Precise Point Research Articles

GNSS Real-Time ZTD/PWV Retrieval Based on PPP with Broadcast Ephemerides

GNSS precise point positioning (PPP) plays an important role in retrieving atmospheric water vapor values and performing numerical weather prediction. However, traditional PPP relies on real-time orbits and clocks, which require continuous internet or satellite communication. Improved broadcast ephemerides of GNSSs offer new opportunities for PPP with broadcast ephemerides (BE-PPP) instead of using precise ephemeride products. Therefore, we investigated the feasibility of utilizing BE-PPP for retrieving zenith tropospheric delay (ZTD) and precipitable water vapor (PWV) data. We processed the GPS/Galileo observations from 80 IGS stations during a 30-day experiment to retrieve ZTD values using both real-time PPP (RT-PPP) and BE-PPP solutions. Then, we processed observations from 20 EUREF Permanent GNSS Network (EPN) stations to retrieve PWV data. The IGS final tropospheric products were used to validate the ZTD, and radiosonde (RDS) and ERA5 data were used to validate the PWV. The results show that the real-time ZTD from BE-PPP agrees well with that from RT-PPP: the standard deviation (STD) of the ZTD is 1.07 cm when using BE-PPP and 0.6 cm when using RT-PPP. Furthermore, the STD of the PWV is 1.69 mm when using BE-PPP, and 0.96 mm when using RT-PPP, compared to the ERA5-PWV. Compared to the RDS-PWV, the STD is 3.09 mm when using BE-PPP and 1.39 mm when using RT-PPP. In conclusion, the real-time ZTD/PWV products obtained using the BE-PPP solution are consistent with those of RT-PPP and meet the requirements of NWP, so this method can be used as an effective complement to RT-PPP to expand its application potential.

A lightweight ZWD model with high spatiotemporal resolution established based on ERA5 and GNSS observation

The use of a high-precision a priori zenith wet delay can effectively improve the convergence time and increase the accuracy of precise point positioning (PPP). Considering the limitations of empirical and blind ZWD models, a new lightweight ZWD model was developed based on GNSS observations and ERA5 precipitable water vapor (PWV) and temperature information that can provide reliable ZWD with 0.25° spatial resolution and hourly temporal resolution without relying on massive meteorological parameters. The correlation between the ERA5 PWV/temperature and the GNSS-derived ZWD was first analyzed in 2020 in this study. Subsequently, a functional mapping model based on machine learning was established, considering the effects of spatial and temporal factors, such as time, topography, geographical location. The validation results showed the proposed model's RMSE/STD/Bias were 1.70/1.70/0cm compared with GNSS ZWD, respectively. Furthermore, an independent GNSS and radiosonde ZWD in 2021, was introduced to validate the generalization ability of the proposed model, and the RMSE/STD/Bias values were 1.63/1.49/0.2cm and 2.77/2.63/0.23cm, respectively. The ZWD model developed in this study effectively reduces the dependence on meteorological data from numerical weather models, which is beneficial for broadcasting ZWD data and enhances precise regional positioning and navigation.

Real-time uncombined PPP using BDS-3 PPP-B2b products with different multi-frequency integrations and refined stochastic model

BDS-3 geostationary orbit (GEO) satellites broadcast PPP-B2b real-time precise products to support real-time precise point positioning (RT-PPP) without dependence on the ground network communication. Since all BDS-3 satellites can provide multi-frequency signals, we investigate the effect of different multi-frequency integrations and the refinement of multi-frequency stochastic model for PPP-B2b RT-PPP. Given that the retrieval of PPP-B2b real-time precise corrections relies on the B1C and B2b frequencies, this study first investigates the kinematic uncombined (UC) RT-PPP performance of the B1C/B2b integration with a comparison to the conventional B1I/B3I integration. The results indicate that the convergence time (with a convergence threshold of 20 cm) of the RT-PPP with the B1C/B2b integration is shortened by 16 %, 15 %, and 12 % over the B1I/B3I integration in the east, north, and up directions, respectively. Further, this study compares the kinematic UC RT-PPP performance of the B1C/B2b dual-frequency integration, B1C/B2b/B3I triple-frequency integration, and B1C/B2b/B3I/B1I/B2a five-frequency integration. Compared with the dual-frequency integration, the positioning performance of the triple-frequency integration is slightly improved. By contrast, the performance improvement of the five-frequency integration is more significant, which can reach 6 %, 32 %, and 9 % for the convergence time, and 11 %, 9 %, and 6 % for the positioning accuracy in three directions, respectively. To further enhance the multi-frequency PPP performance, a refined stochastic model for the BDS-3 five-frequency integrated PPP-B2b RT-PPP is proposed by taking the inconsistency of signal quality among multi-frequency signals into account. After applying the refined stochastic model, the convergence time of the five-frequency kinematic RT-PPP is shortened by 10 %, 14 %, and 9 % to 32, 7, and 19 min in east, north, and up directions, respectively. The positioning accuracy (the root mean square of all the positioning errors excluding the first two hours) of the five-frequency RT-PPP with the refined stochastic model can reach the optimal level, which is 9.9, 6.5, and 14.0 cm in three directions, respectively.

