Single-frequency Precise Point Positioning Research Articles

An evaluation of the positioning ability of the real-time ionosphere-free single-frequency precise point positioning technique in the Arctic and Antarctic polar regions under different ionospheric scintillations

This contribution presents an evaluation of the positioning ability of the real-time (RT) ionosphere-free (IF) single-frequency precise point positioning (SF-PPP) technique in Arctic and Antarctic under different auroral activities. Firstly, Global Positioning System (GPS)-only observations obtained from International GNSS Service (IGS) stations in the Arctic were evaluated with RT IF SF-PPP under all possible auroral activities. Then, a series of kinematic experiments were conducted using a zodiac boat on Livingston Island, located on the Antarctic Peninsula, under different auroral activities. Observations from the kinematic experiments were also evaluated using the RT IF SF-PPP. The outcomes indicate that the IF SF-PPP approach is not affected by ionospheric activities. Furthermore, the results reveal that the RT IF SF-PPP provides dm- and m-level positioning accuracy for horizontal and vertical components, respectively. The findings demonstrate that the RT IF SF-PPP technique can be reliably employed in real-time navigation applications in the Arctic and Antarctic.

A reduced-condition-number algorithm for single-frequency precise point positioning based on regularized Kalman filter

Single-frequency receivers are low cost and portable, thus being widely applied in engineering; the extended Kalman filter (EKF) is commonly used to perform single-frequency precise point positioning (SF-PPP). However, the positioning performance of SF-PPP is seriously influenced by various errors. Due to the large process noise and initial variance of the estimated parameters, the weight matrix of state parameters will be ill-conditioned, and since the noise of the pseudo-range is much higher than that of the carrier phase, the weight matrix of observations presents as ill-conditioned. Additionally, the condition number of the normal matrix will jump on the conditions of cycle slip, new emerging satellites, and signal outages. To reduce the condition number of the normal matrix, the regularized Kalman filter (RKF) algorithm is proposed, with additional support for the maximum variance matrix and singular value decomposition, thereby improving the accuracy and stability of SF-PPP. Through static and dynamic experiments, it is found that the proposed method can reduce both the ill-conditioning of the weight matrices of the observations and the state parameters. The condition number of the normal matrix is <500 per epoch, and the convergence time is shortened by >40%. Compared with the SF-PPP using EKF, centimeter-level static positioning accuracies of 1.13, 0.73, and 2.92 cm and decimeter-level kinematic positioning accuracies of 12.5, 10.8, and 27.3 cm in the east, north, and vertical components, respectively, using RKF; this yielded 38.3, 29.8, and 45.2% and 39.6, 41.9, and 21.3% improvement in the static and kinematic scenarios, respectively.

Analysis of spatial–temporal characteristics for BDS-3 broadcast ionospheric models (BDS Klobuchar and BDGIM) in multi-GNSS real-time single-frequency precise point positioning

With the full operation of BDS-3 broadcast ionospheric models, i.e., the BeiDou global ionospheric delay correction model (BDGIM) and the BDS Klobuchar model, its impact on the multi-GNSS real-time (RT) single-frequency (SF) precise point positioning (PPP) needs to be investigated for low-cost GNSS users. The GPS Klobuchar model as a reference is also considered in this study. Two types of SF-PPP models including the ionosphere-corrected (IC) and ionosphere-weighted (IW) strategies are adopted in the positioning domain. GPS + GLONASS + Galileo + BDS-3 observations from 40 multi-GNSS experiment (MGEX) stations distributed in different latitudes are selected for conducting RT SF-PPP during the ionospheric quiet and active periods. The experiment shows that the positioning accuracy of IC RT SF-PPP can be degraded with the increase of the ionospheric activity levels or the decrease of latitudes. Except for low-latitude regions during the ionospheric active period, the 3D positioning accuracy of the northern hemisphere can be improved by at least 15.2 % compared to the southern hemisphere in the IC model with the BDS Klobuchar. The BDGIM model has the best performance among all IC RT SF-PPP solutions, but its 3D positioning accuracy can reach the sub-meter level only in mid-latitude regions. With the adoption of ionospheric constraints, the convergence of the IW model is always superior to that of the group and phase ionospheric correction (GRAPHIC) model, and the improvement of convergence in mid-latitude regions is clearly better than that in low-latitude regions. Due to the quality limitation of the BDS Klobuchar model, it has the longest convergence time among all IW models regardless of ionospheric conditions or latitude regions. Compared to the GPS Klobuchar, the significant improvement of convergence for the BDGIM-constrained RT SF-PPP is mainly presented in low-latitude regions of the northern hemisphere. The horizontal positioning accuracy of the BDGIM-constrained model is always improved in comparison with the GRAPHIC model, but there is a degradation in the vertical component, and the improvement of 3D positioning accuracy is no more than 11.7 %. In summary, the BDGIM-constrained model has the best performance among all RT SF-PPP solutions, its 3D positioning accuracy has the ability to achieve 0.25 m at present.

