GPS positioning precision is affected by various error sources, and traditional combinations of GPS carrier phase observations have their own limitations such as the wide-lane, the narrow-lane and the ionospheric-free...GPS positioning precision is affected by various error sources, and traditional combinations of GPS carrier phase observations have their own limitations such as the wide-lane, the narrow-lane and the ionospheric-free combinations. To obtain the optimal positioning precision, a new linear combination method is addressed through the variance-covariance （VCV） of the GPS multi-frequency carrier phase combination equations, and the impact of the positioning precision is analyzed with the changing of the observation errors deduced by the law of error propagation. For the high precision positioning with only one carrier phase combination, the optimal combination method is deduced and further validated by an example of a baseline resolution with 60 km length. The result indicates that this method is the simplest, and the positioning precision is the best. Therefore, it is useful for long baseline quick positioning for different precision requirements in various distances.展开更多
This paper presents a new method of improving Global Positioning System(GPS)positioning precision. Based on the altitude hold mode, the method does not need any other equipment. Under this constraint condition, the To...This paper presents a new method of improving Global Positioning System(GPS)positioning precision. Based on the altitude hold mode, the method does not need any other equipment. Under this constraint condition, the Total Least Squares(TLS) algorithm is used to prove that the method is effective. Theoretical analysis shows that the algorithm can significantly improve the GPS positioning precision.展开更多
Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigat...Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigation satellite systems(GNSSs)have been a valuable tool in monitoring seismic motions,allowing permanent displacement computation to be unambiguously achieved.As a valuable tool presented to the seismic commu nity,the GSeisRT software developed by Wuhan University(China)can realize multi-GNSS precise point positioning with ambiguity resolution(PPP-AR)and achieve centimeterlevel to sub-centimeter-level precision in real time.While the stable maintenance of a global precise point positioning(PPP)service is challenging,this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network.This capability makes GSeisRT especially suitable for proprietary GNSS networks and,more importantly,the highest possible positio ning precision and reliability can be obtained.According to real-time results from the Network of the Americas,the mean root mean square(RMS)errors of kinematic PPP-AR over a 24 h span are as low as 1.2,1.3,and 3.0 cm in the east,north,and up components,respectively.Within the few minutes that span a typical seismic event,a horizontal displacement precision of 4 mm can be achieved.The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%-40%higher than that of the global PPP/PPP-AR.Since 2019,GSeisRT has successfully recorded the static,dynamic,and peak ground displacements for the 2020Oaxaca,Mexico moment magnitude(Mw)7.4 event;the 2020 Lone Pine,California Mw 5.8 event;and the 2021 Qinghai,China Mw 7.3 event in real time.The resulting immediate magnitude estimates have an error of around 0.1 only.The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Ne tworks Center,the EarthScope Consortium of the United States,the National Seismological Center of Chile,Institute of Geological and Nuclear Sciences Limited(GNS Science Te PūAo)of New Zealand,and the Geospatial Information Agency of Indonesia.展开更多
This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testi...This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testing.During the simulation phase,a GNSS receiver captured vi-bration waveforms generated by a single-axis motion simulator based on preset signal parameters,analyzing how different satellite system configurations affect the efficiency of extracting vibration parameters.Subsequently,field tests were conducted on a high-rise steel singletube tower.The results indicate that in the simulation environment,no matter the PPP positioning data under single GPS or multisystem combination,the vibration frequency of singleaxis motion simulator can be accurately extracted after frequency do-main analysis,with multisystem setups providing more precise amplitude parameters.In the field test,the natural vibration periods of the main vibration modes of high-rise steel single-tube tower measured by PPP technology closely match the results of the first two modes derived from finite element analysis.The first mode period calculated by the em-pirical formula is approximately 6%higher than those determined through finite element analysis and PPP.This study demonstrates the potential of PPP for structural vibration analysis,offering significant benefits for assessing dynamic responses and monitoring the health of towering structures.展开更多
Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecis...Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecision ZTD model.However,existing ZTD models only consider the impact of linear terms on ZTD estimation,whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study.A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the realtime linear and nonlinearity ZTD(RLNZ)model.This model uses the ZTD estimated from the Global Pressure and Temperature 3(GPT3)model as the initial value.The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model are first considered.In addition,nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method.Finally,the RLNZ-derived ZTD is obtained at an arbitrary location.The western United States,with height difference ranging from-500 to 4000 m,is selected,and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory(NGL)and the data of 9 radiosonde(RS)stations in the year 2021 are used.Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model.Statistical results show the averaged root mean square(RMS),Bias,and mean absolute error(MAE)of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm,respectively.The average improvement rate of the RLNZ model is 33% when compared to the GPT3 model.Finally,the application of the proposed RLNZ model in simulated real-time Precise Point Positioning(PPP)indicates that the accuracy of PPP in N,E and U components is improved by 8%,2%,and 6% when compared with that from the GPT3-based PPP.Meanwhile,the convergence time in N and U components is improved by 23% and 7%,respectively.Such results verify the superiority of the proposed RLNZ model in retrieving realtime ZTD maps for GNSS positioning and navigation applications.展开更多
