Ionospheric Error Research Articles

Ionospheric Vertical Correlation Distance Calculation Based on COSMIC Electron Density Profile Data

AbstractBackground error covariance is an important part of ionospheric assimilation and contains correlation information of the ionospheric background field and error information of the model background field, determines the influence degree of observations on models, and controls the vertical electron density distribution of assimilation results. For more accurate background error covariance determination along the ionosphere vertical direction, we used Constellation Observing System for Meteorology Ionosphere and Climate occultation electron density profile data for vertical correlation distance calculation considering IRI 2016 model errors. The vertical direction correlations are asymmetrical above and below the reference altitude, and with increasing altitude, the vertical correlation distance growth rate may decline or remain unchanged. There are correlation differences in different solar activity years, varying with local time, geomagnetic latitude, and altitude. The vertical correlation distances in high‐solar activity years are greater than that in low‐solar activity years. The correlation distances difference at different times decreases with latitude, with the largest correlation distances at low latitudes. The nighttime distances vary slightly with latitude, while the sunrise correlation distances vary the most relative to other periods. At the same altitude, the correlation distances in the daytime low‐latitude region are the smallest overall, while the correlation distances between the daytime mid‐latitude region and sunrise time are the largest. The point where vertical correlation distances growth stabilize may be correlated with ionospheric hmF2 and upper transition. The IRI model is the most widely used background model in ionospheric assimilation, and the study results could facilitate more accurate vertical background error covariance for ionospheric assimilation.

TECX-TCN: Prediction of ionospheric total electron content at different latitudes in China based on XGBoost algorithm and temporal convolution network

The correction of ionospheric delay error through the estimation of ionospheric total electron content (TEC) parameters is very important for the accuracy and rapid convergence of precise point positioning (PPP), especially for single frequency PPP position and double frequency undifferenced and uncombined PPP models. This paper studies the prediction method of ionospheric TEC by analyzing various influencing factors. Firstly, considering the influence of latitude, the TEC values of different observation stations in China at middle and low latitudes are used for research. Secondly, due to the influence of solar storms, the years with and without solar storms are selected for comparative study. At the same time, the moving average value of TEC and the lag value of each solar and geomagnetic index are also added. Because the influence of each feature on ionospheric TEC is not clear, the importance score of each feature is obtained according to the EXtreme Gradient Boosting (XGBoost) algorithm to establish a reasonable feature combination. Then, the temporal convolution network (TCN) is used to train according to data of the collected solar cycle and predict data for the next year. Through experiments, the prediction model with feature selection can obtain higher prediction accuracy, the error reaches ∼2TECU at middle latitude region and ∼3 TECU at low latitude region. Finally, compared with other algorithms, our ionospheric TEC prediction algorithm based on XGBoost and TCN (TECX-TCN) significantly has better performance. When the solar activity is low, its RMSE can reach ∼2.5TECU, the correlation coefficient can reach ∼0.9, and even in the low latitude area with high solar activity, its RMSE can reach ∼5TECU, the correlation coefficient can reach ∼0.85.

Ka/C dual frequency ranging system for ocean altimetry satellite and analysis of ionospheric error

Abstract In view of the future development trend of ocean altimetry satellites, the design idea of Ka/C dual frequency combination system is proposed, that is, the mode of using an altimeter antenna to contain Ka and C frequencies (35.7 and 5.3 GHz, respectively) for combined ranging. First, the random error model of altimeter measuring the distance from the altimeter phase center to the sea surface is given, and the analysis shows that the ionospheric correction error is one of the important factors. Second, the calculation of typical ionospheric parameters shows that the influence of ionospheric higher order terms on altimeter ranging is below the mm level, and its influence can be ignored. The rigorous expression for the first-order and second-order term correction of ionosphere error are given, respectively, by using dual frequency and three frequencies. The computational experiment of Jason-2 and SARAL satellite show that the maximum magnitude of ionospheric error correction in Ku band can reach 11 cm, while the maximum magnitude of ionospheric error correction in Ka band can reach 2 cm. For high-precision applications, ionospheric corrections must be made for single Ka frequency. After Ka/C dual frequency combination is adopted, error correction can be directly conducted without global ionospheric map (GIM) model, and its accuracy will be further improved than GIM model. Under 1 Hz sampling conditions, the ionospheric correction accuracy of Ka/C combination can be better than 2.5 mm, basically eliminating the influence of the ionosphere, and the total ranging accuracy can reach 3.5 cm considering the propagation error.

