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A priori variance–covariance matrix (VCM) estimation of global navigation satellite systems (GNSS) double difference observations in relative positioning is challenging. Existing methods have been limited to estimate variances only or present variables challenging to acquire a priori, unfeasible for observation planning. Ignoring the covariances produces misleading results and compromises reliance on GNSS positioning design. In this study, we propose models to estimate the VCM a priori for planning, based on simple variables accessible to any professional: observation time span, vector length, and ephemeris type. Using a database of over 140,000 GNSS vectors with double difference (DD) observations, we group the data by time span and length range and extract standard deviations and covariances for the linear regression process. The Isolation Forest algorithm is employed to filter outlying observations. Our models provide standard deviations and root square covariances in a local coordinate system, requiring only vector length, observation time span, and ephemeris type as input. Additionally, the equations can be easily implemented in a simple spreadsheet. The results show high coefficients of determination (R2 > 0.8). We tested the models in a simulated GNSS network and verified broadcast ephemeris resulted in 6.5 to 16.7 times larger error ellipsoids compared to the precise ephemeris, indicating higher uncertainty. Ellipsoids differed in flattening and orientation when compared to the null covariance (variance only) approach. Although VCM models better reflect the precision of relative positioning observations, they did not affect the number of non-controllable observations in the observation's reliability tests. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Indian mapping agency, Survey of India (SOI), is ambitiously implementing nation-wide network of Continuously Operating Reference Stations (CORS) to improve the accuracy of derived three-dimensional relative positions of the Global Navigational Satellite System (GNSS) over the regions. However, it does not only improve the accuracy but also reduce the cost of reliable data acquisition. Recently, SOI has established a number of CORS networks and continues to cover the entire India for its suitability in the infrastructure projects and in the generation and updating of revenue maps. The present article attempts to measure the accuracy of a single baseline static survey carried out using the CORS network by studying fifteen stations established in different parts of Uttar Pradesh and Madhya Pradesh. To study the accuracy using the established CORS network, 7 days of continuous observed data from fifteen stations of Uttar Pradesh and Madhya Pradesh have been processed. The study has been done taking a base–rover combination with varying distance (D) from 30 to 160 km and the time duration (T) at 20 min, 1 h, 2 h, 4 h, 8 h, 12 h, and 24 h using observational CORS data (including both GPS and GLONASS). The present study shows that (i) dependence of accuracy on distance (D) up to 160 km is almost negligible when final ephemeris data of GPS satellite orbit (International GPS Service) have been used and (ii) the positional accuracy improved with an increase in observation duration. Finally, regression analysis has been done to establish the relationship between distance (D), duration (T), and accuracy for the given CORS network. [ABSTRACT FROM AUTHOR]

In the Global Navigation Satellite System (GNSS), array antennas, widely used in anti-jamming applications but seldom used in high-precision applications, can obstruct successful ambiguity resolution (AR) by introducing large phase biases. However, the phase pattern of the entire array antenna can potentially be large and asymmetrical. Based on these phase pattern characteristics, researchers tend to determine the orientation of a user array antenna by searching over a set of orientation candidates for the desired value closest to the true orientation. The search result is determined by comparing the relative positioning solutions between the user array antenna and a reference station. The proposed method combines two search strategies: spatial dimension search (SDS) and time dimension search (TDS). Furthermore, the proposed method is assessed in terms of the accuracy of orientation search results and relative positioning solutions with a short baseline at Curtin University, demonstrating the validity of the scheme. Multiple longer baselines formed by International GNSS Service (IGS) stations are also tested, and the results indicate that the proposed method is effective for baselines shorter than 2 km. Finally, to quantitatively study the type of phase pattern to which our method is applicable, we measure the characteristics of phase patterns with the peak value and a Frobenius norm-based asymmetry value. We also analyze the impact of the pattern characteristics on the performance of the proposed method. [ABSTRACT FROM AUTHOR]

