Grid Ionospheric Vertical Error Research Articles

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.

Maximum eigenvalue detection for local ionospheric anomaly - theory, cases, statistics, and potential application

At low latitudes in China, local ionospheric anomalies are frequent and difficult to capture, posing positioning errors and safety risks to GNSS users. This leads to conservative error bounds in GNSS augmentation systems. For example, in Satellite Based Augmentation System (SBAS), the presence of under-sampled regions and the ionospheric instability at low latitudes can result in an over-conservative error bound, i.e., Grid Ionospheric Vertical Error (GIVE) with reduced availability. Ionospheric irregularity detectors could be used to exclude anomalies from the grid model to share the integrity risk and tighten the GIVE. The detection method needs to have theoretical validity and sensitivity to small local anomalies. However, current irregularity detectors are designed for Ionospheric Grid Point (IGP), dealing with wide-area spatial anomalies. The problem of decreased availability resulting from the over-conservative error bound caused by the frequent local ionospheric anomalies is unsolved, especially at low latitudes and the equatorial region. To further enhance the GNSS performance, the applicability analysis of a maximum eigenvalue-based ionospheric irregularity detector, which is sensitive to local-scale spatial anomalies, is presented. The detection capability of MED for ionospheric anomalies is demonstrated by theory, cases, statistics, and simulation applications. This method can also be used for ionospheric monitoring in geodesy or geophysics.

Reexamining Low-Latitude Ionospheric Error Bounds: An SBAS Approach for Brazil

The ionosphere in low-latitude regions is a major challenge for a satellite-based augmentation system (SBAS). The intense dynamics of this layer of the atmosphere in this part of the globe is one of the main reasons why Brazil discarded years ago the idea of deploying its own SBAS. In this article, we re-examine the ionospheric error bounds for a high-density ground station network in Brazil by updating previous work that assessed specific parameters for low latitudes, especially the ones related to the generation of the ionospheric error bounds expressed by the grid ionospheric vertical error (GIVE). Ionospheric delay maps and their respective GIVE values were generated by varying the functional model used in the interpolation of the grid points and the decorrelation parameter of the measurements for quiet and active days of the ionosphere. The resulting GIVE maps show values significantly higher than the bounds found in mid-latitudes and represent one of the main contributions of this article. An availability assessment for APV-I shows that the planar fit model with a spatial decorrelation standard deviation of 1 m provides the best availability for quiet days, while a quadratic fit with a decorrelation parameter of 2 m results in better availability for active days. Even though it would be possible to provide some service in quiet days within the area with a higher density of reference stations, the resulting availability is not ideal for a real SBAS when the ionosphere is more active.

Beidou wide-area augmentation system clock error correction and performance verification

On December 27, 2018, the Beidou-3 System (BDS-3) has completed the deployment of 18 Medium Earth Orbit (MEO) satellites combined as a space constellation. In addition to the augmentation information for the new system signals B1C and B2a, the BDS-3 is compatible with the three augmentation information broadcast by the BDS-2 system for B1I and B3I signals: equivalent clock error correction, User Differential Ranging Error (UDRE) and Grid Ionosphere Vertical Error (GIVE). In this paper, the observation data of Beidou monitoring network are used to analyze the pseudo-range observation quality of the smooth transition signals B1I and B3I of BDS-2 and BDS-3. At the same time, the relationship between the equivalent clock error correction and the prediction error of the satellite clock is analyzed by using the Two-Way Satellite Time and Frequency Transfer (TWSTFT) data. The results show that the correlation between the equivalent clock error correction and the monitored clock error by using the TWSTFT data is greater than 60%. We calculate the UDRE by using the equivalent clock error correction. The results show that the satellite equivalent clock error correction can improve the accuracy of User Equivalent Range Error (UERE) by about 50%. This paper also compares the positioning accuracy of the BDS-2 satellites with the BDS-2 satellites combined BDS-3 satellites. The results show that the three-dimensional positioning accuracy is improved by about 30% after the BDS-3 satellites are added.