High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicres...High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method （ESLM）, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.展开更多
The motor’s configuration is designed and the dynamic analysis equations based on its simplified model are deduced. A testing system utilizing grating is set up to test this new motor, and the theoretical movement pr...The motor’s configuration is designed and the dynamic analysis equations based on its simplified model are deduced. A testing system utilizing grating is set up to test this new motor, and the theoretical movement principle for the motor is proved by experiments. The pulse waveforms are applied to drive the motor to move in steps. The motor has a displacement resolution of 10 nm and a maximum velocity of 0.6 mm/s. It can drive a 200 g slider whose range is 20 mm. A one-dimensional precision positioning platform is fabricated by using the new hybrid piezoelectric motor. The prototype is made up of two servomotors and two piezoelectric motors, which are controlled automatically by a computer. The positioning range of the platform is 10 cm.展开更多
Traditionally, basis weight control valve is driven by a constant frequency pulse signal. Therefore, it is difficult for the valve to match the control precision of basis weight. Dynamic simulation research using Matl...Traditionally, basis weight control valve is driven by a constant frequency pulse signal. Therefore, it is difficult for the valve to match the control precision of basis weight. Dynamic simulation research using Matlab/Simulink indicates that there is much more overshoot and fluctuating during the valve-positioning process. In order to improve the valve-positioning precision, the control method of trapezoidal velocity curve was studied. The simulation result showed that the positioning steady-state error was less than 0.0056%, whereas the peak error was less than 0.016% by using trapezoidal velocity curve at 10 positioning steps. A valve-positioning precision experimental device for the stepper motor of basis weight control valve was developed. The experiment results showed that the error ratio of 1/10000 positioning steps was 4% by using trapezoidal velocity curve. Furthermore, the error ratio of 10/10000 positioning steps was 0.5%. It proved that the valve-positioning precision of trapezoidal velocity curve was much higher than that of the constant frequency pulse signal control strategy. The new control method of trapezoidal velocity curve can satisfy the precision requirement of 10000 steps.展开更多
For the smaller thrust,it is difficult to achieve 3Dtrans-scale precision positioning based on previous stick-slip driving.A large thrust trans-scale precision positioning stage is studied based on the inertial stick-...For the smaller thrust,it is difficult to achieve 3Dtrans-scale precision positioning based on previous stick-slip driving.A large thrust trans-scale precision positioning stage is studied based on the inertial stick-slip driving.The process of the movement is divided into two steps,i.e.,the″sliding″phase and the″stickness″phase.In the whole process,the kinematics model of the inertial stick-slip driving is established,and it reveals some factors affecting the velocity of inertial stick-slip driving.Furthermore,a simulation of movement is preformed by Matlab-Simulink software,and the whole process of the inertial stick-slip driving is displayed.After one experimental prototype is designed,the back and forth velocity is tested.Finally,the simulation verifies the accuracy of the kinematics model.展开更多
The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the...The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.展开更多
Selecting the optimal reference satellite is an important component of high-precision relat/ve positioning because the reference satellite directly influences the strength of the normal equation. The reference satelli...Selecting the optimal reference satellite is an important component of high-precision relat/ve positioning because the reference satellite directly influences the strength of the normal equation. The reference satellite selection methods based on elevation and positional dilution of precision （PDOP） value were compared. Results show that all the above methods cannot select the optimal reference satellite. We introduce condition number of the design matrix in the reference satellite selection method to improve structure of the normal equation, because condition number can indicate the ill condition of the normal equation. The experimental results show that the new method can improve positioning accuracy and reliability in precise relative positioning.展开更多
The Global Navigation Satellite System (GNSS) is widely utilized for accurate positioning.One commonly applied method to obtain precise coordinate estimates is by implementing the relative positioning in network mode....The Global Navigation Satellite System (GNSS) is widely utilized for accurate positioning.One commonly applied method to obtain precise coordinate estimates is by implementing the relative positioning in network mode.However,this approach can be complex and challenging.Fortunately,The Japan Aerospace Exploration Agency (JAXA) offers freely available satellite orbit and clock correction products called Multi-GNSS Advanced Demonstration Tool for Orbit and Clock Analysis (MADOCA),which can enhance positioning accuracy through the precise point positioning (PPP) method.This study focuses on evaluating PPP static mode positioning using MADOCA products and comparing the results with the highly precise relative positioning method.By analyzing a network of 20 GNSS stations in Indonesia,we found that the PPP method using MADOCA products provided favorable positioning estimates.The median discrepancies and the corresponding median absolute deviation (MAD) for easting,northing,and up components were estimated as 9±18 mm,10±9 mm,and 3±40 mm,respectively.These results indicate that PPP with MADOCA products can be a reliable alternative for establishing Indonesia's horizontal control networks,particularly for orders 0,1,2,and 3,and for a broad spectrum of geoscience monitoring activities.However,considerations such as epoch transformations and seismic activities should be taken into account for accurate positioning applications that comply with the definition of the national reference framework.展开更多
