Positioning-control Based on Trapezoidal Velocity Curve for High-precision Basis Weight Control Valve

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.

Large Thrust Trans-scale Precision Positioning Stage Based on Inertial Stick-Slip Driving

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.

Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

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.

Reference satellite selection method for GNSS high-precision relative positioning

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.

An ERA5 tropospheric parameters-augmented approach for improving GNSS precise point positioning

Precise Point Positioning(PPP) technology has developed into a potent instrument for geodetic positioning, ionospheric modeling, tropospheric atmospheric parameter detection, and seismic monitoring.As atmospheric reanalysis data products’ accuracy and spatiotemporal resolution have improved recently, it has become important to apply these products to obtain high-accuracy tropospheric delay parameters, like zenith tropospheric delay(ZTD) and tropospheric horizontal gradient. These tropospheric delay parameters can be applied to PPP to reduce the convergence time and to increase the accuracy in the vertical direction of the position. The European Centre for Medium-Range Weather Forecasts Reanalysis 5(ERA5) atmospheric reanalysis data is the latest product with a high spatiotemporal resolution released by the European Center for Medium-Range Weather Forecasts(ECMWF). Only a few researches have evaluated the application of ERA5 data to Global Navigation Satellite System(GNSS)PPP. Therefore, this study compared and validated the ZTD products derived from ERA5 data using ZTD values provided by 290 global International GNSS Service(IGS) stations for 2016-2017. The results indicated a stable performance for ZTD, with annual average bias and RMS values of 0.23 cm and 1.09 cm,respectively. Further, GNSS observations for one week in each of the four seasons(spring: DOY 92-98;summer: DOY 199-205;autumn: DOY 275-281;and winter: DOY 22-28) from 34 multi-GNSS experiments(MGEX) stations distributed globally in 2016 were considered to evaluate the performance of ERA5-derived tropospheric delay products in GNSS PPP. The performance of ERA5-enhanced PPP was compared with that of the two standard GNSS PPP schemes(without estimated tropospheric horizontal gradient and with estimated tropospheric horizontal gradient). The results demonstrated that ERA5-enhanced GNSS PPP showed no significant improvement in the convergence times in both the Eastern(E) and Northern(N) directions, while the average convergence time over four weeks in the vertical(U)direction improved by 53.3% and 52.7%, respectively(in the case of pngm station). The average convergence times for each week in the U direction of the northern and southern hemisphere stations indicated a decrease of 16.3%, 12.6%, 9.6%, and 9.1%, and 16.9%, 9.6%, 8.9%, and 14.5%, respectively.Regarding positioning accuracy, ERA5-enhanced PPP showed an improvement of 13.3% and 16.2% over the two standard PPP schemes in the U direction, respectively. No significant improvement in the positioning performance was observed in both the E and N directions. Thus, this study demonstrated the potential application of the ERA5 tropospheric parameters-augmented approach to Beidou navigation and positioning.

Novel Linear Piezoelectric Motor for Precision Position Stage

Conventional servomotor and stepping motor face challenges in nanometer positioning stages due to the complex structure, motion transformation mechanism, and slow dynamic response, especially directly driven by linear motor. A new butterfly-shaped linear piezoelectric motor for linear motion is presented. A two-degree precision position stage driven by the proposed linear ultrasonic motor possesses a simple and compact configuration, which makes the system obtain shorter driving chain. Firstly, the working principle of the linear ultrasonic motor is analyzed. The oscillation orbits of two driving feet on the stator are produced successively by using the anti-symmetric and symmetric vibration modes of the piezoelectric composite structure, and the slider pressed on the driving feet can be propelled twice in only one vibration cycle. Then with the derivation of the dynamic equation of the piezoelectric actuator and transient response model, start-upstart-up and settling state characteristics of the proposed linear actuator is investigated theoretically and experimentally, and is applicable to evaluate step resolution of the precision platform driven by the actuator. Moreover the structure of the two-degree position stage system is described and a special precision displacement measurement system is built. Finally, the characteristics of the two-degree position stage are studied. In the closed-loop condition the positioning accuracy of plus or minus 〈0.5 μm is experimentally obtained for the stage propelled by the piezoelectric motor. A precision position stage based the proposed butterfly-shaped linear piezoelectric is theoretically and experimentally investigated.

