2014 and January 2022 from the aspect of simulation and measured STEC during the periods of 2014 and 2022 from the aspect of actual measurements over China, respectively. Compared to the modified single-layer model mapping function (MSLM-MF), the experimental results indicate that (1) The APMF can significantly reduce the ionospheric projection error, and the fluctuation in errors with different azimuth angles is small. (2) According to the evaluation based on the NeQuick simulation during the TEC peak time, when the ionosphere is quite active, the upper and lower quartiles of the absolute projection error boxplot of the APMF relative to the MSLM-MF in January 2014 are reduced by 56.1% and 60.0%, respectively, and in January 2022, they are reduced by 67.7% and 65.2%, respectively. Similarly, the upper whiskers in the boxplot are reduced by 54.7% and 67.5% in January 2014 and January 2022, respectively; the APMF performance in terms of the root mean square error (RMSE) is improved by 47.0% in January 2014 and 58.3% in January 2022. (3) According to the evaluation based on the measured STEC from GNSS raw data during the TEC peak time, the upper and lower quartiles of the absolute mapping error boxplot of the APMF relative to the MSLM-MF in 2014 are reduced by 48.9% and 46.9%, respectively, while in 2022, they are reduced by 48.3% and 41.2%, respectively. The upper whiskers in the boxplot are reduced by 41.8% and 35.2% in 2014 and 2022, respectively; the APMF performance in terms of RMSE is improved by 44.6% in 2014 and 39.2% in 2022.

Ionospheric Error Models for Satellite-Based Navigation—Paving the Road towards LEO-PNT Solutions

Low Earth Orbit (LEO) constellations have recently gained tremendous attention in the navigational field due to their larger constellation size, faster geometry variations, and higher signal power levels than Global Navigation Satellite Systems (GNSS), making them favourable for Position, Navigation, and Timing (PNT) purposes. Satellite signals are heavily attenuated from the atmospheric layers, especially from the ionosphere. Ionospheric delays are, however, expected to be smaller in signals from LEO satellites than GNSS due to their lower orbital altitudes and higher carrier frequency. Nevertheless, unlike for GNSS, there are currently no standardized models for correcting the ionospheric errors in LEO signals. In this paper, we derive a new model called Interpolated and Averaged Memory Model (IAMM) starting from existing International GNSS Service (IGS) data and based on the observation that ionospheric effects repeat every 11 years. Our IAMM model can be used for ionospheric corrections for signals from any satellite constellation, including LEO. This model is constructed based on averaging multiple ionospheric data and reflecting the electron content inside the ionosphere. The IAMM model’s primary advantage is its ability to be used both online and offline without needing real-time input parameters, thus making it easy to store in a device’s memory. We compare this model with two benchmark models, the Klobuchar and International Reference Ionosphere (IRI) models, by utilizing GNSS measurement data from 24 scenarios acquired in several European countries using both professional GNSS receivers and Android smartphones. The model’s behaviour is also evaluated on LEO signals using simulated data (as measurement data based on LEO signals are still not available in the open-access community; we show a significant reduction in ionospheric delays in LEO signals compared to GNSS. Finally, we highlight the remaining open challenges toward viable ionospheric-delay models in an LEO-PNT context.