SBAS performance improvement with a new undersampled ionosphere threat model based on relative coverage metric

Ionospheric delay error is one of the most significant error sources for single frequency SBAS (Satellite Based Augmentation System) users and its error bound is the key point for PL (protection level) calculation. To satisfy the integrity specifications for users anywhere in the service region, the error bound need to be inflated according to various threat. Among them, the undersampled threat plays an important role in the inflation. The fundamental reason for the undersampled threat lies in the disagreement of the linear planar model to the actual ionosphere characteristics, which cannot be accurately described by the discrete IPP (Ionospheric Pierce Point) samples. Ionosphere threat model is established to handle this problem. It uses historical irregular ionosphere data to generate the two-dimensional lookup table which illustrates the relationship between the IPP distribution and the maximum estimation error. How to abstract the metrics to describe the discrete two-dimensional IPP distribution is the key to the establishment of ionosphere threat model. In this paper, we conclude the properties of a ‘good’ metric from a physical point of view and propose the Relative COVerage (RCOV) metric. Based on the measured data from IGS (International GNSS Service) stations, taking the regions of Europe (20°N~70°N, −30°W~60°E) as an example, the ionosphere threat model based on RCOV metric is established and compared with the RCM (Relative Centroid Metric) model used in WAAS (Wide Area Augmentation System) and MSAS (MTSAT Satellite based Augmentation System). At the same time, the integrity of the ionosphere GIVE (Grid Ionosphere Vertical Error) results is verified. The experimental results show that under the experimental configuration given in this paper, the RCOV metric proposed can improve the system availability on the premise of meeting the integrity requirements.

Ionosphere modeling in the context of Algerian Satellite-based Augmentation System

To guarantee safety-critical implementation of Algerian Satellite-based Augmentation Systems (SBAS), a comprehensive study of the impact of space weather on Global Navigation Satellite Systems (GNSS) over this region is necessary. In this work, three typical ionospheric algorithms: inverse distance weighting (IDW), kriging, and planar-fit were applied on GPS dual-frequency data from seven GPS stations spread over Algerian territory during three major geomagnetic storms of different intensity in addition to a quiet geomagnetic period. The performance of these ionospheric algorithms was investigated based on the broadcast ionospheric vertical delay (Grid Ionospheric Vertical Delay, GIVD) and its corresponding confidence bound error (Grid Ionospheric Vertical Error, GIVE) at two Ionospheric Grid Points (IGPs): (35°N, 5°E) and (30°N, 5°E), located in the Algerian mid-latitudes. The obtained GIVDs were compared to their corresponding delays estimated at nearby user stations as a first reference and to EGNOS messages as a second reference. In addition, the Global Ionospheric Maps (GIMs) from the International GNSS Service (IGS) was incorporated in the analysis. Our results indicate that the studied models provided equivalent accuracy even though kriging slightly outperformed the other models in most of the cases of study. The EGNOS model showed less agreement with the ground truth data during 2013 and 2015, while in 2017 became more accurate after the upgrade. The analysis of estimated GIVEs shows the ability of the three ionospheric models to protect and to safely bound GIVD errors while kriging is intended to provide better availability of Algerian SBAS. In addition, EGNOS GIVEs exhibit effective protection of users at the edge of its service area.

Moderate Geomagnetic Storm Condition, WAAS Alerts and real GPS Positioning Quality

The most significant part of the Wade Area Augmentation System (WAAS) integrity data consists of the User Differential Range Error (UDRE) and the Grid Ionospheric Vertical Error (GIVE). WAAS solutions are not completely appropriate to determine the GIVE term within the entire wade area coverage zone taking in account real irregular structure of the ionosphere. It leads to the larger confidence bounding terms and lower expected positioning availability in comparison to the reality under geomagnetic storm conditions and system outages. Thus a question arises: is the basic WAAS concept appropriate to provide the same efficiency of the integrity monitoring for both “global differential correction (i.e. clock, ephemeris etc)” and “local differential correction (i.e. ionoshrere, troposhpere and multipath)”? The aim of this paper is to compare official WAAS integrity monitoring reports and real positioning quality in US coverage zone (CONUS) and Canada area under geomagnetic storm conditions and system outages. In this research we are interested in comparison between real GPS positioning quality based on one-frequency C/A ranging mode and HAL (VAL) values which correspond to the LP, LPV and LPV200 requirements. Significant mismatch of the information between WAAS integrity data and real positioning quality was unfolded as a result of this comparison under geomagnetic storms and system outages on February, 2011 and June 22, 2015. Based on this result we think that in order to achieve high confidence of WAAS positioning availability alerts real ionospheric measurements within the wide area coverage zone must be involved instead of the WAAS GIVE values. The better way to realize this idea is to combine WAAS solutions to derive “global differential corrections” and LAAS solutions to derive “local differential corrections”.