The recruitment of the Low Earth Orbit(LEO)constellation is recognized as an effective way to augment Global Navigation Satellite System(GNSS)Precise Point Positioning(PPP)in the near future.Its potential to accelerat...The recruitment of the Low Earth Orbit(LEO)constellation is recognized as an effective way to augment Global Navigation Satellite System(GNSS)Precise Point Positioning(PPP)in the near future.Its potential to accelerate PPP convergence has been proved with simulated data.However,the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective,which hampers the understanding and exploitation of the enhancement of LEO.In this article,the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification.To show the characteristics of the ambiguities during convergence,eigenvalue decomposition is used to divide the ambiguities into orthogonal components,named geometric-related component,clock-error-related component,and independent component.The results show that the precision of geometric-related components of ambiguities,which correlates with position parameters,is low at a single epoch,while the precision can be greatly improved with the fast geometric change of LEO.On the other hand,the precision of clock-error-related components of ambiguities,which correlates with clock errors,cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry,which causes the precision of each ambiguity to be low.Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.展开更多
The development of this technology has favored the advances noted in recent years in the field of precise positioning. It has also paved the way for a wide range of research into the evaluation of their performance an...The development of this technology has favored the advances noted in recent years in the field of precise positioning. It has also paved the way for a wide range of research into the evaluation of their performance and reliability, their potential use in different fields, the improvement of performance and combined systems, etc. Single-frequency GNSS receivers, which for a long time remained the only category of low-cost GNSS receivers, often limited by their level of accuracy (metric) mainly due to their single-frequency nature, have been joined in the last decade by dual-frequency GNSS receivers developed by certain manufacturers of positioning equipment. These receivers now offer possible alternatives to the relatively expensive conventional (topographic quality) or geodetic receivers and. In this study, the performance of these low-cost dual-frequency receivers was evaluated in static and real-time kinematic GNSS positioning modes. Static positioning was carried out on three points with sessions of 2 h and 4 h over three days with antenna swapping (CHC i50, Leica GS14 and Emlid Reach RS2+). Real-time observations were carried out on eleven (11) points in open, poorly open and not at all open environments, in order to assess not only performance but also receiver sensitivity in environments with a high risk of multipath. The results obtained showed an average agreement of 2 cm in planimetry between the low-cost Emlid RS2+ receiver and the Leica GS14 and CHC i50 receivers. The differences in altimetry are nevertheless greater (sometimes up to decimetres for certain points). Real-time positioning results provided an average convergence of around 1 cm on the E, N and H components with the results from the low-cost Emlid Reach RS2+ and Ublox ZED-F9P receivers and the CHC i50 receiver. Analysis of the results obtained has enabled us to highlight the various issues and challenges associated with this new generation of GNSS receivers, with a view to enhancing their appropriation and optimal integration in the professional and research worlds.展开更多
Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method an...Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method and the appropriate positioning flow, we process GPS data from six IGS （International GNSS Service） sites （e.g., MIZU, TSK2, USUD, MTKA, AIRA and KSMV） located in Japan and obtain the positioning results with centimeter scale precision. The displacement time series of the six sites are analyzed using the least squares spectral analysis method to estimate deformations caused by the Mw9.0 mainshock and the Mw7.9 aftershock, and the cumulative displacements after 1 day. Mainshock displacements at station MIZU, the nearest site to the mainshock in the North （N）, East （E）, and Up （U） directions, are -1.202 m, 2.180 m and -0.104 m, respectively, and the cumulative deformations after 1 day are -1.117 m, 2.071 m and -0.072 m, respectively. The displacements at station KSMV, the nearest site to the Mw7.9 aftershock in the N, E and U directions, are -0.032 m, 0.742 m and -0.345 m, respectively. The other sites obviously experienced eastern movements and subsidence. The deformation vectors indicate that the horizontal displacements caused by the earthquake point to the epicenter and rupture. Elastic bounds evidently took place at all sites. The results indicate that the crustal movements and earthquake were part of a megathrust caused by the Pacific Plate sinking under the North American Plate to the northeast of Japan island arc.展开更多
A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of l...A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS （STDGG） and zenith tropospheric delay （ZTD） values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.展开更多