Validating Ionospheric Models Against Technologically Relevant Metrics

AbstractNew, open access tools have been developed to validate ionospheric models in terms of technologically relevant metrics. These are ionospheric errors on GPS 3D position, HF ham radio communications, and peak F‐region density. To demonstrate these tools, we have used output from Sami is Another Model of the Ionosphere (SAMI3) driven by high‐latitude electric potentials derived from Active Magnetosphere and Planetary Electrodynamics Response Experiment, covering the first available month of operation using Iridium‐NEXT data (March 2019). Output of this model is now available for visualization and download via https://sami3.jhuapl.edu. The GPS test indicates SAMI3 reduces ionospheric errors on 3D position solutions from 1.9 m with no model to 1.6 m on average (maximum error: 14.2 m without correction, 13.9 m with correction). SAMI3 predicts 55.5% of reported amateur radio links between 2–30 MHz and 500–2,000 km. Autoscaled and then machine learning “cleaned” Digisonde NmF2 data indicate a 1.0 × 1011 el. m3 median positive bias in SAMI3 (equivalent to a 27% overestimation). The positive NmF2 bias is largest during the daytime, which may explain the relatively good performance in predicting HF links then. The underlying data sources and software used here are publicly available, so that interested groups may apply these tests to other models and time intervals.

Estimation of dusk time F-region electron density vertical profiles using LSTM neural networks: A preliminary investigation

The vertical profile of the ionosphere density plays a significant role in the development of low-latitude Equatorial Plasma Bubbles (EPBs), that in turn lead to ionospheric scintillation which can severely degrade precision and availability of critical users of the Global Navigation Satellite System (GNSS). Accurate estimation of ionospheric delays through vertical electron density profiles is vital for mitigating GNSS errors and enhancing location-based services. The objective of this study is to propose a neural network, trained with radio occultation data from the COSMIC-1 mission, that generates average ionospheric electron density profiles during dusk, focusing on the pre-reversal enhancement of the zonal electric field. Results show that the estimated profiles exhibit a clear seasonal pattern, and reproduce adequately the climatological behavior of the ionosphere, thus presenting strong appeal on ionospheric error attenuation.

A Review of Selected Applications of GNSS CORS and Related Experiences at the University of Palermo (Italy)

Services from the Continuously Operating Reference Stations (CORS) of the Global Navigation Satellite System (GNSS) provide data and insights to a range of research areas such as physical sciences, engineering, earth and planetary sciences, computer science, and environmental science. Even though these fields are varied, they are all linked through the GNSS operational application. GNSS CORS have historically been deployed for three-dimensional positioning but also for the establishment of local and global reference systems and the measurement of ionospheric and tropospheric errors. In addition to these studies, CORS is uncovering new, emerging scientific applications. These include real-time monitoring of land subsidence via network real-time kinematics (NRTK) or precise point positioning (PPP), structural health monitoring (SHM), earthquake and volcanology monitoring, GNSS reflectometry (GNSS-R) for mapping soil moisture content, precision farming with affordable receivers, and zenith total delay to aid hydrology and meteorology. The flexibility of CORS infrastructure and services has paved the way for new research areas. The aim of this study is to present a curated selection of scientific papers on prevalent topics such as network monitoring, reference frames, and structure monitoring (like dams), along with an evaluation of CORS performance. Concurrently, it reports on the scientific endeavours undertaken by the Geomatics Research Group at the University of Palermo in the realm of GNSS CORS over the past 15 years.

The implementation of dual frequency positioning for ionospheric effects correction

Brazil is located in a tropical region near the equator line, where the solar incidence is more intense. For this reason, the effect of ionospheric refraction on satellite signals is more expressive. In order to mitigate this effect, the use of dual frequency positioning technique is effective in the position solution, reducing distortions caused by ionospheric refraction. In this article, dual frequency GPS data was analyzed, in order to prove its effectiveness in correcting the ionospheric error in comparison with single frequency GPS data.

MLP-based user-applicable method for SBAS GIVD calibration: A comparative study based on CODE final GIM products