New Regional Satellite Positioning Constellation Scheme Discussion

The characteristics of present “Beidou” satellite positioning system are analyzed. In order to perfect our country regional satellite positioning system, the idea of “Beidou” geosychronous earth orbit （GEO） satellites combined with some middle earth orbit （MEO） satellites constellation is put forward. The details of general satellite constellation optimized method are described, using this method the multiple positioning constellation design results are gained. And those results belong to two type of sehems, one is 2 GEO plus some MEO satellites and the other is 3 GEO plus some MEO satellites. Through simulation and comparison, among those multiple design results, final optimized regional positioning constellation is given. In order to check the chosen constellation cover performance, the position dilution of preeision（PDOP） is calculated, and with ,satellite constellation simulation software Satlab many coverage performances of the chosen constellation substellar point track, elevation, azimuth and visible satellites number changing situation are also simulated.

Estimation of annual variation of water vapor in the Arctic Ocean between 80°–87°N using shipborne GPS data based on kinematic precise point positioning

The measurement of atmospheric water vapor （WV） content and variability is important for meteorological and climatological research. A technique for the remote sensing of atmospheric WV content using ground-based Global Positioning System （GPS） has become available, which can routinely achieve accuracies for integrated WV content of 1-2 kg/m2. Some experimental work has shown that the accuracy of WV measurements from a moving platform is comparable to that of （static） land-based receivers. Extending this technique into the marine environment on a moving platform would be greatly beneficial for many aspects of meteorological research, such as the calibration of satellite data, investigation of the air-sea interface, as well as forecasting and climatological studies. In this study, kinematic precise point positioning has been developed to investigate WV in the Arctic Ocean （80°-87°N） and annual variations are obtained for 2008 and 2012 that are identical to those related to the enhanced greenhouse effect.

Signal quality analysis and quality check of BDS3 Precise Point Positioning in the Arctic Ocean

This study analyzes the signal quality and the accuracy of BeiDou 3 rd generation Satellite Navigation System(BDS3) Precise Point Positioning(PPP) in the Arctic Ocean. Assessment of signal quality of BDS3 includes signal to noise ratio(SNR), multipath(MP), dilution of precision(DOP), and code-minus-carrier combination(CC). The results show that, 5 to 13 satellites are visible at any time in the Arctic Ocean area as of September 2018, which are sufficient for positioning. In the mid-latitude oceanic region and in the Arctic Ocean, the SNR is 25–52 dB Hz and the MP ranges from-2 m to 2 m. As the latitude increases, the DOP values show large variation, which may be related to the distribution of BDS satellites. The CC values of signals B1 I and BIC range from-5 m to 5 m in the mid-latitude sea area and the Arctic Ocean, which means the effect of pseudorange noise is small. Moreover, as to obtain the external precise reference value for GNSS positioning in the Arctic Ocean region is difficult, it is hard to evaluate the accuracy of positioning results. An improved isotropy-based protection level method based on Receiver Autonomous Integrity Monitoring is proposed in the paper, which adopts median filter to smooth the gross errors to assess the precision and reliability of PPP in the Arctic Ocean. At first, the improved algorithm is verified with the data from the International GNSS Service Station Tixi. Then the accuracy of BDS3 PPP in the Arctic Ocean is calculated based on the improved algorithm. Which shows that the kinematic accuracy of PPP can reach the decimeter level in both the horizontal and vertical directions, and it meets the precision requirements of maritime navigation.