Because the signals of global positioning system （GPS） satellites are susceptible to obstructions in urban environment with many high buildings around, the number of GPS useful satellites is usually less than six. I...Because the signals of global positioning system （GPS） satellites are susceptible to obstructions in urban environment with many high buildings around, the number of GPS useful satellites is usually less than six. In this case, the receiver autonomous integrity monitoring （RAIM） method earmot exclude faulty satellite. In order to improve the performance of RAIM method and obtain the reliable positioning results with five satellites, the series of receiver clock bias （RCB） is regarded as one useful satellite and used to aid RAIM method. From the point of nonlinear series, a grey-Markov model for predicting the RCB series based on grey theory and Markov chain is presented. And then the model is used for aiding RAIM method in order to exclude faulty satellite. Experimental results demonstrate that the prediction model is fit for predicting the RCB series, and with the clock-based RAIM method the faulty satellite can be correctly excluded and the positioning precision of GPS receiver can be improved for the case where there are only five useful satellites.展开更多
A three-dimensional positioning method for global positioning system(GPS)receivers based on three satellites was proposed.In the method,the measurement equation used for positioning calculation was expanded by means o...A three-dimensional positioning method for global positioning system(GPS)receivers based on three satellites was proposed.In the method,the measurement equation used for positioning calculation was expanded by means of two measures.In this case,the measurement equation could be solved,and the function of positioning calculation could be performed.The detailed steps of the method and how to evaluate the positioning precision of the method were given,respectively.The positioning performance of the method was demonstrated through some experiments.It is shown that the method can provide the three-dimensional positioning information under the condition that there are only three useful satellites.展开更多
Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address t...Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address this issue,this paper proposes a real⁃time BDS⁃3 precise unidirectional timing model based on uncombined(UC)observations using the BDS⁃3 PPP⁃B2b service.This model resolves the challenge of the amplified observation noise inherent in the IF combination model.The experiment involved selecting eight global navigation satellite system(GNSS)observation stations within China and collecting continuous observation data for 15 d.A comparative analy⁃sis with the traditional dual⁃frequency IF combination PPP timing model showed that the BDS⁃3 UC PPP timing based on the BDS⁃3 PPP⁃B2b service can achieve a timing preci⁃sion of 0.5 ns.In addition,it was found that due to global positioning system(GPS)satellite clock products in the BDS⁃3 PPP⁃B2b service not being unified to the standard time,the GPS IF PPP timing method based on the BDS⁃3 PPP⁃B2b service is not recommended for precise timing.In summary,the BDS⁃3 UC PPP timing model proposed in this paper is suitable for precise timing,providing observa⁃tion values with smaller noise,and its timing accuracy is comparable to that of the BDS⁃3 IF PPP,with slightly better frequency stability.展开更多
An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to charact...An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to characterize the integrity status of the precise Orbit,Clock(OC)and Code Bias(OCB)corrections,and deriving the corresponding algorithms to detect and exclude anomalies,and to evaluate the real-time accuracy levels of the OCB.Compared to many prior works whose interests focused on analyzing and improving the averaged long-term accuracy,this work is established from integrity perspective.In particular,a two-layer fault detection and identification approach is developed to reduce the miss detection and false alert probabilities.The test statistics are constructed based on the raw observations from a network of worldwide sparsely distributed monitor stations.In addition,a realistic data-driven model is established to compute the Quality Indicators(QI)for healthy OCB products.The proposed scheme is validated respectively for multi-constellation OC and code bias,using historical correction data.The results suggest that the detection algorithms can effectively identify and alert the faults,so that the remaining correction errors approximate well to Gaussian distributions.Moreover,the computed QI are shown to be consistent with the truth error variations in real time.Most importantly,the position domain verification shows noticeable positioning accuracy and robustness improvements under both nominal and faulty conditions of the OCB correction data.展开更多
基金Supported by the Key Laboratory of Geological Hazards on Three Gorges Reservoir Area,Ministry of Education, China(No.2006KDZ05).
文摘GPS positioning precision is affected by various error sources, and traditional combinations of GPS carrier phase observations have their own limitations such as the wide-lane, the narrow-lane and the ionospheric-free combinations. To obtain the optimal positioning precision, a new linear combination method is addressed through the variance-covariance （VCV） of the GPS multi-frequency carrier phase combination equations, and the impact of the positioning precision is analyzed with the changing of the observation errors deduced by the law of error propagation. For the high precision positioning with only one carrier phase combination, the optimal combination method is deduced and further validated by an example of a baseline resolution with 60 km length. The result indicates that this method is the simplest, and the positioning precision is the best. Therefore, it is useful for long baseline quick positioning for different precision requirements in various distances.
文摘This paper presents a new method of improving Global Positioning System(GPS)positioning precision. Based on the altitude hold mode, the method does not need any other equipment. Under this constraint condition, the Total Least Squares(TLS) algorithm is used to prove that the method is effective. Theoretical analysis shows that the algorithm can significantly improve the GPS positioning precision.