GNSS standard point positioning method based on spherical harmonic expansion of signal propagation path relating errors

The errors affecting standard point positioning mainly include the ionospheric delay error, tropospheric delay error, clock bias, and multipath effect. The errors are divided into two categories depending on the relation to the signal propagation path: errors related to the propagation path and errors unrelated to the propagation path. The ionospheric delay error, tropospheric delay error, and multipath effect are related to the satellite signal propagation path. Based on this characteristic, a new GPS standard point positioning algorithm based on spherical harmonic expansion (SPP-SH) is proposed, which uses spherical harmonic expansion to represent the errors related to the propagation path. We hope to continuously promote the further development of standard point positioning (SPP) by proposing this new algorithm and to further reduce the redundancy of SPP algorithms and improve the efficiency and reliability of the algorithms. The most important purpose of this manuscript is to validate the proposed SPP-SH algorithm based on GPS data provided by IGS stations. Pseudorange data of multiple continuous epochs are used to achieve a sequential sliding point positioning solution, and the truncated singular value decomposition and iteration method correcting characteristic values are used to solve the ill-conditioned equations in the SPP-SH algorithm. The SPP-SH algorithm is implemented and verified using IGS station data. The positioning accuracy of the SPP-SH algorithm for both dual-frequency data and single-frequency data is better than that of a traditional SPP algorithm. By analyzing the positioning results of the stations at different latitudes, when the spherical harmonic expansion is expanded to the same degree, the positioning accuracy in low latitude areas is poor because the station is seriously affected by factors such as the ionosphere and water vapor, while the positioning accuracy at high latitude stations is the best. The proposed SPP-SH algorithm is also realized in the kinematic scene based on the dual-frequency data collected dynamically. The kinematic data is collected by an Android phone which supports receiving dual-frequency GPS observations. To validate the reliability of the SPP-SH algorithm, two strategies are designed to validate the results, which proves that the newly proposed method can be used for positioning with low accuracy in kinematic conditions.

Neustrelitz Total Electron Content Model for Galileo Performance: A Position Domain Analysis

Ionospheric error is one of the largest errors affecting global navigation satellite system (GNSS) users in open-sky conditions. This error can be mitigated using different approaches including dual-frequency measurements and corrections from augmentation systems. Although the adoption of multi-frequency devices has increased in recent years, most GNSS devices are still single-frequency standalone receivers. For these devices, the most used approach to correct ionospheric delays is to rely on a model. Recently, the empirical model Neustrelitz Total Electron Content Model for Galileo (NTCM-G) has been proposed as an alternative to Klobuchar and NeQuick-G (currently adopted by GPS and Galileo, respectively). While the latter outperforms the Klobuchar model, it requires a significantly higher computational load, which can limit its exploitation in some market segments. NTCM-G has a performance close to that of NeQuick-G and it shares with Klobuchar the limited computation load; the adoption of this model is emerging as a trade-off between performance and complexity. The performance of the three algorithms is assessed in the position domain using data for different geomagnetic locations and different solar activities and their execution time is also analysed. From the test results, it has emerged that in low- and medium-solar-activity conditions, NTCM-G provides slightly better performance, while NeQuick-G has better performance with intense solar activity. The NTCM-G computational load is significantly lower with respect to that of NeQuick-G and is comparable with that of Klobuchar.

Single-band VLBI Absolute Astrometry

The ionospheric path delay impacts single-band, very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously in two bands, but delays in only one band are available for a subset of observations; and when observations are made in one-band design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declination and I developed a procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron content from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin-shell model of the ionosphere. I showed that we are able to model the ionospheric path delay to the extent that no noticeable systematic errors emerge and we are able to assess adequately the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.