Difficulties Faced by Iraqi EFL learners in Using Past Tense

Iraqi English as a Foreign Language (EFL) learners typically spend around eight years studying English before entering university. During the last four years of high school, students get frequent and rigorous instruction in English tenses. In addition, when they Upon entering the institution, students enroll in the English department where they engage in a rigorous four-year study of the English language. The curriculum is built with a focus on teaching tense. Grammar is taught for a total of three hours each week over a span of thirty weeks per year during these four years. However, Iraqi English as a Foreign Language (EFL) learners have significant difficulties in many grammatical aspects, particularly in the understanding and use of tenses. This article is a data analysis research that seeks to detect grammatical mistakes, including their nature, kinds, and origins. It is presumed in this context that you are now experiencing a difficulty, and I would want to know what specific issue you encountered in the past. The Past tense is used to describe previous activities that occurred either at a precise point in time, which may be indicated by a time phrase or inferred from the surrounding context. The past continuous tense is used to depict acts or occurrences that occurred at a period prior to the present moment.

Fast and robust analog in-memory deep neural network training

Analog in-memory computing is a promising future technology for efficiently accelerating deep learning networks. While using in-memory computing to accelerate the inference phase has been studied extensively, accelerating the training phase has received less attention, despite its arguably much larger compute demand to accelerate. While some analog in-memory training algorithms have been suggested, they either invoke significant amount of auxiliary digital compute—accumulating the gradient in digital floating point precision, limiting the potential speed-up—or suffer from the need for near perfectly programming reference conductance values to establish an algorithmic zero point. Here, we propose two improved algorithms for in-memory training, that retain the same fast runtime complexity while resolving the requirement of a precise zero point. We further investigate the limits of the algorithms in terms of conductance noise, symmetry, retention, and endurance which narrow down possible device material choices adequate for fast and robust in-memory deep neural network training.

Precipitable water vapor retrieval for rainfall forecasting using BDS-3 PPP-B2b signal in the coastal region of China

Abstract Currently, rainfall cannot be accurately forecast because of poor network communication at the ocean. The advantage of the BeiDou Global Navigation Satellite System (BDS-3) precise point positioning (PPP-B2b) signal, which does not rely on network communication to receive data, is that it can provide precipitable water vapor (PWV) retrieval application services for the open seas in eastern China, where the communication system presents difficulties. In this study, data from stations in the coastal region of China were used to establish a rainfall forecasting method for monitoring extreme weather on the sea. First, the service performance of PPP-B2b was explored. Then, based on 17 Chinese coastal stations, the PWV accuracy was evaluated. Finally, based on an analysis of the relationship between PWV and actual rainfall, a threshold rainfall forecasting method based on a sliding window was constructed. The experimental results show that the PWV accuracy varies slightly depending on the geographic location, in which the mean absolute error in the North Sea region is the smallest (2.1 mm), that of the South China Sea region is the largest (2.60 mm), and that of the East China Sea region is in the middle (2.48 mm). The optimal predictors of the constructed 12 h sliding-window threshold rainfall prediction method are a PWV maximum of 49 mm, PWV increase of 5 mm, and PWV increase rate of 1.2 mm h−1. The prediction results can reach a critical success index value of more than 45%, indicating high prediction accuracy and applicability to the coastal region of China during the same period.