Investigating the contribution of BDS-3 observations to multi-GNSS single-frequency precise point positioning with different ionospheric models

Due to the advantages of low-cost and high precision, single-frequency precise point positioning (SF-PPP) plays a vital role in the booming market of the SF global navigation satellite system (GNSS) receivers. With the full completion of the BeiDou global navigation satellite system (BDS-3), its contribution to single-GNSS SF-PPP is worthy of comprehensive exploration. In this study, three SF-PPP models including ionosphere-corrected (IC), ionosphere-free (IF), and ionosphere-weighted (IW) strategies are analyzed, and four ionospheric models including the GPS Klobuchar, BDGIM (BeiDou global ionospheric delay correction model), CNES real-time VTEC (vertical total electron content) and GIM (global ionospheric maps) are used for conducting SF-PPP. As to GPS/GLONASS/Galileo-only IC SF-PPP, its 3D positioning accuracy can be improved by 6.9–11.6 % with the adoption of BDS-3 observations. Similarly, for the IF SF-PPP solution, the corresponding positioning accuracy and convergence time can be improved by at least 17.3 and 38.3 %, respectively. In IW SF-PPP, the convergence performance of the CNES-VTEC-constrained SF-PPP is much better than that of both GPS Klobuchar- and BDGIM-constrained solutions. When using the BDGIM constraints, the horizontal/vertical convergence time of GPS/Galileo + BDS-3 solutions can be shortened by at least 16.5/27.9 % in comparison with GPS/Galileo-only solutions. While for GIM-constrained SF-PPP, the convergence improvement is only shown in the vertical component. In summary, the GIM-constrained SF-PPP with quad-system observations has the best performance, compared to IF solution, its convergence time can be shortened by 82.8 % to 5.5 min in horizontal and 29.7 % to 26.0 min in vertical when converging to 0.3 m. Note that the corresponding improvements in the BDGIM-constrained solution are relatively limited with only 5 %. At present, the quad-system IW SF-PPP has the ability to achieve cm-level fast positioning, with an RMS of 0.06 m in horizontal, showing promising applications in engineering and scientific fields.

Method of Development of a New Regional Ionosphere Model (RIM) to Improve Static Single-Frequency Precise Point Positioning (SF-PPP) for Egypt Using Bernese GNSS Software

Due to the lack of coverage of IGS in Africa, especially over North Africa, and the construction revolution of infrastructure in Egypt, a geodetic CORS stations network was established in 2012. These CORS stations are operated by the Egyptian Surveying Authority (Egy. SA) and cover the whole of Egypt. The paper presents a fully developed regional ionosphere model (RIM) depending on the Egyptian CORS stations. The new model and the PPP solution were obtained using Bernese GNSS V. 5.2 software. An observation data series of eight days (DOY 201–208)/2019 was used in this study. Eighteen stations were used to develop the RIM model for each day; fifteen stations were used to validate the new RIM model. A static SF-PPP solution was obtained using the CODE-GIM and RIM models. Comparing the outcomes to the reference network solution, based on the recently developed RIM model, the solution showed a mean error of 0.06 m in the East direction, 0.13 m in the North direction, and 0.21 m in the height direction. In the East, North, and height directions, this solution improves the SF-PPP result achieved by the Global Ionosphere Maps (CODE-GIM) model by 60%, 68%, and 77%, respectively.

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.