Single-station quad-constellation GNSS regional ionospheric modelling for navigation

Conventionally, regional ionospheric models (RIMs) are established using GNSS at multiple stations. However, this will severely rely on the availability of the local GNSS observation network. In this study, a single-station quad-constellation GNSS regional ionospheric modelling (SQG-RIM) approach is proposed by establishing the RIM with the GPS/GLONASS/BDS/Galileo observations at a single station. To facilitate its application, an algorithm is further proposed to divide the entire modelling region into the core area and the non-core area. Compared with the global ionospheric map (GIM), the SQG-RIM in the core area can increase the ionospheric error correction rate by about 9%. Further, the SQG-RIM is applied to single point positioning (SPP) using a differentiated weighting scheme for different signal-passing areas. Test results indicate that the three-dimensional quad-constellation SPP accuracies are improved by 57% and 52% after applying the SQG-RIM as compared to the Klobuchar and GIM models, respectively.

Ionospheric correction of S-band tracking radar data using NavIC S-band signals in missile test range applications

AbstractIn missile test ranges, complex missions demand precise trajectory generated by radar. Both the radar and Global Navigation Satellite System (GNSS) signals are affected by atmospheric effects, degrading their accuracy and performance. The Indian Regional Navigation Satellite System/Navigation with Indian Constellation (IRNSS/NavIC) transmits signals in the S-band together with the L-band. This paper presents a novel experimental technique to improve the tracking accuracy of S-band radars using the concurrent NavIC S-band signal. The ionospheric delay using the NavIC S-band signal is calculated first, and the results are used to improve the trajectory data of simultaneously operating S-band radars. This is a unique application of the NavIC S-band signals apart from its conventional usage. During a launch mission, for low elevation angles, the ionospheric error is found to be ~130 m while at higher elevation angles the error values are found to be ~1–3 m. The concept is validated using data from a missile test mission. This report on the use of S-band GNSS signals for the correction of S-band radar range data offers a clear advantage of simplicity and accuracy.

Multilayer Ionospheric Model Constrained by Physical Prior Based on GNSS Stations

The need for accurate modeling of the ionosphere plays an important role in the global navigation satellite system (GNSS) positioning. The traditional multi-layer VTEC model without prior has been used for modeling the ionospheric delay error. However, it is assumed that the electron density of the ionosphere is compressed into multiple thin layers at fixed heights in the lack of capturing ionospheric physics. In this paper, the data enhancement method by virtual observations is proposed to build the constrained multi-layer VTEC model to capture physical features from empirical ionospheric models. The extraction methods of physical knowledge have been developed by prior VTEC based on principal component analysis and model coefficients based on emulated basis function. The constrained multi-layer modeling has been verified based on simulation and real measurement of GNSS data in Yunnan, China collected from Qianxun Ground-based Augmentation System on November 3, 2021. The receiver DCB error estimated by the multi-layer model with prior constraint is significantly lower than that of the single-layer model and the traditional multi-layer model. The experimental test shows that the constrained multi-layer model achieves the accuracy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.5 \,\rm {TECU}$</tex-math></inline-formula> for the independent reference station. The dSTEC of the proposed two multi-layer models are significantly lower than those of the single-layer model for low elevation angles, and the RMSE of dSTEC is reduced by 63 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> with the cutoff elevation angle of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{\circ }$</tex-math></inline-formula> . The spatial distribution of the multi-layer VTEC model shows consistency with the tomography model to verify vertical feature capturing capability. Compared with the Un-differenced and Un-combined Precise Point Positioning (UCPPP) without ionospheric constraint, the multi-layer constrained model based on the test data improves the convergence time approximately by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$36.55\%$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$18.78\%$</tex-math></inline-formula> in the horizontal (H), up (U) directions, respectively. These results demonstrate that the proposed multi-layer models not only improve ionospheric delay estimation precision but also can obtain the VTEC distribution capturing the physical characteristics of the ionosphere. The proposed multi-layer models may be valuable for the ionospheric delay modeling of satellite navigation systems in harsh variable ionospheric conditions.