Satellite-Based Augmentation Systems (SBASs) are designed to enhance the performance of Global Navigation Satellite Systems (GNSSs) for civil aviation users. As SBAS Geostationary Earth Orbit (GEO) satellite signals are received in a wide area, far more non-aeronautical GNSS users utilize SBAS to improve navigation performance. Since ionospheric delay is the principal error source of GNSS and a leading correction aspect of SBAS, the GEO-broadcast ionospheric data quality of six SBASs over the past three years is assessed in this article. Results show that European Geostationary Navigation Overlay Service (EGNOS), System for Differential Correction and Monitoring (SDCM), and Wide-Area Augmentation System (WAAS) have the highest Grid Ionospheric Vertical Delay (GIVD) accuracy judged by the residual Standard Deviation (STD), then followed by BeiDou SBAS (BDSBAS) and Multi-functional Satellite Augmentation System (MSAS), while GPS-Aided GEO Augmented Navigation (GAGAN) is the worst. The 6 m Grid Ionospheric Vertical Error (GIVE) availability is over 90 percent of the time for most Ionospheric Grid Points (IGPs) of all tested SBASs. However, GAGAN and WAAS have a significant availability decline at 3 m GIVE. In addition, the integrity limits of MSAS and WAAS are fairly conservative. In contrast, the confidence bounds of BDSBAS and SDCM are excessively radical that fail to meet the integrity requirement. To improve the ionospheric data quality received from SBAS, a Multi-Layer Perceptron (MLP)-based user-applicable GIVD calibration method is proposed in the article. A well-trained MLP learned temporal and spatial correlations of the IGP delays and extracted transfer functions between broadcast and reference GIVDs to eliminate error. The SBAS processing errors in Differential Code Bias (DCB) compensation, GIVD estimation modeling, and GEO message quantization are rectified by the MLP trained by abundant historical data with Center for Orbit Determination in Europe (CODE) final Global Ionospheric Maps (GIMs) as reference. Test results on real-time data show that over 85 percent IGPs have STD decline after calibration. The STD declination rates of six SBASs except for SDCM are over 15 percent, and the Mean Absolute Error (MAE) and Root Mean Square Error (RMS) calibration effects are dramatic for all systems. Finally, the average GIVEs are reduced by more than 50 percent for EGNOS, GAGAN, MSAS, and WAAS with a 99.9 percent integrity level maintained. Despite no promotion on availability for BDSBAS and SDCM, the proposed method compensates for the integrity issues of the systems.

Research on single-epoch ambiguity resolution method based on BDS-3 ionosphere-reduced combinations

In conventional ambiguity resolution method for single-epoch, narrow-lane (NL) observations are often inaccurately fixed due to improper treatment of error sources such as ionospheric and tropospheric delays. Therefore, based on the multi-frequency observation data of the BeiDou Global Navigation Satellite System (BDS-3), this paper adopts a single-epoch resolution method based on the ionosphere-reduced combinations. Firstly, select the appropriate combination observations of extra wide-lane (EWL) and wide-lane (WL) and get its fixed ambiguity. Then the ambiguity of the WL combination with high observation accuracy is obtained by linear combination, which goes to constrain the fixation of NL ambiguity. Secondly, different from the conventional method, the ionosphere-reduced combinations observations were selected as NL, thus significantly weakening the influence of first-order ionospheric delay error on the fixation of narrow-lane ambiguity. The experimental results show that compared with the conventional methods, the method adopted in this paper can significantly improve the fixing success rate of the wide-lane ambiguity. In the NL ambiguity resolution part, using the ionosphere-reduced combinations as NL for solving improved the average fixing success rate from 68.6%/44.4%/35.7%/27.6% to 97.4%/95.4%/95.6%/87.3% compared to the conventional method of using the base frequency as NL for solving. Furthermore, the N/E/U positioning accuracy improved by an average of 63.05%/64.37%/52.27%. To sum up, this method effectively improves the success rate of NL ambiguity fixing and positioning accuracy.