Stochastic Modeling of Smartphones GNSS Observations Using LS-VCE and Application to Samsung S20

In recent years, numerous smartphones have been equipped with global navigation satellite system (GNSS) technology, enabling individuals to utilize their own devices for positioning and navigation purposes. In 2016, with the launch of a mobile app by Google, namely GnssLogger, smartphone users with Android version 7 or higher were able to record raw GNSS measurements (i.e., pseudorange, carrier phase, Doppler, and carrier-to-noise density ratio (C/N0)). Since then, enhancing the accuracy and efficiency of smartphone positioning has become an interesting area of research. Precise point positioning (PPP) is a powerful method providing precise real-time positioning of a single receiver, and it can be applied to smartphone observations as well. Achieving high-precision PPP requires selecting appropriate functional and stochastic models. In this study, we investigate the development of more reliable stochastic models for smartphone GNSS observations. The least-square variance component estimation (LS-VCE) method is applied to double-difference (DD) pseudorange and carrier phase observations from two Samsung S20s to obtain appropriate variances for GPS and GLONASS. According to the results, there is no significant correlation between the pseudorange and carrier phase observations of GPS and GLONASS on the L1 frequency. Furthermore, the quality of GLONASS carrier phase observations is comparable to that of GPS. The model's performance is then assessed with respect to single-frequency precise point positioning (SF-PPP) using a dataset collected in kinematic mode from a Samsung S20 smartphone. A significant improvement of 25.1% and 32.7% on the root-mean-square (RMS) of horizontal positioning and the 50th percentile error, respectively, was achieved when employing the obtained stochastic model.

Multi-Frequency BDS-3 Real-Time Positioning Performance Assessment Using New PPP-B2b Augmentation Service

A new precise point positioning (PPP)-B2b augmentation service broadcast by the BeiDou Navigation Satellite System (BDS-3) geosynchronous Earth orbit (GEO) satellite can provide real-time and high-precision orbit and clock offset corrections for global navigation satellite system (GNSS) users in China and its surrounding areas. It has great significance and research value for real-time and high-precision positioning applications. First, orbit, clock offset, and differential code bias (DCB) of PPP-B2b products are evaluated. Second, the influence of PPP-B2b service on the enhanced positioning of single-frequency (SF), dual-frequency (DF), and Multi-Frequency (MF) real-time PPP using 30 days of BDS-3 observations is verified. The result shows that the standard deviation (STD) of clock offset and the root mean square (rms) of orbit in the 3-D direction for medium Earth orbit (MEO) satellites are 0.118 ns and 0.286 m, respectively, which is 75.9% and 18.3% higher than that of broadcast ephemeris. The statistical results show that the median positioning accuracy of static SF PPP, DF PPP, and MF PPP is better than 0.20/0.09/0.08 m, and the convergence time is better than 51/10/8 min. The median positioning accuracy of kinematic SF PPP, DF PPP, and MF PPP is better than 0.40/0.12/0.12 m, and the convergence time is better than 145/16/12 min. Using the PPP-B2b products, the positioning accuracy of DF PPP and MF PPP is comparable and close to that of DF PPP using the precise products, while the convergence time of MF PPP is improved by 24.8% and 27.7% over DF PPP in static and kinematic solutions, respectively.

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.

A Modified Single-Frequency PPP Method for the Positioning and Time Transfer with BDS-3.

In this paper, time-frequency transfer and positioning experiments with signal coexistence in the BDS system were conducted using the four types of open service signals of the BDS-3 satellite (B1I, B1C, B2a, and B3I), as well as the B2I signals broadcast by the BDS-2 satellites. The experiments used the single-frequency PPP (precise point positioning) method. The experiment validated a modified version of the group and phase ionospheric correction (GRAPHIC) technique. The results demonstrate that, with a single frequency, 18 selected stations may provide positioning results accurate to within a few decimeters. The positioning accuracy of five frequencies signals is improved by 40.4%, 32.2%, 80.3%, 12.4%, and 10.3% when compared to the positioning accuracy of the same signals when using the general observation approach. Currently, the frequency stability may be as precise as dual frequencies with BDS.

Evaluation of BDS-3 B1C/B2b Single/Dual-Frequency PPP Using PPP-B2b and RTS SSR Products in Both Static and Dynamic Applications