Ionospheric Phase Delay Correction for Time Series Multiple-Aperture InSAR Constrained by Polynomial Deformation Model

As a supplement to time-series interferometric synthetic aperture radar (TS-InSAR), time-series multiple-aperture InSAR (TS-MAI) can measure the spatiotemporal changes in SAR along-track surface deformation. TS-MAI is often applied with low-frequency SAR data (e.g., L-band data) due to its ability to retain high interferometric coherence. However, the low-frequency SAR signal is vulnerable to ionospheric delays, which can significantly degrade the measurement accuracy of TS-MAI. This letter presents an approach to correct the ionospheric errors in TS-MAI. A polynomial cubic model is employed to constrain the ground deformation, which is then incorporated into the observation model for effectively separating the deformation signal and the ionospheric delays. The proposed method is tested using the L-band ALOS-1 PALSAR-1 datasets covering the Tocopilla area in Chile between November 2007 and March 2011. The correction performance and accuracy of the proposed method are demonstrated by comparing the range split-spectrum interferometry (RSSI)-based method and the local GPS data, respectively. The root mean square error (RMSE) improvement rates between TS-MAI and GPS are 72.17% for the SRGD site and 84.51% for the VLZL site, and their correlation coefficients increase from 0.23 and 0.50 to 0.52 and 0.61 after the correction.

Impact of Errors in Environmental Correction on Gravity Field Recovery Using Interferometric Radar Altimeter Observations

As a new type of altimeter, interferometric radar altimeter (InRA) has significant potential in marine gravity field recovery due to its high spatial resolution. However, errors in environmental correction on gravity field recovery using InRA observations are unclear. In this study, four kinds of these errors, including wet and dry troposphere, ionosphere, and sea state bias (SSB) correction errors, are simulated. The impact of these errors on gravity field recovery are analyzed and discussed. The results show that, among the four types of errors in environmental correction, the wet troposphere and SSB have a more significant impact on the accuracy of sea surface height computing, and the wet troposphere has the most significant impact on the accuracy of gravity field recovery. The maximum error of gravity anomaly caused by the wet troposphere residual errors is nearly 2 mGal, and the relative error of the recovered gravity anomaly is around 6.42%. We can also find that SSB has a little more significant impact than dry troposphere and ionosphere, where dry troposphere and ionosphere have an almost identical impact, on DV and GA inversion accuracy.

Enhanced neural network model for regional ionospheric modeling and evaluation under different solar-geomagnetic conditions

Monitoring spatiotemporal variations of ionospheric vertical total electron content (VTEC) is crucial for space weather and satellite positioning. In the present study, an enhanced neural network (ENN) model is proposed to capture the changing characteristics of ionospheric VTEC and compared with the traditional mathematical models, i.e. the POLYnomial (POLY) model, generalized trigonometric series function and spherical harmonic function (SHF) model. The ionospheric VTEC data obtained from 31 permanent global positioning system stations in the southwest region of China on 26 August and 8 September, 2017, were used to test the performance of the mentioned models under different Solar-geomagnetic conditions. The ENN model is derived from the ensemble learning method, and the disadvantage that simple backpropagation neural network learners that are not robust enough is weakened by the ENN model. After statistical analysis and single-frequency precise point positioning (SF-PPP) experiments, it is demonstrated that the ENN model is superior to the above three mathematical models, regardless of the solar-geomagnetic conditions. In terms of mean absolute error, root mean square error, standard deviation, and mean absolute percentage error, the ENN model outperforms the SHF model, which is the best mathematical model in the analysis, by 40.7%, 30.20%, 29.88%, 38.04% under quiet solar-geomagnetic conditions, and by 37.66%, 29.93%, 30.96%, 32.01% under active solar-geomagnetic conditions. In addition, the accuracy of the SF-PPP is greatly affected by the error caused by ionosphere. In the static SF-PPP experiment of this study, the ENN model can better correct ionospheric error. Under quiet and active solar-geomagnetic conditions, the SF-PPP accuracy can be improved by 85.1% and 85.2% with the ionosphere delay correction from the ENN model.

An improved phase-smoothed-code algorithm using GNSS dual-frequency carrier epoch-difference geometry-free combination observations