DCB estimation and analysis using the single receiver GPS/GLONASS observations under various seasons and geomagnetic activities

Global Navigation Satellite Systems (GNSS) have many applications in surveying, geodesy, and everyday life, so the accuracy of observations is very important. To have accurate results, many errors should be corrected, including ionospheric errors. Estimating the Differential Code Bias (DCB) and Total Electron Content (TEC) is essential to reduce ionospheric errors. This study's main aim is to determine how the combination of GPS (Global Positioning System) and GLONASS (GLObal NAvigation Satellite System) observations affect the estimation of DCB of satellites (SDCB) and receivers (RDCB) under the effects of geomagnetic storms and seasonal changes. The MATLAB-based software GR_DCB (GPS and GLONASS DCB estimation) was developed to estimate the SDCB and RDCB based on GPS and GLONASS observations. Theresults were tested using data from the International GNSS Service (IGS) network from nine stations and compared to previous studies to assess the effectiveness of the developed code. The findings are consistent with IGS products and more precise than previous studies that relied solely on GPS observations. An analysis of the effects of the geomagnetic storm on DCB variance is considered for June 22–23, 2015. During the geomagnetic storm, all GPS and GLONASS stations exhibited a fall in RDCB, led by a modest increase in some stations. The SDCB had no observed change on storm days compared with quiet days. The seasonal change affected GPS and GLONASS stations RDCB. Winter, which has the highest RDCB mean values, is also the season when a deviation in RDCB is the greatest. Autumn and Summer had the lowest dispersion in RDCB over the season and the lowest RDCB values.

A novel approach to enhancing the Klobuchar algorithm to mitigate the effect of ionospheric delay errors on static single-frequency receivers

Abstract The demand for real-time high-precision positioning for global navigation satellite system applications is difficult to satisfy. In this regard, a single-frequency receiver is found to play an important role in overcoming this challenge, especially in developing countries where economic factors are a major restriction. Hence, the development of built-in models, such as the Klobuchar model, is an important objective for single-frequency users to mitigate the effect of ionospheric delay errors in real-time applications. Accordingly, this study aims to devise a new approach to enhance the behavior of the Klobuchar model and increase its efficiency in resolving the aforementioned problem. The new approach seeks to enhance the behavior of the Klobuchar model without refining or increasing its coefficients. To eliminate the ionospheric delay disturbance, the proposed methodology applies normalization and filtration processes to the raw ionospheric delay probability distribution estimated by the unified least squares technique. A final assessment of the new method for enhancing the Klobuchar behavior in predicting the precise position of a single-frequency static receiver under different weather conditions around the globe is presented in this paper.

ACCURACY ASSESSMENT OF PRECISE POINT POSITIONING WITH MULTI-CONSTELLATION GNSS DATA UNDER STRONG SOLAR BURST EFECTS

Solar variations modify a layer of the Earth’s upper atmosphere known as the ionosphere. This is of particular concern for the aviation sector because of the way its communications and navigation systems can be affected. At the same time, one of the most complex atmospheric effects is the response of ionospheric regions to geomagnetic storms. The ionospheric response during the same storm can vary in time in different locations, which can introduce significant errors/displacement (meters) in single-frequency relative GNSS positioning (DGNSS technology). The residual effect can be somewhat mitigated by using dual- or multi-frequency GNSS, but dual frequency is not a guarantee against degradation of relative observations results, especially during significant geomagnetic storms. In this regard, PPP absolute positioning technology can be effective. However, another atmospheric effect – ionospheric scintillation can have a significant impact on the accuracy of both GNSS positioning approaches. The main goal of this study was to analyze the effect of second-order ionospheric delay during geomagnetic storms and ionospheric scintillations on GNSS positioning using the PPP method. GNSS data corrected and uncorrected for higher-order ionospheric delay, respectively, were processed by the static PPP-AR method using the PRIDE-PPPAR ver.2.2.6 software for the selected periods of geomagnetic storms. From the analysis of the influence of second-order ionospheric errors, it follows that their values can reach almost 4 cm for first-frequency signals under different states of ionospheric disturbances for the GPS constellation and almost an order of magnitude less for the GNSS quadroconstellation. The appearance of stronger geomagnetic storms increases the second-order ionospheric errors by several millimeters.