Characterization of the precision of PPP solutions as a function of latitude and session length

Abstract This study investigates the impact of observation session duration and station latitude on the precision of Precise Point Positioning (PPP). Global Positioning System-only Receiver Independent Exchange files from 516 continuous stations spanning latitudes from 90°N to 90°S across the Americas (30°–130°W) were binned into sessions of 1, 2, 3, 4, 6, and 12 h and processed using the GPSPACE PPP software. These sub-daily solutions, along with the original 24 h ones, were compared against a reference coordinate derived from an extended linear trajectory model for each station. Analysis of the results, considering both accuracy and precision, was conducted across the entire latitude range of the study. We found that the precision of a PPP solution approximately follows a power-law relationship with observation duration. Parameters for these power-law relationships were determined for all latitude ranges that allow users to predict a result’s uncertainty as a function of session length. Findings indicate that longer observation sessions lead to reduced positioning errors, with vertical scatter decreasing with increasing latitude. Since all these stations are characterized by good to excellent sky view, our power-law rule-of-thumb provides a lower bound on the occupation time needed to achieve target positioning precision at locations with poorer sky visibility.

Calibration of Receiver-Dependent Pseudorange Bias and Its Impact on BDS Augmentation Positioning Accuracy

Pseudorange bias refers to the receiver-dependent and satellite-dependent constant bias in the pseudorange resulting from the nonideal characteristics of a signal. The impact of pseudorange bias on high-precision satellite navigation services has long been ignored. This paper proposes a pseudorange bias calibration method for two collocated receivers. Then, we calibrate pseudorange biases for two types of collocated receivers at a monitoring station within China and evaluate their impact on two high-precision services: BeiDou Navigation Satellite System 3 (BDS-3) dual-frequency pseudorange augmentation and precise point precision (PPP). Theoretical analysis reveals that the calibrated pseudorange biases contribute 17.2% and 7.7% to the user equivalent ranging error (UERE) of BDS-3 and Global Positioning System (GPS) dual-frequency pseudorange augmentation, respectively, and that the convergence time of the GPS static and kinematic PPP increases from 6 min and 26 min to 19 min and 58 min, respectively. The experimental results indicate that the calibrated pseudorange biases are consistent as the receiver location and time vary. The spatial distribution consistency is generally better than 0.1 m, and the temporal consistency is better than 0.15 m. The pseudorange biases for BDS-3 B1C and B2a are approximately 0.7 m and 0.1 m, respectively, whereas those for GPS L1C/A and L2P are both approximately 0.25 m. Furthermore, The results show that after correction of the pseudorange biases, the average convergence time for BDS-3/GPS static PPP decreases from 48.83/24.03 min to 38.54/21.12 min, respectively, a decrease of approximately 21%/12%. For BDS-3/GPS/BDS-3 + GPS kinematic PPP, the average convergence time decreases from 109.53/45.10/39.15 min to 62.99/40.83/22.94 min, respectively, a decrease of approximately 42%/41%/9%. Similarly, the three-dimensional positioning accuracy for BDS-3/GPS/BDS-3 + GPS dual-frequency pseudorange augmentation improves from 3.25/3.94/2.49 m to 2.65/3.69/2.16 m, respectively, increasing by approximately 6.3%, 18.5%, and 13.3%, respectively. The above analysis and experiments demonstrate that pseudorange bias is an important error source affecting both dual-frequency pseudorange augmentation and PPP services.

Multi-GNSS Precise Point Positioning with Ambiguity Resolution Based on the Decoupled Clock Model

Multi-GNSS Precise Point Positioning with Ambiguity Resolution Based on the Decoupled Clock Model

PPP based on factor graph optimization

Abstract Kalman or Kalman-related filtering methods are routinely applied in precise point positioning (PPP). However, in robot simultaneous localization and mapping (SLAM) systems, the factor graph optimization (FGO) has proved advantages over filtering methods in recent years, e.g., reducing the linearization errors and support of plug-and-play feature for multiple sensor fusion. Therefore, it would be interesting to apply the FGO to PPP. In addition, it will also facilitate the tight integration of PPP with Visual/LiDAR SLAM. In this work, PPP is solved under the factor graph optimization framework. A factor graph for PPP has been constructed. Results from 268 IGS-MGEX stations show that the factor graph optimization method can achieve a similar performance with that of Kalman filtering. First, the positioning accuracy in the convergence period can be improved for PPP based on factor graph optimization because it optimizes the entire state variables based on all the available observations. For applications that do not require real-time processing, the observation after the current states, e.g., future observations, can also be used to enhance the current state estimation. Second, the accuracy of static PPP is almost the same for the two methods with millimeter-accuracy for horizontal directions and centimeter-accuracy for vertical directions. Third, the kinematic PPP for both methods can achieve centimeter-level accuracy in horizontal directions and decimeter-level accuracy in vertical directions. Although the performance is comparable, it is noted that the computational efficiency of factor graph optimization method is still a problem. For each epoch, the average of elapsed time for Kalman filtering is 132 microseconds, while that of factor graph optimization method is 9664 microseconds. The elapsed time of factor graph optimization method can be further improved if the fix-window optimization technique is applied, which will be investigated in the future.