The BeiDou Global Navigation Satellite System (BDS-3) can provide PPP-B2b satellite-based Precise Point Positioning (PPP) real-time service to the Asia–Pacific region via PPP-B2b signal transmitted from the three Geostationary Earth Orbit (GEO) satellites. This paper provides a comprehensive evaluation of the accuracies of the satellite’s precise real-time orbit and clock products, including BDS-3 PPP-B2b precise products and the precise real-time products provided by four IGS centers (CAS, DLR, GFZ, and WHU). In addition, the influences of these real-time precise satellite products on the PPP positioning accuracy with single-frequency and dual-frequencies are also studied. Furthermore, the accuracies of broadcast ephemeris and IGS ultra-rapid products are studied, as well as their impact on PPP accuracies. Results illustrate that the orbits accuracies of PPP-B2b orbits are 9.42 cm, 21.26 cm, and 28.65 cm in the radial, along-track, and cross-track components, which are slightly lower than those of real-time orbits provided by the four IGS centers. However, the accuracy of PPP-B2b clock biases is 0.18 ns, which is higher than those provided by IGS Real-Time Service (RTS). In the static positioning test, the 3D positioning accuracy of B1I+B3I dual-frequencies PPP and B1C single-frequency PPP are centimeter-level while using PPP-B2b service, which is slightly lower in horizontal components compared to those obtained based on IGS RTS products. The results of the dynamic vehicle test indicate that the positioning accuracies of B1I+B2b dual-frequency PPP are about 50 cm and 120 cm in horizontal and vertical components, which are close to those of B2b single-frequency PPP using PPP-B2b service. Generally, the PPP-B2b orbit and clock accuracies on real-time PPP present similar performance to that based on IGS RTS.

Investigation of Precise Single-Frequency Time and Frequency Transfer with Galileo E1/E5a/E5b/E5/E6 Observations

With the rapid upgrade of global navigation satellite system (GNSS) single-frequency (SF) receivers and the increasing market demand for low-cost hardware, SF precise point positioning (PPP) technology has been widely applied in the time and frequency field. The five-frequency signals provided by the whole constellation of Galileo bring more opportunities for the application of SF PPP in time and frequency transfer. In this contribution, using Galileo’s multi-frequency observations, three SF PPP time and frequency transfer models, i.e., the un-combined (UC) model, the ionosphere-free-half (IFH) model, and the ionosphere-weighted constraints (IWCs) model are established. SF PPP time and frequency transfer performance with Galileo E1, E5a, E5b, E5, and E6 multi-frequency observations is evaluated using four links (947.7 km to 1331.6 km) with five external high-precision atomic clocks stations. The results show that the time and frequency transfer performance of SF-UC and SF-IWC is better than that of SF-IFH, and the timing accuracy of SF-UC and SF-IWC is similar. SF PPP time and transfer performance with E5, E5a, E5b, and E6 signals is improved compared with traditional E1 signal. Among them, the frequency stability of E5 improves the most (about 58%), and that of E6 improves the least (about 14%). In addition, the difference in frequency stability between SF and double-frequency (DF) PPP decreases gradually with an increase in average time, and the frequency stability difference between SF and DF PPP can reach 2 × 10−16 in 120,000 s, indicating that SF PPP has the potential to achieve DF PPP frequency stability. Considering the possible frequency data loss during actual observation, the cost of the GNSS SF receiver, and the advantages of Galileo multi-frequency observations, SF PPP can also meet the long-time time and frequency transfer requirements, and the SF-IWC model based on Galileo E5 observations is more recommended.

Assessment of Real-Time GPS/BDS-2/BDS-3 Single-Frequency PPP and INS Tight Integration Using Different RTS Products

Due to the virtues of low-cost and high positioning accuracy, Single-Frequency Precise Point Positioning (SF-PPP) is becoming a prospective technique. However, SF-PPP is not as widely used as dual-frequency and triple-frequency PPP at present, owing to the effect of ionospheric delay residuals after model rectification. In recent years, with the evolution of multi-constellation Global Navigation Satellite Systems (multi-GNSS, i.e., GPS, BDS-2, and BDS-3), it has become possible to obtain credible and continuous positioning results using SF-PPP. However, such performance would be significantly degraded in challenging environments (i.e., boulevards, tunnels, and tall buildings). Under these circumstances, GNSS signals are obstructed, and it is difficult to provide sufficient observations for SF-PPP. Therefore, the Inertial Navigation System (INS) is employed to promote the positioning performance of SF-PPP. The PPP/INS integration is regarded as one of the most efficient approaches in GNSS-denied environments. To satisfy the request of supplying real-time positioning information, the Real-Time Services (RTS) of the International GNSS Service (IGS) provide real-time precise orbit and clock products for globally distributed users through the internet. In this paper, a real-time GPS/BDS-2/BDS-3 SF-PPP and INS tight integration model is proposed, and it is assessed using the data gathered by vehicle and real-time products afforded by CAS (Chinese Academy of Sciences), GFZ (Deutsche GeoForschungsZentrum), and WHU (Wuhan University). The outcomes illustrate the following: (1) GPS + BDS SF-PPP/INS can provide more accurate and continuous positioning solutions compared with those of GPS + BDS SF-PPP, with improvements of 52.8%, 31.1%, and 42.8% in the north, east, and vertical components, respectively. (2) In general, the orbit and clock products’ accuracies in terms of GPS afforded by the three analysis centers are consistent with each other. For BDS, the orbit product from WHU is more accurate compared to those of CAS and GFZ. However, the accuracy of the clock product afforded by WHU is lower compared with those provided by the other two centers, especially for BDS-2 satellites. (3) The positioning accuracy in terms of Root Mean Square (RMS) values based on GFZ products are much higher than the results based on CAS and WHU products in the three directions.