During the last decade Global Positioning System (GPS) Continuous Operating Reference Stations networks have become a new important data source for meteorology. This has dramatically improved the ability to remotely sense the atmosphere under the influence of severe mesoscale and synoptic systems. The zenith tropospheric delay (ZTD) is one of the atmospheric variables continuously observed, and its horizontal variations, the horizontal tropospheric gradients, are routinely computed nowadays within the dual‐frequency GPS processing, but their interpretation and relationship with the weather is still an open question. The purpose of this paper is to contribute in this direction by studying the effect that Hurricane Harvey had on the spatial and temporal behavior of the ZTDs and gradients, when it reached Texas coast, during 18–31 August 2017. The results show that ZTD time series present a clear and rapid increase larger than 10 cm in a few hours when the hurricane reached the area. Gradients behaviors show that the hurricane also produced significant changes on them, since the magnitude and predominant directions before and after the hurricane arrived are completely different. Noticeably, the gradient vectors before the landing are consistently related to the horizontal winds and pressure fields. In this manuscript we demonstrate that the ZTD gradients can show a consistent signature under severe weather events, strongly suggesting their potential application for short‐term weather forecasting.

In this study, the potential of PPP (Precision Point Positioning) method in crustal deformation studies was investigated with the help of relative GNSS (Global Navigation Satellite System) analyses. For this purpose, data of six GNSS stations, three (GIRS, SINP and ZONG) of which are located to the north of the North Anatolian Fault (NAF) zone and the other three (RHIY, ANKR and BILE) are located to the south of the NAF zone, were obtained and analyzed between the years of 2011-2018 (8 years long). The analyzes were carried out by means of the CSRS online service for the PPP method and the GAMIT / GLOBK V10.7 academic GNSS analysis software for the relative positioning technique. The obtained coordinates are analyzed with the help of Kalman filter to estimate the velocities of each station for the North, East and Up components as fixed on the ORID IGS (International GNSS Service) station which located on the Eurasian plate. It was found that the 3D positioning error calculated from the velocity differences between the both methods ranged from 0.1 mm to 2.4 mm levels. Thus, it is concluded that PPP method can be used successfully in crustal deformation studies. [ABSTRACT FROM AUTHOR]

This study aimed to validate the interferometric synthetic aperture radar (InSAR) method by using relative and absolute Global Navigation Satellite System (GNSS) techniques. In this context, two land subsidence areas, one high (Mexico City) and one medium (Aguascalientes), were monitored between 2014 and 2018 by using Sentinel 1A satellite data. The monitoring was carried out with the Small Baseline Subset (SBAS) technique using 46 images for Mexico City and 18 images for Aguascalientes. Concordantly, the GNSS Continuously Operating Reference Station (CORS) data in the regions were analyzed with relative and Precise Point Positioning (PPP) GNSS analysis techniques. The time series obtained from three different analyses were compared and the results were evaluated in light of statistical criteria. According to the results, it is determined that the InSAR-SBAS technique can vary up to ± 20 mm from the displacement values obtained from GNSS due to various noise sources. Such deviations were limited to a few samples, and in general the differentiations were reasonable in the range of 7–8 mm. The difference between the deformation velocity estimation results obtained from the three different methods varied between 3 and 10 mm/year. In this context, these findings suggest that the InSAR-SBAS technique is an effective method for monitoring land deformation with the accuracy of sub-centimeter decided. In addition, PPP which has become an increasingly popular technique showed fast and reliable results in the range of 5–10 mm for InSAR verification. Moreover, with this study, most current results for Mexico City, which is the world's fastest subsiding metropole, were achieved. In the central region of the city, the detected 300 mm/year of subsidence rate was updated as 370 mm/year. In addition, Aguascalientes was monitored by using the Sentinel 1A satellite mission for the first time in this study. The 60 mm/year subsidence rate obtained for Aguascalientes in previous studies was updated and it was estimated that there are zones where this rate reaches up to − 115 mm/year levels. In this regard, it was concluded that the deformation rate has increased for both regions since the previous monitoring studies. [ABSTRACT FROM AUTHOR]