Estimation of ionospheric delay of NavIC/IRNSS signals using the Taylor Series Expansion

The delay in Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) signals due to the ionosphere are decisive because it leads to significant changes in the positional accuracy of the system. In this paper, we try to estimate the ionospheric time delay (ionodelay) precisely using the local Taylor Series Expansion (TSE) algorithm for a single frequency NavIC/IRNSS system. The performance of the local TSE algorithm is examined by considering two cases. In case I, the TSE was validated under the influence of an intense geomagnetic storm (8 September 2017) by considering NavIC/IRNSS data from the Indian equatorial and Equatorial Ionization Anomaly (EIA) regions. In case II, based on the quiet and disturbed days data, the local TSE model was examined at different locations in the local area (<10 km) using two NavIC/IRNSS receivers (i.e. reference and rover). The results of ionodelay and positional accuracy (Three Dimensional Distance Root Mean Square [3DRMS], Circular Error Probability [CEP], and Spherical Error Probability [SEP]) of NavIC/IRNSS for both the cases indicates that the single frequency local TSE algorithm performs the same as the reference dual frequency model, where as the global eight coefficient Klobuchar and the regional Grid Ionospheric Vertical Error (GIVE) model behaves differently. Therefore, the single-frequency TSE model improves the performance of the NavIC/IRNSS receiver in the local area, and the mathematical coefficient computation and additional frequency hardware cost have been reduced, with the acceptance of a maximum 0.8 m of errors.

The GIVE Ionospheric Delay Correction Approach to Improve Positional Accuracy of NavIC/IRNSS Single-Frequency Receiver

The Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) is an independent navigation system developed for the Indian subcontinent by the Indian Space Research Organisation (ISRO). The positional accuracy of this system is mainly affected by the ionosphere of the low-latitude equatorial Indian subcontinent, as large ionospheric gradients and intense irregularities are present in it. The objective of this study is to improve the positional accuracy of NavIC/IRNSS systems by applying ionospheric correction using the most suitable single-frequency model. The data to be analysed were collected from the NavIC/IRNSS receiver provided by the Space Applications Centre, ISRO. A comparative analysis between the dual-frequency model and single-frequency model (e.g. GIVE model, coefficient-based model) was performed on the data from the NavIC/IRNSS receiver. Different ionospheric models were applied to compute ionospheric delay (ionodelay) on a quiet day (3 < K P < 5). Our result shows that both the single-frequency Grid Ionosphere Vertical Error (GIVE) model and dual frequency model outperform remarkably compared to the traditional coefficient-based model. The GIVE model was also analysed on FAR categorized satellites for different stormy days of different months. It was observed that during stormy days also, the 3D position computed by applying the GIVE model was nearly the same as the dual-frequency model.

An Improved Ionospheric Spatial Threat Model for SBAS

A conservative Grid ionospheric vertical delay error (GIVE) estimation would lead to conservative Protection levels (PLs) estimation and affects Satellitebased augmentation systems (SBAS) service performance. To reduce the margin in GIVE estimation, an improved spatial threat model is presented. A new parameter ofMinimum separation distance (MSD) is introduced. The new model is described with the MSD, Relative centroid metric (RCM) and fit radius as inputs. Ionospheric delay measurements during storms are used to construct the new spatial threat model. Simulation results show that, with the new model, there is at least 9.5% reduction in User ionospheric vertical delay errors (UIVEs), while the user ionospheric delay estimation errors can be bounded at the same time. Even on severe ionosphere disturbed days, at least 5% improvement of PLs (95%) could be achieved for more than 20% Conterminous united states (CONUS) area, leading to higher system service performance.