基金funded by National Science Foundation of China(42025401)National Key Research and Development Program of China(2022YFB3903800)。
文摘Precise coseismic displacements in earthquake/tsunamic early warning are necessary to characterize earthquakes in real time in order to enable decision-makers to issue alerts for public safety.Real-time global navigation satellite systems(GNSSs)have been a valuable tool in monitoring seismic motions,allowing permanent displacement computation to be unambiguously achieved.As a valuable tool presented to the seismic commu nity,the GSeisRT software developed by Wuhan University(China)can realize multi-GNSS precise point positioning with ambiguity resolution(PPP-AR)and achieve centimeterlevel to sub-centimeter-level precision in real time.While the stable maintenance of a global precise point positioning(PPP)service is challenging,this software is capable of estimating satellite clocks and phase biases in real time using a regional GNSS network.This capability makes GSeisRT especially suitable for proprietary GNSS networks and,more importantly,the highest possible positio ning precision and reliability can be obtained.According to real-time results from the Network of the Americas,the mean root mean square(RMS)errors of kinematic PPP-AR over a 24 h span are as low as 1.2,1.3,and 3.0 cm in the east,north,and up components,respectively.Within the few minutes that span a typical seismic event,a horizontal displacement precision of 4 mm can be achieved.The positioning precision of the GSeisRT regional PPP/PPP-AR is 30%-40%higher than that of the global PPP/PPP-AR.Since 2019,GSeisRT has successfully recorded the static,dynamic,and peak ground displacements for the 2020Oaxaca,Mexico moment magnitude(Mw)7.4 event;the 2020 Lone Pine,California Mw 5.8 event;and the 2021 Qinghai,China Mw 7.3 event in real time.The resulting immediate magnitude estimates have an error of around 0.1 only.The GSeisRT software is open to the scientific community and has been applied by the China Earthquake Ne tworks Center,the EarthScope Consortium of the United States,the National Seismological Center of Chile,Institute of Geological and Nuclear Sciences Limited(GNS Science Te PūAo)of New Zealand,and the Geospatial Information Agency of Indonesia.
基金The National Natural Science Foundation of China(No.41974214).
文摘This study explores the use of the Global Navigation Satellite System(GNSS)precise point positioning(PPP)technology to determine the natural vibration periods of towering structures through simulations and field testing.During the simulation phase,a GNSS receiver captured vi-bration waveforms generated by a single-axis motion simulator based on preset signal parameters,analyzing how different satellite system configurations affect the efficiency of extracting vibration parameters.Subsequently,field tests were conducted on a high-rise steel singletube tower.The results indicate that in the simulation environment,no matter the PPP positioning data under single GPS or multisystem combination,the vibration frequency of singleaxis motion simulator can be accurately extracted after frequency do-main analysis,with multisystem setups providing more precise amplitude parameters.In the field test,the natural vibration periods of the main vibration modes of high-rise steel single-tube tower measured by PPP technology closely match the results of the first two modes derived from finite element analysis.The first mode period calculated by the em-pirical formula is approximately 6%higher than those determined through finite element analysis and PPP.This study demonstrates the potential of PPP for structural vibration analysis,offering significant benefits for assessing dynamic responses and monitoring the health of towering structures.
基金supported by the National Natural Science Foundation of China(42274039)Shaanxi Provincial Innovation Capacity Support Plan Project(2023KJXX-050)+2 种基金The Open Grants of the State Key Laboratory of Severe Weather(2023LASW-B18)Scientific and technological research projects for major issues in military medicine and aviation medicine(2022ZZXM012)Local special scientific research plan project of Shaanxi Provincial Department of Education(22JE012)。
文摘Zenith Tropospheric Delay(ZTD)is an important factor that restricts the high-precision positioning of global navigation satellite system(GNSS),and it is of great significance in establishing a real-time and highprecision ZTD model.However,existing ZTD models only consider the impact of linear terms on ZTD estimation,whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study.A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the realtime linear and nonlinearity ZTD(RLNZ)model.This model uses the ZTD estimated from the Global Pressure and Temperature 3(GPT3)model as the initial value.The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model are first considered.In addition,nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method.Finally,the RLNZ-derived ZTD is obtained at an arbitrary location.The western United States,with height difference ranging from-500 to 4000 m,is selected,and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory(NGL)and the data of 9 radiosonde(RS)stations in the year 2021 are used.Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model.Statistical results show the averaged root mean square(RMS),Bias,and mean absolute error(MAE)of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm,respectively.The average improvement rate of the RLNZ model is 33% when compared to the GPT3 model.Finally,the application of the proposed RLNZ model in simulated real-time Precise Point Positioning(PPP)indicates that the accuracy of PPP in N,E and U components is improved by 8%,2%,and 6% when compared with that from the GPT3-based PPP.Meanwhile,the convergence time in N and U components is improved by 23% and 7%,respectively.Such results verify the superiority of the proposed RLNZ model in retrieving realtime ZTD maps for GNSS positioning and navigation applications.
基金supported by the National Key Basic Research Program of China (2011CB013104)National Natural Science Foundation of China (U1134004)+2 种基金Guangdong Provincial Natural Science Foundation (2015A030312008)Science and Technology Program of Guangzhou (201510010281)Guangdong Provincial Science and Technology Plan (2013B010402014)
文摘High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method （ESLM）, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.
文摘The motor’s configuration is designed and the dynamic analysis equations based on its simplified model are deduced. A testing system utilizing grating is set up to test this new motor, and the theoretical movement principle for the motor is proved by experiments. The pulse waveforms are applied to drive the motor to move in steps. The motor has a displacement resolution of 10 nm and a maximum velocity of 0.6 mm/s. It can drive a 200 g slider whose range is 20 mm. A one-dimensional precision positioning platform is fabricated by using the new hybrid piezoelectric motor. The prototype is made up of two servomotors and two piezoelectric motors, which are controlled automatically by a computer. The positioning range of the platform is 10 cm.