Precise point positioning is a GNSS based positioning method that is known to regaining more precise information about major systematical errors in its functional model. This method is seen as an advanced version of the conventional absolute positioning method that is able to offer higher accuracy of the estimate parameter. Contrarily, the relative positioning method is able to achieve high precise of the estimated parameters by using two or more receiver. Nowadays because of this development, the PPP technique it started to grow on the detriment of the relative GNSS positioning. PPP, it is able to offer point determination by processing undifferenced dual frequency receiver, combine with precise orbit and clock corrections offered by JPL to obtain centimeter/millimeter accuracy. The aim of this paper is to make a comparative study between Precise Point Positioning (PPP) versus relative positioning under different conditions. [ABSTRACT FROM AUTHOR]

In this study, the accuracy of Precise Point Positioning (PPP) method was investigated. For this purpose, a microgeodetic network containing 5 stations was established and 8-hour GNSS Global Navigation Satellite System (GNSS) sessions for three consecutive days were performed. At the same time, the baselines between the stations in this network were measured by Electronic Distance Meter (EDM) and the height differences are measured by the geometric leveling method. The results obtained from classical terrestrial measurements, which are considered to be highly accurate (3 mm in horizontal and few mm invertical), were compared with the results of PPP and the relative GNSS methods. As a result of the comparisons, it was seen that the values obtained from the relative GNSS analysis approximated with the classical method with the levels of 1-6 mm in the horizontal and 10-20 mm in the vertical direction. For the PPP method, it was seen that the same values varied between 1-28 mm in horizontal and 5-8 cm in the vertical component. The standard deviation values of these changes were determined as ± 2.20 mm in horizontal and ± 16.46 mm in vertical for the relative positioning technique and ± 11.43 mm in the horizontal and ± 59.48 mm in vertical component for PPP method. [ABSTRACT FROM AUTHOR]

During the last decade Global Positioning System (GPS) Continuous Operating Reference Stations networks have become a new important data source for meteorology. This has dramatically improved the ability to remotely sense the atmosphere under the influence of severe mesoscale and synoptic systems. The zenith tropospheric delay (ZTD) is one of the atmospheric variables continuously observed, and its horizontal variations, the horizontal tropospheric gradients, are routinely computed nowadays within the dual‐frequency GPS processing, but their interpretation and relationship with the weather is still an open question. The purpose of this paper is to contribute in this direction by studying the effect that Hurricane Harvey had on the spatial and temporal behavior of the ZTDs and gradients, when it reached Texas coast, during 18–31 August 2017. The results show that ZTD time series present a clear and rapid increase larger than 10 cm in a few hours when the hurricane reached the area. Gradients behaviors show that the hurricane also produced significant changes on them, since the magnitude and predominant directions before and after the hurricane arrived are completely different. Noticeably, the gradient vectors before the landing are consistently related to the horizontal winds and pressure fields. In this manuscript we demonstrate that the ZTD gradients can show a consistent signature under severe weather events, strongly suggesting their potential application for short‐term weather forecasting. Key Points: Major hurricane over dense GPS network gives unique opportunity to study ZTD gradientsThe ZTD gradients show changes in orientation and magnitude when synoptic front approaches [ABSTRACT FROM AUTHOR]

Over the last few years, several institutions, research centers, and organizations have developed different strategies for GPS data processing and analysis to obtain high accurate coordinates. They are taking into considerations overcoming restrictions and limitations such as necessity of using relative positioning, time consuming, and high cost of different processing software. One of these developed strategies is the web–based online GNSS (Global Navigation Satellite Systems) processing service which estimates coordinates with centimeter or decimeter level accuracy. This study aims to represent the most popular of these services, namely AUSPOS, OPUS, APPS, GAPS, Trimble RTX, and CSRS–PPP, also to perform in-between comparison of these services with respect to their achieved accuracy using field observations with different durations. The obtained results were compared with a real field data measured using traditional relative positioning technique with high accuracy standards. The set of data used in this study was performed in the Eastern zone in Egypt. The results of this comparison indicate that these services can be used as an alternative method for relative positioning technique due to their simplicity, cost-effective and saving in time. They saved about 75 % from the time required for traditional method to produce coordinate with reasonable accuracy. The maximum standard deviation obtained was 15.4 cm from APPS service with time less than two hours, while the minimum standard deviation was 0.07 cm and obtained from CSRS–PPP with time duration from 6 to 12 hours. For achieving more accurate results, it is recommended to use time duration more than two hours. [ABSTRACT FROM AUTHOR]