Comparison of availability and reliability among different combined-GNSS/RNSS precise point positioning

With emergence of the BeiDou Navigation Satellite System(BDS), the Galileo Satellite Navigation System(Galileo), the Quasi-Zenith Satellite System(QZSS)and the restoration of the Global Navigation Satellite System(GLONASS), the single Global Positioning System(GPS) has been gradually expanded into multiple global and regional navigation satellite systems(multi-GNSS/RNSS). In view of differences in these 5 systems, a consolidated multi-GNSS/RNSS precise point positioning(PPP) observation model is deduced in this contribution. In addition, the performance evaluation of PPP for multi-GNSS/RNSS is conducted using a large number of the multi-GNSS experiment(MGEX) station datasets. Experimental results show that multi-GNSS/RNSS can guarantee plenty of visible satellites effectively. Compared with single-system GPS, PDOP, HDOP, and VDOP values of the multi-GNSS/RNSS are improved by 46.8%, 46.5% and 46.3%, respectively. As for convergence time, the static and kinematic PPP of multi-GNSS/RNSS are superior to that of the single-system GPS, whose reliability, availability, and stability drop sharply with the increasing elevation cutoff. At satellite elevation cutoff of 40 °, the single-system GPS fails to carry out continuous positioning because of the insufficient visible satellites, while the multi-GNSS/RNSS PPP can still get positioning solutions with relatively high accuracy, especially in the horizontal direction.

Impact of Tropospheric Delay Gradients on Total Tropospheric Delay and Precise Point Positioning

GPS signals are electromagnetic waves that are affected by the Earth’s atmosphere. The Earth’s atmosphere can be categorized, according to its effect on GPS signals, into the ionosphere (ionospheric delay) and neutral atmosphere (tropospheric delay). The first-order ionospheric delay can be eliminated by linear combination of GPS observables on different frequencies. However, tropospheric delay cannot be eliminated because it is frequency-independent. The total tropospheric delay can be divided into three components. The first is the dry component, the second part is the wet component, and the third part is the horizontal gradients which account for the azimuthal dependence of tropospheric delay. In this paper, the effect of modeling tropospheric gradients on the estimation of the total tropospheric delay and station position is investigated. Long session, one month during January 2015, of GPS data is collected from ten randomly selected globally distributed IGS stations. Two cases are studied: the first case, the coordinates of stations are kept fixed to their actual values and the tropospheric delay is estimated twice, with and without tropospheric gradients. In the second case, the station position is estimated along with the total tropospheric delay with and without tropospheric gradients. It is shown that the average bias of the estimated total tropospheric delay when neglecting tropospheric gradients ranges from ?1.72 mm to 2.14 mm while the average bias when estimating gradients are ?0.898 mm to 1.92 mm which means that the bias is reduced by about 30%. In addition, the average standard deviation of the bias is 4.26 mm compared with 4.52 mm which means that the standard deviation is improved by about 6%.

Application of precise point positioning technology in airborne gravity measurement

The precise point positioning （PPP） technology is applied to an airborne gravity survey. By analyzing the advantages and disadvantages of several velocity and acceleration measurement methods and in combination with an actual marine gravity survey, the position difference method is confirmed to be a useful survey method for velocity and acceleration. Finally, the practicability of using PPP in airborne marine gravity survey is verified by measured data.

Performance analysis of real-time and post-mission kinematic precise point positioning in marine environments

This article focuses on the performance analysis of both real-time and post-mission kinematic precise point positioning(PPP)in challenging marine environments.For this purpose,a real dynamic experiment lasting 6 h was carried out on a lake dam in?orum City of Turkey.While the kinematic test was continuing,the real-time PPP coordinates were obtained for each measurement epoch with a commercial real-time PPP(RT-PPP)service,namely the Trimble Center Point RTX.Then the post-mission PPP(PM-PPP)coordinates were calculated by using Multi-GNSS data and the Multi-GNSS Experiment(MGEX)precise products.The kinematic RT-PPP and PM-PPP results showed that the PPP coordinates were consistent with the relative solution at centimetre and decimetre level in horizontal and height components,respectively.This study implies that PPP technique is a powerful tool for highly accurate positioning in both real-time and post-mission modes,even for dynamic applications in harsh environments.