Analysis of a grid ionospheric vertical delay and its bounding errors over West African sub-Saharan region

Investigating the effects of the Equatorial Ionization Anomaly (EIA) ionosphere and space weather on Global Navigation Satellite Systems (GNSS) is very crucial, and a key to successful implementation of a GNSS augmentation system (SBAS) over the equatorial and low-latitude regions. A possible ionospheric vertical delay (GIVD, Grid Ionospheric Vertical Delay) broadcast at a Ionospheric Grid Point (IGP) and its confidence bounds errors (GIVE, Grid Ionospheric Vertical Error) are analyzed and compared with the ionospheric vertical delay estimated at a nearby user location over the West African Sub-Saharan region. Since African sub-Saharan ionosphere falls within the EIA region, which is always characterized by a disturbance in form of irregularities after sunset, and the disturbance is even more during the geomagnetically quiet conditions unlike middle latitudes, the need to have a reliable ionospheric threat model to cater for the nighttime ionospheric plasma irregularities for the future SBAS user is essential. The study was done during the most quiet and disturbed geomagnetic conditions on October 2013. A specific low latitude EGNOS-like algorithm, based on single thin layer model, was engaged to simulate SBAS message in the study. Our preliminary results indicate that, the estimated GIVE detects and protects a potential SBAS user against sampled ionospheric plasma irregularities over the region with a steep increment in GIVE to non-monitored after local sunset to post midnight. This corresponds to the onset of the usual ionospheric plasma irregularities in the region. The results further confirm that the effects of the geomagnetic storms on the ionosphere are not consistent in affecting GNSS applications over the region. Finally, this paper suggests further work to be investigated in order to improve the threat integrity model activity, and thereby enhance the availability of the future SBAS over African sub-Saharan region.

Availability prediction method for EGNOS

Following the recent development of wide-area differential technology, satellite-based augmentation systems (SBASs) have been applied in many fields. However, the capability of monitoring stations used for generating error correction might degenerate with the aging of ground equipment over time, and the poor geometry between ranging and integrity monitoring stations (RIMS) and satellites could affect the reliability of navigation systems in supplying safety of life service. Therefore, it is necessary to predict SBAS availability so that users can choose a safe and efficient navigation system. Predictions of user difference range error indicator (UDREI) and grid ionospheric vertical error indicator (GIVEI) are the two difficulties in predicting SBAS availability. Considering the effect of geometry on UDREI, satellite geometric dilution of precision is defined to distinguish different geometries such that the relationship between the number of visible RIMS and UDREI in different geometries can be obtained. With regard to the effect of geometry on GIVEI, a weighted number of visible ionospheric pierce points (IPPs) is defined to describe the geometric IPP distribution such that the relationship between the number of visible IPPs and GIVEI in different geometries can be achieved. Finally, experiments are performed to evaluate the effectiveness of our proposed method. With the prediction algorithm, the prediction is consistent with actual performance over 75.17% of the entire European region. In particular, when focusing on central Europe, where the distribution of RIMS is uniform, the level of consistency can reach 95–100%. It can be concluded that the prediction performance of the algorithm is encouraging and that this model may be considered a good contender for predicting SBAS availability.

Preliminary analysis of grid ionospheric vertical error for GAGAN

The inverse distance weighted model (IDWM) represents a geo-spatial interpolation technique used for estimation of ionospheric vertical delays at the ionospheric grid points (IGPs) and user ionospheric pierce points (IPPs). The GPS Aided Geo Augmented Navigation (GAGAN) system is planned for air-navigation over the Indian service region using a space based augmentation. One of the main needs for GAGAN is to develop a suitable grid-based ionospheric model for estimating the vertical delay and its error bound, i.e., grid ionospheric vertical error (GIVE) at all the IGPs covering the Indian subcontinent. Dual frequency GPS receiver data obtained from 17 total electron content (TEC) stations are considered in the analysis. For a typical IGP (25°N, 75°E), variations in the GIVE for a few days of quiet ionosphere are presented. For a quiet and magnetically moderate day, the mean and standard deviations of the user IPP (UIPP) estimation error and the mean GIVE are presented using the IDWM with Klobuchar, Junkins and bilinear models.