For short baseline real-time kinematic (RTK) positioning, the atmosphere and broadcast ephemeris errors can be usually eliminated in double-differenced (DD) processing for synchronous observations. However, in the case of possible communication latency time, these errors may not be eliminated in DD treatments due to their variations during latency time. In addition, the time variation of these errors may present different characteristics among GPS, GLONASS, BDS, and GALILEO due to different satellite orbit and clock types. In this contribution, the formulas for studying the broadcast orbit and clock offset errors and atmosphere error in asynchronous RTK (ARTK) model is proposed, and comprehensive experimental analysis is performed to numerically show time variations of these errors and their impacts on RTK results from short-baselines among four systems. Compared with synchronous RTK, the degradation of position precision for ARTK can reach a few centimeters, but the accuracy degradation to a different degree by different systems. BDS and Galileo usually outperform GPS and GLONASS in ARTK due to the smaller variation of broadcast ephemeris error. The variation of broadcast orbit error is generally negligible compared with the variation of broadcast clock offset error for GPS, BDS, and Galileo. Specifically, for a month of data, the root mean square (RMS) values for the variation of broadcast ephemeris error over 15 seconds are 11.2, 16.9, 7.3, and 3.0 mm for GPS, GLONASS, BDS, and Galileo, respectively. The variation of ionosphere error for some satellites over 15 seconds can reach a few centimeters during active sessions under a normal ionosphere day. In addition, compared with other systems, BDS ARTK shows an advantage under high ionosphere activity, and such advantage may be attributed to five GEO satellites in the BDS constellation.

For global navigation satellite system (GNSS) carrier phase relative positioning, the baseline vector can be filtered in each dimension to decrease the noise in static situation. However, the baseline vector may change in dynamic situation, so the filtering method cannot be used. The baseline length is taken as constant in some situations such as orientation and attitude determination. The noise of averaged baseline length is far less than the noise of the single epoch baseline vector if different baseline lengths are averaged by the previous results. Therefore based on previous baseline length, an algorithm was proposed in this paper to decrease the noise of dynamic baseline vector. A mathematical model was developed to combine the averaged baseline length and current baseline vector, and a weight matrix of the mathematical model was deduced. A theoretical expression was found for the noise decreasing on the basis of variation transmission. Simulation and Held tests were carted out to evaluate the performance of the proposed algorithm. The results show that, test result matches with the result of theoretical analysis, the proposed algorithm is easy to be implemented, and can effectively decrease the noise of the baseline vector to 80% approximately without additional hardware resources. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Precise point positioning is a GNSS based positioning method that is known to regaining more precise information about major systematical errors in its functional model. This method is seen as an advanced version of the conventional absolute positioning method that is able to offer higher accuracy of the estimate parameter. Contrarily, the relative positioning method is able to achieve high precise of the estimated parameters by using two or more receiver. Consequently, it utilizes more resources in performing observation. Hence, this contribution attempts to explore some considerable aspects that can make the PPP method has a comparable precision of the National Standard of Horizontal Reference Network (SNI JKH). Based on the experiments, with data rate of 0.03 Hz for GPS and GLONASS observation shown that result of the PPP method is comparable to the relative method, whenever the observation is performed in minimum duration of six hours. Moreover, the 3th order of accuracy can be achieved after a demanding observation period, depends on processing strategy.

Future driver assistance systems will rely on accurate, reliable and continuous knowledge on the position of other road participants, including pedestrians, bicycles and other vehicles. The usual approach to tackle this requirement is to use on-board ranging sensors inside the vehicle. Radar, laser scanners or vision-based systems are able to detect objects in their line-of-sight. In contrast to these non-cooperative ranging sensors, cooperative approaches follow a strategy in which other road participants actively support the estimation of the relative position. The limitations of on-board ranging sensors regarding their detection range and angle of view and the facility of blockage can be approached by using a cooperative approach based on vehicle-to-vehicle communication. The fusion of both, cooperative and non-cooperative strategies, seems to offer the largest benefits regarding accuracy, availability and robustness. This survey offers the reader a comprehensive review on different techniques for vehicle relative positioning. The reader will learn the important performance indicators when it comes to relative positioning of vehicles, the different technologies that are both commercially available and currently under research, their expected performance and their intrinsic limitations. Moreover, the latest research in the area of vision-based systems for vehicle detection, as well as the latest work on GNSS-based vehicle localization and vehicular communication for relative positioning of vehicles, are reviewed. The survey also includes the research work on the fusion of cooperative and non-cooperative approaches to increase the reliability and the availability. [ABSTRACT FROM AUTHOR]