High-precision GPS orbit determination by integrating the measurements from regional ground stations and LEO onboard receivers

High-precision Global Navigation Satellite System (GNSS) orbit and clock products are crucial for precise applications. An evenly distributed global network enables continuous tracking for GNSS satellites, while a regional network may result in tracking gaps in the areas where monitoring stations are not deployed. This also means that the orbit determination accuracy based on a regional network is not comparable to that with a global network. Integrating the measurements from regional ground stations and Low Earth Orbit (LEO) satellites onboard receivers is a potential approach for generating GNSS orbit and clock products with centimeter-level accuracy, which is particularly important for BDS and the local commercial providers relying on a regional network. In the integrated Precise Orbit Determination (POD), LEO satellites are used to compensate for the drawback of regional ground stations in the precise orbit and clock determination of GNSS satellites. To validate the role of LEO satellites in the orbit determination with a regional network, 6 International GNSS Service stations around China and 13 LEO satellites from January 20 to 26, 2019, including GRACE-C/D, SWARM-A/B/C, Jason-3, Sentinel-3A/B, and SAT-A/B/C/D/E are selected in this study to perform the integrated POD. The orbit and clock accuracies of GPS and LEO satellites are evaluated by comparison with precise products. The average Root Mean Square (RMS)of GPS orbit errors in the radial (R), along-track (T) and cross-track (N) directions are 2.27 cm, 3.45 cm, and 3.08 cm, respectively, and the clock accuracy is better than 0.15 ns based on a comparison with the final products provided by Center for Orbit Determination in Europe (CODE). The LEO orbit accuracy is better than 2 cm in the R direction, and the position errors are mostly within 4 cm. The results indicate that the integrated POD can generate high-precision orbit and clock products for GPS and LEO satellites based on regional network stations. Finally, the integrated POD products are assessed for Precise Point Positioning (PPP). Simulated kinematic PPP has a comparable performance in terms of the convergence time and positioning accuracy. With more LEO satellites available, the orbit and clock determination accuracy and PPP positioning accuracy can be improved.

Gdcov2sinex: a Python conversion tool from GipsyX’s gdcov file to SINEX file

The Solution INdependent EXchange (SINEX) file format, an international standard for the exchange of information, is essential in the Global Navigation Satellite System (GNSS) processing strategies that integrate different software applications. GNSS data processing using Jet Propulsion Laboratory’s (JPL) GipsyX software, which employs the Precise Point Positioning (PPP) technique, generates positions and covariance matrices in gdcov files, a GipsyX file format specific for storing this information. GipsyX software provides a tool, named mkDailySinex.py, to convert from gdcov file to SINEX file, but it is designed specifically for creating daily JPL SINEX files and does not function properly for non-JPL GipsyX users. I have developed a Python 3 program, named gdcov2sinex.py, which solves this problem, enabling any user to perform the SINEX conversion and, therefore, apply the processing strategies that integrate GipsyX with other software, such as GAMIT/GLOBK. The new python tool presented herein takes advantage of the capabilities of mkDailySinex.py and provides all its default options, but also expands the number of selectable options, which can be useful to the user. The source code, user manual, and a sample dataset of gdcov2sinex.py are provided as electronic supplementary material of this paper.

Low-latitude ionospheric responses and positioning performance of ground GNSS associated with the geomagnetic storm on March 13–14, 2022

Interplanetary coronal mass ejections (ICMEs) and the driven geomagnetic storms have a profound influence on the ionosphere, potentially leading to a degradation in positioning performance. In this study, we made a comprehensive analysis of the entire process of the impact of a typical ICME and its driven geomagnetic storm on the low-latitude ionosphere during March 13–14, 2022 (π-day storm) and the positioning performance of Global Navigation Satellite System (GNSS). During the passage of the ICME event, significant ionospheric scintillation, and TEC (total electron content) disturbances were observed in the low-latitude Hong Kong region. The ICME sheath region intensively compressed the magnetosphere via solar wind dynamic pressure enhancement and subsequently drove the storm main phase. It is found that both the magnetospheric compression that formed the storm initial phase and the storm main phase caused ionospheric scintillation. In comparison, the intensity of the ionospheric scintillation caused by the intense magnetospheric compression just before the storm main phase is even more pronounced. We also analyzed the impact of storms on standard point positioning (SPP), precise point positioning (PPP) and real-time kinematic (RTK) techniques. The positioning accuracies of single-frequency SPP and PPP experienced the most severe decline, and there was a noticeable increase in the initialization time for dual-frequency static PPP and RTK during the event. RTK demonstrated a shorter convergence time and higher accuracy during this event, but it was limited to short-baseline RTK (<30 km).