Performance Analysis of Korean WADGPS Algorithms with NDGPS Data

To provide more accurate and reliable positioning and timing services to Korean nationwide users, the Ministry of Maritime Affairs and Fisheries of Korea is implementing Korean NDGPS (Nationwide DGPS), which is operational partly. And it also has a plan to construct WADGPS (Wide Area Differential GPS) system using sites and equipments of the NDGPS reference stations. For that, Seoul National University GNSS Laboratory is implementing and testing prototypes of WRS (Wide-area Reference Station) and WMS (Wide-area Master Station). Until now, because there are not enough installed WRSs to be used for computing wide area correction information, we cannot test algorithms of WMS with the data processed actually in WRSs. Therefore to evaluate the performance of the algorithms, we made a MATLAB program which can process RINEX (Receiver INdependent Exchange) format data with WADGPS algorithm. Using that program which consists of WRS, WMS and USER modules, we processed the data collected at NDGPS reference stations, which are saved in RINEX format. In WRS module, we eliminate the atmospheric delay error from the pseudorange measurement, smooth the measurement by hatch filter and calculate pseudorange corrections for each satellite. WMS module collects the processed data from each reference stations to generate the wide area correction information including estimated satellite ephemeris errors, ionospheric delays at each grid point, UDRE (User Differential Range Error), GIVE (Grid Ionosphere Vertical Error) and so on. In USER part, we use the measurements of reference stations as those of users and estimate the corrected users' positions and protection levels (HPL, VPL). With the results of estimation, we analyzed the performance of the algorithms. We assured the estimated UDRE /GIVE values and the protection levels bound the corresponding errors effectively. In this research, we can expect the possible performance of WADGPS in Korea, and the developed modules will be useful to implementation and improvement of the algorithms.

Performance Evaluation of the Wide Area Augmentation System for Ionospheric Storm Events

One of the greatest challenges in developing accurate and reliable satellite-based augmentation systems (SBAS) is modeling of ionospheric effects. Wide area GPS networks are generally sparse (station spacings of 500-1000 km), and ionosphere models can suffer degraded performance in regions where large spatial gradients in total electron content (TEC) exist. Of particular concern for Wide Area Augmentation System (WAAS) users is the feature called storm enhanced density, which is associated with large TEC gradients at mid-latitudes. This effect is a significant source of error in the WAAS correction models. The Canadian GPS Network for Ionosphere Monitoring (CANGIM) consists of three GPS reference stations in western Canada, augmented by two additional sites in the northern United States. In addition to measures of ionospheric activity, WAAS messages are collected continuously at these sites and decoded (post-mission) at University of Calgary. Localization schemes have been developed to compute WAAS ionosphere corrections for any location in North America. In this paper, performance of the broadcast WAAS ionosphere model is quantified through comparison with truth data from over 400 GPS reference stations in North America. WAAS ionosphere model accuracies throughout North America are evaluated for intense storm events, and compared with WAAS Grid Ionosphere Vertical Error (GIVE) bounds. Limitations in the WAAS ionosphere model are identified for enhanced ionospheric activity and, in particular, the storm enhanced density phenomenon.

Sudden ionospheric delay decorrelation and its impact on the Wide Area Augmentation System (WAAS)

In the absence of selective availability, the ionosphere represents the largest source of positioning error for single‐frequency users of the Global Positioning System (GPS). In differential GPS systems such as the Wide Area Augmentation System (WAAS), vertical ionospheric delays are modeled at regularly spaced intervals in geographic latitude and longitude. The broadcast bound on the error at each of these points is designated the grid ionospheric vertical error (GIVE). Higher performance standards planned for future implementations of WAAS require a reduction in the magnitude of the GIVE broadcast under nominal conditions. Achieving this reduction depends upon a better understanding of the decorrelation of ionospheric delay, in both space and time. In this paper we focus on temporal decorrelation. We report a methodology for assessing the impact on WAAS posed by a sudden increase in the level of ionospheric disturbance. The methodology is based upon forming an estimate of the probability PD that a WAAS user will confront a sudden increase in the level of ionospheric disturbance following a period of relative calm. We have determined a limiting upper bound of PD to be 4 × 10−7, which lies well within the margin needed to meet WAAS integrity requirements.

Ionospheric Threat Model Methodology for WAAS

: The ionosphere is the largest remaining error source affecting GPS. It also has some of the least predictable spatial and temporal variations. Consequently, the ionosphere becomes the determining factor in system performance for the Wide Area Augmentation System (WAAS). Because the ionosphere cannot be observed at all places simultaneously, the confidence bound, termed the grid ionospheric vertical error (GIVE), can be determined only with the aid of a threat model. The threat model is used to restrict the expected ionospheric behavior. A method is needed for accurately describing the limits of the threat model without being overly pessimistic. This paper describes a methodology for using real data to generate worst-case scenarios from which an appropriate threat model can be determined. This threat model must be coupled with a set of metrics that can distinguish well-observed ionospheric regions.