基金supported by the International S&T Cooperation Program of China(GrantNo.2010DFB43660)National Natural Science Foundation of China(Grant No.51375286)Scientific Research Program Funded by Shaanxi Provincial Education Department(Program No.16JF005)
文摘Traditionally, basis weight control valve is driven by a constant frequency pulse signal. Therefore, it is difficult for the valve to match the control precision of basis weight. Dynamic simulation research using Matlab/Simulink indicates that there is much more overshoot and fluctuating during the valve-positioning process. In order to improve the valve-positioning precision, the control method of trapezoidal velocity curve was studied. The simulation result showed that the positioning steady-state error was less than 0.0056%, whereas the peak error was less than 0.016% by using trapezoidal velocity curve at 10 positioning steps. A valve-positioning precision experimental device for the stepper motor of basis weight control valve was developed. The experiment results showed that the error ratio of 1/10000 positioning steps was 4% by using trapezoidal velocity curve. Furthermore, the error ratio of 10/10000 positioning steps was 0.5%. It proved that the valve-positioning precision of trapezoidal velocity curve was much higher than that of the constant frequency pulse signal control strategy. The new control method of trapezoidal velocity curve can satisfy the precision requirement of 10000 steps.
基金supported by the National Natural Science Foundation of China(No.51175358)the Natural Science Foundation of Jiangsu Province (No.BK20140345)+2 种基金Colleges and Universities Natural Science Foundation of Jiangsu Province (No.14KJB460025)the National Science Foundation for Post-Doctoral Scientists of China (No.2014M551651)the Natural Science Foundation of Jiangsu Province for Post-Doctoral Scientists (No. 1401073C)
文摘For the smaller thrust,it is difficult to achieve 3Dtrans-scale precision positioning based on previous stick-slip driving.A large thrust trans-scale precision positioning stage is studied based on the inertial stick-slip driving.The process of the movement is divided into two steps,i.e.,the″sliding″phase and the″stickness″phase.In the whole process,the kinematics model of the inertial stick-slip driving is established,and it reveals some factors affecting the velocity of inertial stick-slip driving.Furthermore,a simulation of movement is preformed by Matlab-Simulink software,and the whole process of the inertial stick-slip driving is displayed.After one experimental prototype is designed,the back and forth velocity is tested.Finally,the simulation verifies the accuracy of the kinematics model.
基金supported by“The National Key Research and Development Program of China(No.2020YFA0713502)”“The National Natural Science Foundation of China(No.41874039)”+1 种基金“Jiangsu National Science Foundation(No.BK20191342)”“Fundamental Research Funds for the Central Universities(No.2019ZDPY-RH03)”。
文摘The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.
基金partially sponsored by the National 973 Project of China(2013CB733303)partially supported by the postgraduate independent exploration project of Central South University(2014zzts249)
文摘Selecting the optimal reference satellite is an important component of high-precision relat/ve positioning because the reference satellite directly influences the strength of the normal equation. The reference satellite selection methods based on elevation and positional dilution of precision （PDOP） value were compared. Results show that all the above methods cannot select the optimal reference satellite. We introduce condition number of the design matrix in the reference satellite selection method to improve structure of the normal equation, because condition number can indicate the ill condition of the normal equation. The experimental results show that the new method can improve positioning accuracy and reliability in precise relative positioning.
文摘The Global Navigation Satellite System (GNSS) is widely utilized for accurate positioning.One commonly applied method to obtain precise coordinate estimates is by implementing the relative positioning in network mode.However,this approach can be complex and challenging.Fortunately,The Japan Aerospace Exploration Agency (JAXA) offers freely available satellite orbit and clock correction products called Multi-GNSS Advanced Demonstration Tool for Orbit and Clock Analysis (MADOCA),which can enhance positioning accuracy through the precise point positioning (PPP) method.This study focuses on evaluating PPP static mode positioning using MADOCA products and comparing the results with the highly precise relative positioning method.By analyzing a network of 20 GNSS stations in Indonesia,we found that the PPP method using MADOCA products provided favorable positioning estimates.The median discrepancies and the corresponding median absolute deviation (MAD) for easting,northing,and up components were estimated as 9±18 mm,10±9 mm,and 3±40 mm,respectively.These results indicate that PPP with MADOCA products can be a reliable alternative for establishing Indonesia's horizontal control networks,particularly for orders 0,1,2,and 3,and for a broad spectrum of geoscience monitoring activities.However,considerations such as epoch transformations and seismic activities should be taken into account for accurate positioning applications that comply with the definition of the national reference framework.