The Hatch filter has been widely used in global navigation satellite system (GNSS) single point positioning (SPP). However, the classic phase-smoothed-code (PSC) method is vulnerable to ionospheric cumulative errors, resulting in filter divergence and accuracy degradation in the positioning solution. In this paper, an improved method, i.e, phase epoch-difference geometry-free (GF) combination smoothed code (PESC), is proposed for SPP with raw GNSS measurements. In other words, the dual-frequency carrier-phase observations are used to form epoch-difference GF combinations to obtain the precise between-epoch variations of ionospheric delays. Then, the ionospheric delays of code observations during a continuous satellite arc are converted to the initial epoch’s value. Subsequently, the initial epoch’s ionospheric delay of each arc, setting as a constant value, is estimated along with other parameters through the Kalman filter. GNSS measurements from 20 globally distributed stations from multi-GNSS experiment (MGEX) network on July 7 2021 are selected to validate the feasibility of the new algorithm. Results indicate that the average root mean square (RMS) of PESC-SPP errors is 0.404 m, 0.340 m, and 1.491 m in east (E), north (N), and Up (U) components, respectively, with the improvement of 30.5%, 50.5%, 52.1% and 36.5%, 55.1%, 54.3% in comparison with that of PSC-SPP and SPP, respectively. Data collected in the kinematic experiment on 28th November 2021 is used to evaluate the PESC positioning performance. Results demonstrate that the deviations of epoch-difference slant total electron content (STEC) derived from the PESC-SPP are much smoother and more stable than those of PSC-SPP during continuous satellite arcs, with the average RMS improvements of 33.5%, 66.9%, and 32.9% for GPS, Galileo, and BDS satellites, respectively. The PESC positioning solutions can converge after a few minutes, and the RMS of PESC-SPP errors is 0.779 m, 0.609 m, and 2.060 m in E/N/U components, which is 32.2%, 24.1%, 32.0%, and 27.8%, 18.2%, 16.5% lower than that of SPP and PSC-SPP results, respectively.

NeQuick2 validation using multi-satellite and ground data

Global Navigation Satellite System’s (GNSS) positioning calculation is prone to ionospheric errors. Single frequency GNSS users receive ionospheric corrections through broadcast ionospheric models. Therefore, the accuracy of ionospheric models must be validated based on various geographic and geomagnetic conditions. In this work, an attempt is made to validate NeQuick2 electron density (Ne) using multiple sources of space-based and ground-based data at the Arabian Peninsula and for low solar activity conditions. These sources include space-based data from Swarm, DMSP and COSMIC-2 satellite constellations and ground-based data from GNSS receiver and the ionosonde. The period of this study is 1 year from October 2019 to September 2020. Analysis shows that the agreement between NeQuick2 and experimental Ne close to the peak density height depends on seasons and time of the day with the largest errors found in Autumn and during the daytime. NeQuick2 generally overestimates Ne during the daytime. During the early morning and evening hours, Ne estimates seem to be fairly accurate with slight underestimation in Winter and Spring. Estimation of slab thickness by NeQuick2 is found to be close to the values calculated using collocated ionosonde and GNSS receiver.

Systematic Ionospheric Residual Errors in GNSS Radio Occultation: Theory for Spherically Stratified Media

AbstractThe standard ionospheric correction of bending angles in Global Navigation Satellite System (GNSS) radio occultation (RO) measurements removes most of the influence from the ionosphere, but leaves small systematic residual errors in the corrected data. The main reasons for residual errors at stratospheric and mesospheric altitudes are the neglect of higher‐order terms in the expansion of the ionospheric refractive index, and the fact that the two GNSS signals follow slightly different paths through the ionosphere. Another reason is the neglect of the local electron density at the receiver in orbit. These residual errors depend on the geomagnetic field and the spatial distribution of the ionospheric electron density and its gradients. In this work we derive this dependency to high accuracy for a spherically stratified ionosphere, including the “bi‐local” situation where the ionosphere is different (though still spherically stratified) on the inbound and outbound side of the RO event tangent points. As part of the derivations, we find a small residual error term not previously noted, which can become appreciable for elliptical satellite orbits. The results are verified by ray tracing through simple ionospheric and geomagnetic field models. The accuracy of a higher‐order bi‐local ionospheric residual error correction based on these results would be limited by the uncertainty in knowledge of the electron density and by horizontal electron density gradients along the ray paths.

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.