Multi-frequency smartphone positioning performance evaluation: insights into A-GNSS PPP-B2b services and beyond

In August 2023, Xiaomi unveiled the Redmi K60 Ultra, the first multi-frequency smartphone integrated with BeiDou-3 Navigation Satellite System Precise Point Positioning (PPP-B2b) services and employing PPP technology as the primary positioning method. The positioning enhancement service is provided by the Assisted Global Navigation Satellite System (A-GNSS) location platform developed by the China Academy of Information and Communications Technology. The signaling interaction between the server and the users strictly adheres to the Third Generation of Mobile Communications Technology Partnership Project Long-Term Evolution Positioning Protocol and the Open Mobile Alliance Secure User Plane Location framework. To comprehensively evaluate the Redmi K60 Ultra’s capabilities, this study designed six distinct experimental scenarios and conducted comprehensive research on multi-frequency and multi-GNSS observation noise, Time to First Fix (TTFF), as well as the performance of both GNSS-based and network-based positioning. Experimental results indicate that the GNSS chipset within the Redmi K60 Ultra has achieved a leading position in the consumer market concerning supported satellite constellations, frequencies, and observation accuracy, and is comparable to some low-cost GNSS receivers. A-GNSS positioning can reduce the TTFF from 30 to under 5 s, representing an improvement of over 85% in the cold start speed compared to a standalone GNSS mode. The positioning results show that the A-GNSS PPP-B2b service can achieve positioning performance with RMS errors of less than 1.5 m, 2.5 m, and 4 m in open-sky, realistic, and challenging urban environments. Compared to GNSS-based positioning, cellular network-based Observed Time Difference of Arrival (OTDOA) positioning achieves an accuracy ranging from tens to hundreds of meters in various experimental scenarios and currently functions primarily as coarse location determination. Additionally, this study explores the potential of the Three-Dimensional Mapping-Aided (3DMA) GNSS algorithm in detecting Non-Line-of-Sight signals and enhancing positioning performance. The results indicate that 3DMA PPP, as compared to conventional PPP, can significantly accelerate PPP convergence and improve positioning accuracy by over 30%. Consequently, 3D city models can be utilized as future assistance data for the A-GNSS location platform.

Grey modelling and real-time forecasting for the approximate non-homogeneous white exponential law BDS clock bias sequences

Precise forecasting of satellite clock bias is crucial for ensuring service quality and enhancing the efficiency of real-time precise point positioning (PPP).The grey model with many benefits is an excellent choice for predicting real-time clock bias. However, the absolute prediction error of a small number of satellites is very high in actual forecasting process. In order to address this issue, a non-homogeneous white exponential law grey model has been constructed specifically for predicting clock bias sequences with non-homogeneous class ratio approximating constants. Considering that any model is difficult to apply to different kinds of satellite clocks and clock bias signals, an adaptive selection strategy for forecast model is proposed to ensure more excellent prediction accuracy. Afterwards, a prediction scenario based on the observed products of the BeiDou satellite navigation system (BDS) is created to demonstrate the effectiveness of the approach described in this article. The outcomes of the method are then compared with those of a single grey model and the ultra-rapid predicted products. The outcomes demonstrate that this strategy’s prediction accuracy is less than 1 ns/day and that its prediction uncertainty is much decreased, which may improve data selection for real-time applications like real-time kinematics (RTK) and PPP.

Taiwan Online Precise Point Positioning Service: Methodology and Test Results

Taiwan Online Precise Point Positioning Service: Methodology and Test Results

Intercontinental frequency ratio measurement of 171 Yb and 88 Sr optical lattice clocks

We report a remote, intercontinental frequency comparison between 171Yb (NMIJ) and 88Sr (UMK) optical lattice clocks. The frequencies were compared via the Global Positioning System Precise Point Positioning technique over the period from 10 March 2020, 00:00 UTC until 15 March 2020, 00:00 UTC. The comparison of the optical clocks yields results with a relative frequency uncertainty of 6.3×10−15 .