Research trends in methods for controlling macro-micro motion platforms

With ongoing economic,scientific,and technological developments,the electronic devices used in daily lives are developing toward precision and miniaturization,and so the demand for high-precision manufacturing machinery is expanding.The most important piece of equipment in modern high-precision manufacturing is the macro-micro motion platform(M3P),which offers high speed,precision,and efficiency and has macro-micro motion coupling characteristics due to its mechanical design and composition of its driving components.Therefore,the design of the control system is crucial for the overall precision of the platform;conventional proportional–integral–derivative control cannot meet the system requirements,and so M3Ps are the subject of a growing range of modern control strategies.This paper begins by describing the development history of M3Ps,followed by their platform structure and motion control system components,and then in-depth assessments of the macro,micro,and macro-micro control systems.In addition to examining the advantages and disadvantages of current macro-micro motion control,recent technological breakthroughs are noted.Finally,based on existing problems,future directions for M3P control systems are given,and the present conclusions offer guidelines for future work on M3Ps.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic model.This study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere effect.The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model.This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions.Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE.The position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,respectively.Therefore,weight estimation with LS-VCE can provide more appropriate results.Eventually,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight.According to the results,the LS-VCE has a higher convergence rate than the nominal weight.The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

Obtaining accurate measurements of the sea surface height from a GPS buoy

A dedicated GPS buoy is designed for calibration and validation(Cal/Val)of satellite altimeters since 2014.In order to evaluate the accuracy of the sea surface height(SSH)measured by the GPS buoy,twelve campaigns have been done within China sea area between 2014 and 2021.In six of these campaigns,two static Global Navigation Satellite System stations were installed at distances of<1 km and 19 km from the buoy to assess how the baseline length influenced the derived SSH from the buoy solutions.The GPS buoy data was processed using the GAMIT/GLOBK software+TRACK module and CSRS-PPP tool to achieve the SSH.The SSH was compared with conventionally tide gauge(TG)data to evaluate the accuracy of the buoy with the standard deviation of the height element.The results showed that the difference in the standard deviation of the SSH from the buoy and the TG was less than 16 mm.The SSHs processed with different ephemeris(Ultra-Rapid,Rapid,Final)were not significantly different.When the baseline length was 19 km,the SSH solution of the GPS buoy performed well,with standard bias of less than 26 mm between the heights measured by the buoy and TG,meaning that the buoy could be used for Cal/Val of altimeters.The bias between the Canadian Spatial Reference System-precise point positioning tool and the TRACK varied a lot,and some of them were over 130 mm.This deemed too high to be useful for Cal/Val of satellite altimeters.Moreover,the GPS buoy solutions processed by GAMIT/GLOBK software+TRACK module were used for in-orbit Cal/Val of HY-2B/C satellites in ten campaigns.The SSH and significant wave height of the altimeters showed good agreements with the GPS buoy solutions.

Status of UnDifferenced and Uncombined GNSS Data Processing Activities in China

With the continued development of multiple Global Navigation Satellite Systems(GNSS)and the emergence of various frequencies,UnDifferenced and UnCombined(UDUC)data processing has become an increasingly attractive option.In this contribution,we provide an overview of the current status of UDUC GNSS data processing activities in China.These activities encompass the formulation of Precise Point Positioning(PPP)models and PPP-Real-Time Kinematic(PPP-RTK)models for processing single-station and multi-station GNSS data,respectively.Regarding single-station data processing,we discuss the advancements in PPP models,particularly the extension from a single system to multiple systems,and from dual frequencies to single and multiple frequencies.Additionally,we introduce the modified PPP model,which accounts for the time variation of receiver code biases,a departure from the conventional PPP model that typically assumes these biases to be time-constant.In the realm of multi-station PPP-RTK data processing,we introduce the ionosphere-weighted PPP-RTK model,which enhances the model strength by considering the spatial correlation of ionospheric delays.We also review the phase-only PPP-RTK model,designed to mitigate the impact of unmodelled code-related errors.Furthermore,we explore GLONASS PPP-RTK,achieved through the application of the integer-estimable model.For large-scale network data processing,we introduce the all-in-view PPP-RTK model,which alleviates the strict common-view requirement at all receivers.Moreover,we present the decentralized PPP-RTK data processing strategy,designed to improve computational efficiency.Overall,this work highlights the various advancements in UDUC GNSS data processing,providing insights into the state-of-the-art techniques employed in China to achieve precise GNSS applications.