An Observation Density Based Method for Independent Baseline Searching in GNSS Network Solution

With applications such as precise geodetic product generation and reference frame maintenance, the global GNSS network solution is a fundamental problem that has constantly been a focus of concern. Independent baseline search is a prerequisite step of the double-differenced (DD) GNSS network. In this process, only empirical methods are usually used, i.e., the observation-max (OBS-MAX), which allows for obtaining more redundant DD observations, and the shortest-path (SHORTEST), which helps to better eliminate tropospheric and ionospheric errors between stations. Given the possible limitations that neither of the methods can always guarantee baselines of the highest accuracy to be selected, a strategy based on the ‘density’ of common satellites (OBS-DEN) is proposed. It takes the number of co-viewing satellites per unit distance between stations as the criterion. This method ensures that the independent baseline network has both sufficient observations and short baselines. With single-day solutions and annual statistics computed with parallel processing, the method demonstrates that it has the ability to obtain comparable or even higher positioning accuracy than the conventional methods. With a clearer meaning, OBS-DEN can be an option alongside the previous methods in the independent baseline search.

Performance Analysis of GPS/BDS Broadcast Ionospheric Models in Standard Point Positioning during 2021 Strong Geomagnetic Storms

The broadcast ionospheric model is one of the main methods for eliminating ionospheric delay errors for the Global Navigation Satellite Systems (GNSS) single-frequency users. GPS Klobuchar model (GPSK8) is the widely used broadcast ionospheric model for GPS, while BDS usually implements the BDS Klobuchar model (BDSK8) and BeiDou Global Broadcast Ionospheric Delay Correction Model (BDGIM). Geomagnetic storms may cause interference within the ionosphere and near-Earth space, compromising the accuracy of ionospheric models and adversely affecting the navigation satellite systems. This paper analyzes the static Standard Point Positioning (SPP) accuracy of GPS and BDS by implementing the broadcast ionospheric models and then investigates the impact of strong geomagnetic storms occurring in 2021 on positioning accuracy. The results show that the global 3D positioning accuracy (95%) of GPS + GPSK8, BDS + BDSK8, and BDS + BDGIM are 3.92 m, 4.63 m, and 3.50 m respectively. BDS has a better positioning accuracy in the northern hemisphere than that of the southern hemisphere, while the opposite is valid for GPS. In the mid-latitude region of the northern hemisphere, BDS + BDSK8 and BDS + BDGIM have similar positioning accuracy and are both better than GPS + GPSK8. The positioning accuracy after applying those three broadcast ionospheric models shows the superior performances of winter and summer over spring and autumn (based on the northern hemisphere seasons). With the exception of during winter, nighttime accuracy is better than that of daytime. The strong geomagnetic storm that occurred on the day of year (DOY) 132, 2021 has an impact on the positioning accuracy for only a small number of stations; however, the global average positioning accuracy is not significantly affected. The strong geomagnetic storms that occurred in DOY 307 and DOY 308 have a significant impact on the positioning accuracy of dozens of stations, and the global average positioning accuracy is affected to a certain extent, with some stations experiencing a serious loss of accuracy. Decreased degrees in positioning accuracy is proportional to the intensity of the geomagnetic storm. Of the 33 IGS Multi-GNSS Experiment (MGEX) stations worldwide, those located in the low and mid-latitudes are more significantly affected by the geomagnetic storms compared with higher latitudes. Evident fluctuations of the positioning errors existed during the strong geomagnetic storms, with an increase in extreme values, particularly in the up direction.

An Improved Method of Surface Clutter Simulation Based on Orbiting Radar in Tianwen‐1 Mars Exploration

AbstractMars Orbiter Subsurface Investigation Radar (MOSIR) is carried by China's first Mars probe, Tianwen‐1 orbiter, investigating the Martian subsurface stratification. Surface clutter from topography off‐nadir will overlap with the subsurface echoes, which affects the recognition of Martian subsurface reflections. Surface clutter simulation can effectively distinguish the nadir and off‐nadir radar echoes. In this paper, we choose the facet method to model the Mars surface topography and combine the roughness parameter with the radar backscatter function. We also provide an analytic expression of the echo phase considering the distance variation in the whole facet. The Chinese first Mars landing site is on Utopia Planitia, which is also one of the key investigating regions of MOSIR. Therefore, we also carried on surface clutter simulation of this region and generated simulation radargram with the Chirp Scaling algorithm. Furthermore, we use the contrast method to compensate for ionospheric error introduced by the NeMars Mars ionosphere model. Our surface clutter simulation program will significantly support MOSIR subsurface investigation, and provide a chance to verify the related data processing.

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.