To obtain precise coordinates in Satellite Geodesy, relative positioning and precise point positioning (PPP) techniques are used. In this work a preliminary analysis of the impacts on Dilution of Precision (DOP) and positioning accuracy caused by tracking several GNSS, using single and double frequency receivers, considering two- and 24-hour sessions in two time periods of the year, and, as such, subject to different ionospheric conditions, is presented. These analyses have been performed based on data available from the Brazilian Network for Continuous Monitoring of GNSS (RBMC) and the Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS). The processing results have been obtained using the GNSS Planning Online, IBGE-PPP and RTKLIB software/services, which have confirmed the accuracy improvement in relative and PPP positioning when using more GNSS observations. Another factor which contributes to this improvement is a more favourable satellite constellation used in the solutions. The solar activity, time of year and tracking period of the day also directly impact the quality of positioning. [ABSTRACT FROM AUTHOR]

Abstract: GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galileo signals will come available, the number of observations at the L1 frequency will increase as we will have a GPS and Galileo multi-constellation. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS and this, combined with the increased number of observations, will result in a stronger model for single frequency relative positioning. In this contribution we will develop an even stronger model by combining the attitude determination problem with relative positioning. The attitude determination problem will be solved by the recently developed Multivariate Constrained (MC-) LAMBDA method. We will do this for each spacecraft and use the outcome for an ambiguity constrained solution on the baseline between the spacecraft. In this way the solution for the unconstrained baseline is bootstrapped from the MC-LAMBDA solutions of each spacecraft in what is called: multivariate bootstrapped relative positioning. The developed approach will be compared in simulations with relative positioning using a single antenna at each spacecraft (standard LAMBDA) and a vectorial bootstrapping approach. In the simulations we will analyze single epoch, single frequency success rates as the most challenging application. The difference in performance for the approaches for single epoch solutions, is a good indication of the strength of the underlying models. As the multivariate bootstrapping approach has a stronger model by applying information on the geometry of the constrained baselines, for applications with large observation noise and limited number of observations this will result in a better performance compared to the vectorial bootstrapping approach. Compared with standard LAMBDA, it can reach a 59% higher success rate for ambiguity resolution. The higher success rate on the unconstrained baseline between the platforms comes without extra computational load as the constrained baseline(s) problem has to be solved for attitude determination and this information can be applied for relative positioning. [Copyright &y& Elsevier]

• The first time inverted the unmodeled errors in GNSS relative positioning. • The long-term components (200–2500 epochs) in unmodeled errors are significant, but the short-term components (below 100 epochs) are not. • The unmodeled errors between L1 and L2 frequencies have a clear correlation, with the correlation coefficient being ≥ 75%. • Atmospheric delays are demonstrated to be the primary source of unmodeled errors in long baselines. Unmodeled errors in the global navigation satellite system (GNSS) observation equations are inevitable and have an impact on parameter estimation accuracy. In this study, we focus on inverting unmodeled errors in relative positioning and analyse their characteristics to provide a theoretical foundation for processing. First, we present an inversion method for unmodeled errors and demonstrate its effectiveness using an example. Then, we systematically examine the characteristics of unmodeled errors. The findings indicate that (1) the unmodeled errors in the short baselines are eliminated more effectively, whereas the unmodeled errors in the long baselines are more significant and unpredictable; (2) the long-term components (200–2500 epochs) in unmodeled errors are significant, but the short-term components (below 100 epochs) are not; and (3) unmodeled errors between L1 and L2 frequencies have a clear correlation, with the correlation coefficient being ≥ 75%. Finally, we prove that atmospheric delays are the primary source of unmodeled errors in long baselines. [ABSTRACT FROM AUTHOR]