Investigation of Displacement and Ionospheric Disturbance during an Earthquake Using Single-Frequency PPP

Currently, it is still challenging to detect earthquakes by using the measurements of Global Navigation Satellite System (GNSS), especially while only adopting single-frequency GNSS. To increase the accuracy of earthquake detection and warning, extra information and techniques are required that lead to high costs. Therefore, this work tries to find a low-cost method with high-accuracy performance. The contributions of our research are twofold: (1) an improved earthquake-displacement estimation approach by considering the relation between earthquake and ionospheric disturbance is presented. For this purpose, we propose an undifferenced uncombined Single-Frequency Precise Point Positioning (SF-PPP) approach, in which both the ionospheric delay of each observed satellite and receiver Differential Code Bias (DCB) are parameterized. When processing the 1 Hz GPS data collected during the 2013 Mw7.0 Lushan earthquake and the 2011 Mw9.0 Tohoku-Oki earthquake, the proposed SF-PPP method can provide coseismic deformation signals accurately. Compared to the results from GAMIT/TRACK, the accuracy of the proposed SF-PPP was not influenced by the common mode errors that exist in the GAMIT/TRACK solutions. (2) Vertical Total Electron Content (VTEC) anomalies before an earthquake are investigated by applying time-series analysis and spatial interpolation methods. Furthermore, on the long-term scale, it is revealed that significant positive/negative VTEC anomalies appeared around the earthquake epicenter on the day the earthquake occurred compared to about 4–5 days before the earthquake, whereas, on the short-term scale, positive/negative VTEC anomalies emerged several-hours before or after an earthquake.

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

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

Native Smartphone Single- and Dual-Frequency GNSS-PPP/IMU Solution in Real-World Driving Scenarios

The Global Navigation Satellite System (GNSS) capability in smartphones has seen significant upgrades over the years. The latest ultra-low-cost GNSS receivers are capable of carrier-phase tracking and multi-constellation, dual-frequency signal reception. However, due to the limitations of these ultra-low-cost receivers and antennas, smartphone GNSS position solutions suffer significantly from urban multipath, poor signal reception, and signal blockage. This paper presents a novel sensor fusion technique using Precise Point Positioning (PPP) and the inertial sensors in smartphones, combined with a single- and dual-frequency (SFDF) optimisation scheme for smartphones. The smartphone is field-tested while attached to a vehicle’s dashboard and is driven in multiple real-world situations. A total of five vehicle experiments were conducted and the solutions show that SFDF-PPP outperforms single-frequency PPP (SF-PPP) and dual-frequency PPP (DF-PPP). Solutions can be further improved by integrating with native smartphone IMU measurements and provide consistent horizontal positioning accuracy of &lt;2 m rms through a variety obstructions. These results show a significant improvement from the existing literature using similar hardware in challenging environments. Future work will improve optimising inertial sensor calibration and integrate additional sensors.

Ionospheric Assimilation of GNSS TEC into IRI Model Using a Local Ensemble Kalman Filter

Ionospheric total electron content (TEC) is important data for ionospheric morphology, and also an important parameter for ionospheric correction in Global Navigation Satellite System (GNSS) precise positioning, navigation, and radio science. In this study, we present a data assimilation model for regional ionosphere based on a local ensemble Kalman filter (LEnKF) with the International Reference Ionosphere 2016 (IRI-2016) model as the background, to assimilate ionospheric TEC observations from GNSS. To demonstrate the results, the TEC estimates from the Crustal Movement Observation Network of China (CMONOC), which is about 260 stations in China, are applied as observation. The assessments are performed against the TEC estimates from BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and against the final products from the Center for Orbit Determination in Europe (CODE). The assimilation results are in good agreement with BDS GEO TEC and the CODE TEC on a quiet or disturbed day. The correlation coefficient after assimilation is increased by about 17% compared with that before assimilation, and the RMSE after assimilation is decreased by about 42% compared with that before assimilation. Furthermore, the assimilated method is also evaluated in the single-frequency precise point positioning (PPP). The experimental results indicate that the PPP/Assimilated method can improve the GNSS positioning accuracy more effectively in comparison to the PPP/CODE. These results reveal that the LEnKF method can be considered as a useful tool for ionospheric assimilation.