A new PPP one-way timing approach via BDS-3 PPP-B2b and short-message communication service

In the realm of time-frequency, precise point positioning (PPP) technology has been widely used, the current PPP time transfer or timing necessitates network communication for data transmission, which consequently leads to a reduction in the reliability of PPP timing. Based on the BDS-3 PPP service (PPP-B2b) and the global short message communication (GSMC) service, this study proposes a novel PPP one-way timing method that is not subject to distance limitations or the requirements of network communication. Users can directly obtain the difference with UTC(k). Then, the proposed PPP timing method was validated using four stations equipped with external high-performance atomic clocks, based on a dataset of eight days. According to the findings, the suggested PPP one-way timing technique might reach a timing accuracy of roughly 0.5 ns in environments without a network. In terms of frequency stability, the proposed PPP timing method exhibits a stability of approximately 1.4 × 10−13 at 960 s and a stability of about 3 × 10−14 at 15360 s. Further, even under GSMC communication delays of 1 min, 5 min, and 10 min, the proposed PPP one-way timing accuracy can still achieve better than 0.5 ns.

Tight integration of real-time GNSS PPP and INS: Ionosphere-free combined vs uncombined models

The GNSS Precise Point Positioning (PPP) model is usually established in either an ionospheric-free (IF) combined form or an uncombined (UC) form. These formulations can be equivalent in theory but their applications in practice could still perform differently when integrated with external sensors. In this study, we compared the positioning performance of the two PPP models tightly coupled with the Inertial Navigation System (INS) using a high-grade inertial measurement unit (IMU) in real vehicle navigation tests. The ambiguity resolution (AR) was also exploited in the two PPP models after applying the observable specific biases (OSB) to the GNSS raw code and phase measurements. According to the results, under good satellite observability the UC PPP/INS tightly-coupled integration (TCI) significantly outperforms the IF PPP/INS TCI. The UC TCI model with AR could achieve a positioning accuracy of 4.6 and 3.0 cm in the horizontal and vertical directions, which are improved by 37 % and 63 % respectively relative to the IF TCI model. However, in the case of frequent GNSS signal interruptions or poor satellite observation condition, the IF TCI model shows a superior reliability than the UC TCI. Nevertheless, when the ionospheric parameters are properly constrained in the UC TCI model, substantial improvements in terms of convergence and accuracy are obtained. The UC PPP augmented with external precise ionospheric information would greatly increase the cost, and users may select the appropriate PPP model with INS TCI in real applications in accordance with the demanded accuracy level and measuring conditions.

Assessment of selected ionospheric mapping functions using SF-PPP on different solar activities

In single-frequency precise point positioning (SF-PPP), the ionospheric delays provided by global ionosphere maps (GIMs) are in the vertical direction. Therefore, an ionospheric mapping function is applied to convert the vertical direction to the slant one. However, the performance of mapping functions (MF) applied in SF-PPP under different solar activities is unknown. Meanwhile, understanding their performance can help us better improve the accuracy of the ionospheric mapping function. For this purpose, three traditional ionospheric mapping functions, such as the standard single-layer model mapping function (SLM MF), the modified single-layer model mapping function (MSLM MF), and the Klobuchar MF, are evaluated. Additionally, the mapping function named SGG MF, which considers the effect of ionospheric gradients, is also assessed. The positioning results indicate that the SGG MF has an improvement of (50.3 %, 37.3 %), (31.7 %, 23.4 %), and (16.8 %, 13.3 %) compared with Klobuchar MF, SLM MF, and MSLM MF during the year (2014, 2021), respectively. The mean positioning errors of SLM MF, MSLM MF, and SGG MF are about (0.20 m, 0.05 m), (0.25 m, 0.10 m), and (0.30 m, 0.10 m) smaller than that of Klobuchar MF over high-/mid- latitude during the year (2014, 2021), while the values are (0.25 m, 0.20 m), (0.40 m, 0.35 m), and (0.55 m, 0.50 m) over low-latitude region. Furthermore, the correlation coefficients between positioning results and solar activities are (0.114, 0.354), (0.058, 0.324), (0.098, 0.295), and (0.235, 0.271) for Klobucahr MF, SLM MF, MSLM MF, and SGG MF during corresponding year.