We compute the horizontal displacement in the first/second-order and Merowe Dam control points in a subset of a hybrid triangulation network in northern Sudan. The Global Navigation Satellite Systems (GNSS) and least-squares network adjustment are jointly used to determine the horizontal displacement in the control points. The GNSS observations collected by relative positioning are validated over the control points to create a corresponding subnetwork adjusted by the least-squares. The baselines and network loops show good quality through the statistical indicators that measure the ratio, root mean square (RMS), and reference variance. We apply minimum-constrained adjustment (MCA) and zero-constrained adjustment (ZCA) methods on the subnet. After adjustment. The horizontal displacement is determined as the Euclidean norm of the difference between the Easting/Northing components. The comparison shows large displacements in the first-order (0.6 m), second-order (2 m) points and small displacements (15 cm) in Merowe control points. • A subnetwork of first and second-order control points is selected for testing displacement. • The selected control points are reinforced by new control points established for the Merowe Dam project. • GNSS relative positioning and network adjustment are conducted over the selected control points to compute baselines and loop closures. • Statistical indicators are applied to validate the baseline solutions, and minimum and zero constrained adjustments are applied over the network. • Horizontal displacement is calculated as a euclidean distance between the adjusted coordinates' locations and the original ones. [ABSTRACT FROM AUTHOR]

Keywords: GNSS; GPS; GLONASS; Galileo; BDS; precise point positioning; relative positioning; orbit determination; ionosphere sounding; troposphere sounding; geoscience applications; high-rate positioning; GNSS for geodynamics EN GNSS GPS GLONASS Galileo BDS precise point positioning relative positioning orbit determination ionosphere sounding troposphere sounding geoscience applications high-rate positioning GNSS for geodynamics 1602 1602 1 06/02/20 20200515 NES 200515 In the past two decades, the high-precision Global Positioning System (GPS) has significantly increased the range of geoscience applications and their precision. The studies conducted on the new BDS satellites and redesigned signals have indicated that the signal in space range error (SISRE) of BDS-3 is superior to that of BDS-2 [[1]] and the atomic clock has better frequency stability than GPS BLOCK IIF satellites [[2]]. Katsigianni et al. [[19]] demonstrated that the Galileo-only constellation is already able to achieve comparable PPP accuracy with GPS, and the accuracy can be further improved by combining GPS/Galileo observations or performed ambiguity resolution (AR). 10.3390/rs11222692 6 Wei H., Li J., Zhang S., Xu X. Cycle Slip Detection and Repair for Dual-Frequency LEO Satellite GPS Carrier Phase Observations with Orbit Dynamic Model Information. [Extracted from the article]

For short baseline real-time kinematic (RTK) positioning, the atmosphere and broadcast ephemeris errors can be usually eliminated in double-differenced (DD) processing for synchronous observations. However, in the case of possible communication latency time, these errors may not be eliminated in DD treatments due to their variations during latency time. In addition, the time variation of these errors may present different characteristics among GPS, GLONASS, BDS, and GALILEO due to different satellite orbit and clock types. In this contribution, the formulas for studying the broadcast orbit and clock offset errors and atmosphere error in asynchronous RTK (ARTK) model is proposed, and comprehensive experimental analysis is performed to numerically show time variations of these errors and their impacts on RTK results from short-baselines among four systems. Compared with synchronous RTK, the degradation of position precision for ARTK can reach a few centimeters, but the accuracy degradation to a different degree by different systems. BDS and Galileo usually outperform GPS and GLONASS in ARTK due to the smaller variation of broadcast ephemeris error. The variation of broadcast orbit error is generally negligible compared with the variation of broadcast clock offset error for GPS, BDS, and Galileo. Specifically, for a month of data, the root mean square (RMS) values for the variation of broadcast ephemeris error over 15 s are 11.2, 16.9, 7.3, and 3.0 mm for GPS, GLONASS, BDS, and Galileo, respectively. The variation of ionosphere error for some satellites over 15 s can reach a few centimeters during active sessions under a normal ionosphere day. In addition, compared with other systems, BDS ARTK shows an advantage under high ionosphere activity, and such advantage may be attributed to five GEO satellites in the BDS constellation. [ABSTRACT FROM AUTHOR]