Design and Dynamic Modeling of a 2-DOF Decoupled Flexure-Based Mechanism

Flexure mechanisms with decoupled characteristics have been widely utilized in precision positioning applications.However,these mechanisms suffer from either slow response or low load capability.Furthermore,asymmetric design always leads to thermal error.In order to solve these issues,a novel 2-DOF decoupled mechanism is developed by monolithically manufacturing sets of statically indeterminate symmetric（SIS） flexure structures in parallel.Symmetric design helps to eliminate the thermal error and Finite Element Analysis（FEA） results show that the maximum coupling ratio between X and Y axes is below 0.25% when a maximum pretension force of 200 N is applied.By ignoring the mass effect,all the SIS flexure structures are simplified to ＂spring-damper＂ components,from which the static and dynamics model are derived.The relation between the first resonant frequency of the mechanism and the load is investigated by incorporating the load mass into the proposed dynamics model.Analytical results show that even with a load of 0.5 kg,the first resonant frequency is still higher than 300 Hz,indicating a high load capability.The mechanism＇s static and dynamic performances are experimentally examined.The linear stiffnesses of the mechanism at the working platform and at the driving point are measured to be 3.563 0 N·μm-1 and 3.362 1 N·μm-1,respectively.The corresponding estimation values from analytical models are 3.405 7 N·μm-1 and 3.381 7 N·μm-1,which correspond to estimation errors of-4.41% and 0.6%,respectively.With an additional load of 0.16 kg,the measured and estimated first resonant frequencies are 362 Hz and 365 Hz,respectively.The estimation error is only 0.55%.The analytical and experimental results show that the developed mechanism has good performances in both decoupling ability and load capability;its static and dynamic performance can be precisely estimated from corresponding analytical models.The proposed mechanism has wide potentials in precision positioning applications.

Friction identification and compensation design for precision positioning

Precision positioning systems driven by linear motors are vulnerable to force disturbances owing to the reduction of gear transmission. The friction, included in the disturbance, can be modeled and compensated to improve the servo performance. This paper proposes a modified Stribeck friction model （SFM） and an optimization algorithm for consistency with the positioning platform. The compensators based on the friction model and disturbance observer （DOB） are simulated. The simulation results show that as compared with the DOB compensator （the velocity recovers by 5.19%）, the friction model based compensator （the velocity recovers by 10.66%） exhibits a better performance after adding the disturbance. Moreover, compensation comparisons among the Coulomb friction, traditional SFM, and modified SFM are performed. The experimental results show that the following error with modified SFM compensation improves by 67.67% and 51.63% at a speed of 0.005 m/s and 0.05 m/s, compared with the Coulomb friction compensation. This demonstrates that the proposed model, optimization algorithm, and compensator can reduce the following error effectively.

Stochastic Analysis of Low-Cost Single-Frequency GPS Receivers

Typically, dual-frequency geodetic grade GNSS receivers are utilized for positioning applications that require high accuracy. Single-frequency high grade receivers can be used to minimize the expenses of such dual-frequency receivers. However, user has to consider the resultant positioning accuracy. Since the evolution of low-cost single-frequency (LCSF) receivers is typically cheaper than single-frequency high grade receivers, it is possible to obtain comparable positioning accuracy if the corresponding observables are accurately modelled. In this paper, two LCSF GPS receivers are used to form short baseline. Raw GPS measurements are recorded for several consecutive days. The collected data are used to develop the stochastic model of GPS observables from such receivers. Different functions are tested to determine the best fitting model which is found to be 3 parameters exponential decay function. The new developed model is used to process different data sets and the results are compared against the traditional model. Both results from the newly developed and the traditional models are compared with the reference solution obtained from dual-frequency receiver. It is shown that the newly developed model improves the root-mean-square of the estimated horizontal coordinates by about 10% and improves the root-mean-square of the up component by about 39%.