基金supported by the National Natural Science Funds of China[grant numbers 42104013 and 42225401]the Innovation Program of Shanghai Municipal Education Commission[grant number 2021-01-07-00-07-E00095]+3 种基金Natural Science Fund of Shanghai[grant number 21ZR1465600]the Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee[grant numbers 21511103902 and 22511103003]the industrial Collaborative Innovation Project(Technology)of Shanghai Municipality[grant numbers XTCX-KJ-2023-35 and XTCX-KJ-2022-09]the Fundamental Research Funds for the Central Universities.
文摘The recruitment of the Low Earth Orbit(LEO)constellation is recognized as an effective way to augment Global Navigation Satellite System(GNSS)Precise Point Positioning(PPP)in the near future.Its potential to accelerate PPP convergence has been proved with simulated data.However,the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective,which hampers the understanding and exploitation of the enhancement of LEO.In this article,the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification.To show the characteristics of the ambiguities during convergence,eigenvalue decomposition is used to divide the ambiguities into orthogonal components,named geometric-related component,clock-error-related component,and independent component.The results show that the precision of geometric-related components of ambiguities,which correlates with position parameters,is low at a single epoch,while the precision can be greatly improved with the fast geometric change of LEO.On the other hand,the precision of clock-error-related components of ambiguities,which correlates with clock errors,cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry,which causes the precision of each ambiguity to be low.Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.
文摘The development of this technology has favored the advances noted in recent years in the field of precise positioning. It has also paved the way for a wide range of research into the evaluation of their performance and reliability, their potential use in different fields, the improvement of performance and combined systems, etc. Single-frequency GNSS receivers, which for a long time remained the only category of low-cost GNSS receivers, often limited by their level of accuracy (metric) mainly due to their single-frequency nature, have been joined in the last decade by dual-frequency GNSS receivers developed by certain manufacturers of positioning equipment. These receivers now offer possible alternatives to the relatively expensive conventional (topographic quality) or geodetic receivers and. In this study, the performance of these low-cost dual-frequency receivers was evaluated in static and real-time kinematic GNSS positioning modes. Static positioning was carried out on three points with sessions of 2 h and 4 h over three days with antenna swapping (CHC i50, Leica GS14 and Emlid Reach RS2+). Real-time observations were carried out on eleven (11) points in open, poorly open and not at all open environments, in order to assess not only performance but also receiver sensitivity in environments with a high risk of multipath. The results obtained showed an average agreement of 2 cm in planimetry between the low-cost Emlid RS2+ receiver and the Leica GS14 and CHC i50 receivers. The differences in altimetry are nevertheless greater (sometimes up to decimetres for certain points). Real-time positioning results provided an average convergence of around 1 cm on the E, N and H components with the results from the low-cost Emlid Reach RS2+ and Ublox ZED-F9P receivers and the CHC i50 receiver. Analysis of the results obtained has enabled us to highlight the various issues and challenges associated with this new generation of GNSS receivers, with a view to enhancing their appropriation and optimal integration in the professional and research worlds.
基金supported partially by the National Natural Science Foundation of China(No.40974004 and 40974016)the Key Laboratory of Surveying and Mapping Technology on Island and Reef of NASMG,China(No.2011A01)the Key Laboratory of Advanced Surveying Engineering of NASMG,China(No.TJES1101)
文摘Crustal deformation can provide constraints for studying earthquake rupture and shock wave transmission for the Mw9.0 eastern Japan great earthquake. Using the single- epoch precise point positioning （PPP） method and the appropriate positioning flow, we process GPS data from six IGS （International GNSS Service） sites （e.g., MIZU, TSK2, USUD, MTKA, AIRA and KSMV） located in Japan and obtain the positioning results with centimeter scale precision. The displacement time series of the six sites are analyzed using the least squares spectral analysis method to estimate deformations caused by the Mw9.0 mainshock and the Mw7.9 aftershock, and the cumulative displacements after 1 day. Mainshock displacements at station MIZU, the nearest site to the mainshock in the North （N）, East （E）, and Up （U） directions, are -1.202 m, 2.180 m and -0.104 m, respectively, and the cumulative deformations after 1 day are -1.117 m, 2.071 m and -0.072 m, respectively. The displacements at station KSMV, the nearest site to the Mw7.9 aftershock in the N, E and U directions, are -0.032 m, 0.742 m and -0.345 m, respectively. The other sites obviously experienced eastern movements and subsidence. The deformation vectors indicate that the horizontal displacements caused by the earthquake point to the epicenter and rupture. Elastic bounds evidently took place at all sites. The results indicate that the crustal movements and earthquake were part of a megathrust caused by the Pacific Plate sinking under the North American Plate to the northeast of Japan island arc.
基金Project(41004011)supported by the National Natural Science Foundation of ChinaProject(2014M550425)supported by the China Postdoctoral Science Foundation
文摘A modified algorithm of combined GPS/GLONASS precise point positioning （GG-PPP） was developed by decreasing the number of unknowns to be estimated so that accurate position solutions can be achieved in the case of less number of visible satellites. The system time difference between GPS and GLONASS （STDGG） and zenith tropospheric delay （ZTD） values were firstly estimated in an open sky condition using the traditional GG-PPP algorithm. Then, they were used as a priori known values in the modified algorithm instead of estimating them as unknowns. The proposed algorithm was tested using observations collected at BJFS station in a simulated open-pit mine environment. The results show that the position filter converges much faster to a stable value in all three coordinate components using the modified algorithm than using the traditional algorithm. The modified algorithm achieves higher positioning accuracy as well. The accuracy improvement in the horizontal direction and vertical direction reaches 69% and 95% at a satellite elevation mask angle of 50°, respectively.