Models and performance of SBAS and PPP of BDS

Satellite Based Augmentation System (SBAS) is one of the services provided by the BeiDou Navigation Satellite System (BDS). It broadcasts four types of differential corrections to improve user application performance. These corrections include the State Space Representation (SSR) based satellite orbit/clock corrections and ionospheric grid corrections, and the Observation Space Representation (OSR) based partition comprehensive corrections. The algorithms generating these SBAS corrections are not introduced in previous researches, and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated. In this paper, we present the BDS SBAS algorithms for these differential corrections in detail. Four types of Precise Point Positioning (PPP) function models for BDS Dual-Frequency (DF) and Single-Frequency (SF) users using the OSR and SSR parameters are also proposed. One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System (BDS-2) and BeiDou-3 Navigation Satellite System (BDS-3) satellites, and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections. The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation. The positioning errors in Root Mean Square (RMS) for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions, while for the static SF PPP are 11 cm/24 cm. In the scenarios of simulated kinematic PPP, three Dimension (3D) positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP, and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions. In a real-time single- and dual-frequency kinematic positioning test, the positioning errors of all three components can reach 0.5 m within 30 min, and the positioning accuracy after solution convergence in the N, E and U directions is better than 0.3 m.

Impact and synergies of GIM error estimates on the VTEC interpolation and single-frequency PPP at low latitude region

The vertical total electron content (VTEC) is one of the key quantities to describe variations of the ionosphere and can be provided to users to correct the ionospheric disturbances for GNSS (Global Navigation Satellite System) positioning. The VTEC values and the corresponding standard deviations are routinely provided in the so-called Global Ionosphere Maps (GIM), with a typical time resolution of 2 h (and up to 15 min) on regular grids with 2.5º resolution in latitude and 5º resolution in longitude. To determine the ionospheric corrections from the GIMs for positioning applications, an interpolation has to be applied to the VTEC grid values, which generally degenerates the final VTEC accuracy. In this context, the typically applied bi-linear interpolation of the VTEC values is calculated by introducing a new weighting scheme by means of the standard deviation maps in the ionospheric domain. In the sequel, the impact of the use of the VTEC uncertainties for the interpolation procedure is applied to the GIMs of different centers and assessed in the ionospheric and in the positioning domain. For the assessment of the GIM in the ionospheric domain, the VTEC values calculated are compared with VTEC directly obtained from the given GIM, i.e., without interpolation. In the positioning domain, the impact of the VTEC uncertainties is analyzed by means of single-frequency precise point positioning (PPP), considering four Brazilian stations in challenging regions. The use of the standard deviation values in positioning provides a significant improvement in periods of high solar flux, especially for stations in the region under more intense ionospheric effect (mean rates of improvements up to 47%).

Deep Recurrent Neural Networks for Ionospheric Variations Estimation Using GNSS Measurements

Modeling ionospheric variability throughout a proper total electron content (TEC) parameter estimation is a demanding, however, crucial, process for achieving better accuracy and rapid convergence in precise point positioning (PPP). In particular, the single-frequency PPP (SF-PPP) method lacks accuracy due to the difficulty of dealing adequately with the ionospheric error sources. In order to apply ionosphere corrections in techniques, such as SF-PPP, external information of global ionosphere maps (GIMs) is crucial. In this article, we propose a deep learning model to efficiently predict TEC values and to replace the GIM-derived data that inherently have a global character, with equal or better in accuracy regional ones. The proposed model is suitable for predicting the ionosphere delay at different locations of receiver stations. The model is tested during different periods of time, under different solar and geomagnetic conditions and for stations in various latitudes, providing robust estimations of the ionospheric activity at the regional level. Our proposed model is a hybrid model comprising of a 1-D convolutional layer used for the optimal feature extraction and stacked recurrent layers used for temporal time series modeling. Thus, the model achieves good performance in TEC modeling compared to other state-of-the-art methods.