基金Project(20090580013) supported by the Aeronautic Science Foundation of ChinaProject(ZYGX2010J119) supported by the Fundamental Research Funds for the Central Universities,China
文摘Because the signals of global positioning system （GPS） satellites are susceptible to obstructions in urban environment with many high buildings around, the number of GPS useful satellites is usually less than six. In this case, the receiver autonomous integrity monitoring （RAIM） method earmot exclude faulty satellite. In order to improve the performance of RAIM method and obtain the reliable positioning results with five satellites, the series of receiver clock bias （RCB） is regarded as one useful satellite and used to aid RAIM method. From the point of nonlinear series, a grey-Markov model for predicting the RCB series based on grey theory and Markov chain is presented. And then the model is used for aiding RAIM method in order to exclude faulty satellite. Experimental results demonstrate that the prediction model is fit for predicting the RCB series, and with the clock-based RAIM method the faulty satellite can be correctly excluded and the positioning precision of GPS receiver can be improved for the case where there are only five useful satellites.
基金Project (ZYGX2010J119)supported by the Fundamental Research Funds for the Central Universities of China
文摘A three-dimensional positioning method for global positioning system(GPS)receivers based on three satellites was proposed.In the method,the measurement equation used for positioning calculation was expanded by means of two measures.In this case,the measurement equation could be solved,and the function of positioning calculation could be performed.The detailed steps of the method and how to evaluate the positioning precision of the method were given,respectively.The positioning performance of the method was demonstrated through some experiments.It is shown that the method can provide the three-dimensional positioning information under the condition that there are only three useful satellites.
基金The Basic Science Center Project of the National Natural Science Foundation of China(No.42388102)the Jiangsu Province Natural Resources Science and Technology Project(No.JSZRKJ202404).
文摘Currently,the BeiDou⁃3(BDS⁃3)precise point positioning(PPP)service(PPP⁃B2b)mostly employs the ionosphere⁃free(IF)combination model for precise timing,which tends to amplify the noise in observation values.To address this issue,this paper proposes a real⁃time BDS⁃3 precise unidirectional timing model based on uncombined(UC)observations using the BDS⁃3 PPP⁃B2b service.This model resolves the challenge of the amplified observation noise inherent in the IF combination model.The experiment involved selecting eight global navigation satellite system(GNSS)observation stations within China and collecting continuous observation data for 15 d.A comparative analy⁃sis with the traditional dual⁃frequency IF combination PPP timing model showed that the BDS⁃3 UC PPP timing based on the BDS⁃3 PPP⁃B2b service can achieve a timing preci⁃sion of 0.5 ns.In addition,it was found that due to global positioning system(GPS)satellite clock products in the BDS⁃3 PPP⁃B2b service not being unified to the standard time,the GPS IF PPP timing method based on the BDS⁃3 PPP⁃B2b service is not recommended for precise timing.In summary,the BDS⁃3 UC PPP timing model proposed in this paper is suitable for precise timing,providing observa⁃tion values with smaller noise,and its timing accuracy is comparable to that of the BDS⁃3 IF PPP,with slightly better frequency stability.
基金supported by supported by the National Key Research and Development Plan,China(No.2023YFB3906501)the National Natural Science Foundation of China(No.42227802)the Fundamental Research Funds for the Central Universities,China(No.501JCGG2024133001)。
文摘An integrity monitoring framework is proposed to ensure the quality of the real-time Precise Point Positioning(PPP)correction data at the service end.The key contributions are designing quantitative metrics to characterize the integrity status of the precise Orbit,Clock(OC)and Code Bias(OCB)corrections,and deriving the corresponding algorithms to detect and exclude anomalies,and to evaluate the real-time accuracy levels of the OCB.Compared to many prior works whose interests focused on analyzing and improving the averaged long-term accuracy,this work is established from integrity perspective.In particular,a two-layer fault detection and identification approach is developed to reduce the miss detection and false alert probabilities.The test statistics are constructed based on the raw observations from a network of worldwide sparsely distributed monitor stations.In addition,a realistic data-driven model is established to compute the Quality Indicators(QI)for healthy OCB products.The proposed scheme is validated respectively for multi-constellation OC and code bias,using historical correction data.The results suggest that the detection algorithms can effectively identify and alert the faults,so that the remaining correction errors approximate well to Gaussian distributions.Moreover,the computed QI are shown to be consistent with the truth error variations in real time.Most importantly,the position domain verification shows noticeable positioning accuracy and robustness improvements under both nominal and faulty conditions of the OCB correction data.
