An optimized ion trap geometry to measure quadrupole shifts of ^(171)Yb~＋ clocks

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the （171）Yb ion.This trap will minimize the quadrupole shift due to the harmonic component of the confining potential by an order of magnitude.This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s 2S（1/2）→4f（13）6s2 2F（7/2）and 6s 2S（1/2）→5d2D（3/2） transitions,from which we can deduce the precise values of the quadrupole moments（0s） of the 4f（13）6s2 2F（7/2） and 5d2D（3/2） states.Moreover,it may be able to affirm the validity of the measured 0 value of the4f（13）6s22F（7/2） state,for which three independent theoretical studies defer almost by one order of magnitude from the measurement.We also calculate 0s using the relativistic coupled-cluster（RCC） method.We use these 0 values to estimate the quadrupole shift that can be measured in our proposed ion trap experiment.

Impact of Sampling Rate of IGS Satellite Clock on Precise Point Positioning

Both static and kinematic testings are investigated by using IGS 5rain, 30s and 5s-interval precise satellite clock prod- ucts in precise point positioning （PPP） solution. Test results show that the sampling rate oflGS satellite clock has very little effect on the static PPP solution. All the three types of sampling intervals of precise satellite clock can satisfy mm-cm level of positioning accuracy; higher sampling rate has no significant improvement for PPP solution. However, sampling rate of satellite clock has a significant impact on the PPP solution in kinematic PPP. The higher the interval of satellite clock, the better the accuracy achieved. The accuracy of kinematic PPP achieved by using 30s-interval precise satellite clock is improved by nearly 30-50 percent with re- spect to the solution by using 5min-interval precise satellite clock, but using 5s and 30s-interval satellite clock can almost produce the same accuracy of kinematic solution. Moreover, the use of precise satellite clock products from different analysis centers may also produce more or less effect on the PPP solution.

A square root information filter for multi-GNSS real-time precise clock estimation

Real-time satellite orbit and clock estimations are the prerequisite for Global Navigation Satellite System(GNSS)real-time precise positioning services.To meet the high-rate update requirement of satellite clock corrections,the computational efficiency is a key factor and a challenge due to the rapid development of multi-GNSS constellations.The Square Root Information Filter(SRIF)is widely used in real-time GNSS data processing thanks to its high numerical stability and computational efficiency.In real-time clock estimation,the outlier detection and elimination are critical to guarantee the precision and stability of the product but could be time-consuming.In this study,we developed a new quality control procedure including the three standard steps:i.e.,detection,identification,and adaption,for real-time data processing of huge GNSS networks.Effort is made to improve the computational efficiency by optimizing the algorithm to provide only the essential information required in the processing,so that it can be applied in real-time and high-rate estimation of satellite clocks.The processing procedure is implemented in the PANDA(Positioning and Navigation Data Analyst)software package and evaluated in the operational generation of real-time GNSS orbit and clock products.We demonstrated that the new algorithm can efficiently eliminate outliers,and a clock precision of 0.06 ns,0.24 ns,0.06 ns,and 0.11 ns can be achieved for the GPS,GLONASS,Galileo,and BDS-2 IGSO/MEO satellites,respectively.The computation time per epoch is about 2 to 3 s depending on the number of existing outliers.Overall,the algorithm can satisfy the IGS real-time clock estimation in terms of both the computational efficiency and product quality.

GSTAR:an innovative software platform for processing space geodetic data at the observation level

To meet the demands for the data combination with multiple space geodetic techniques at the observation level,we developed a new software platform with high extensibility and computation efficiency,named space Geodetic SpatioTemporal data Analysis and Research software(GSTAR).Most of the modules in the GSTAR are coded in C++with object-oriented programming.The layered modular theory is adopted for the design of the software,and the antenna-based data architecture is proposed for users to construct personalized geodetic application scenarios easily.The initial performance of the GSTAR software is evaluated by processing the Global Navigation Satellite System(GNSS)data collected from 315 globally distributed stations over two and a half years.The accuracy of GNSS-based geodetic products is evaluated by comparing them with those released by International GNSS Service(IGS)Analysis Centers(AC).Taking the products released by European Space Agency(ESA)as reference,the Three-Dimension(3D)Root-Mean-Squares(RMS)of the orbit differences are 2.7/6.7/3.3/7.7/21.0 cm and the STandard Deviations(STD)of the clock differences are 19/48/16/32/25 ps for Global Positioning System(GPS),GLObal NAvigation Satellite System(GLONASS),Galileo navigation satellite system(Galileo),BeiDou Navigation Satellite System(BDS),Medium Earth Orbit(MEO),and BDS Inclined Geo-Synchronous Orbit(IGSO)satellites,respectively.The mean values of the X and Y components of the polar coordinate and the Length of Day(LOD)with respect to the International Earth Rotation and Reference Systems Service(IERS)14 C04 products are-17.6 microarc-second(μas),9.2μas,and 14.0μs/d.Compared to the IGS daily solution,the RMSs of the site position differences in the north/east/up direction are 1.6/1.5/3.9,3.8/2.4/7.6,2.5/2.4/7.9 and 2.7/2.3/7.4 mm for GPS-only,GLONASS-only,Galileo-only,and BDS-only solution,respectively.The RMSs of the differences of the tropospheric Zenith Path Delay(ZPD),the north gradients,and the east gradients are 5.8,0.9,and 0.9 mm with respect to the IGS products.The X and Y components of the geocenter motion estimated from GPS-only,Galileo-only,and BDS-only observations well agree with IGS products,while the Z component values are much nosier where anomalous harmonics in GNSS draconitic year can be found.The accuracies of the above products calculated by the GSTAR are comparable with those from different IGS ACs.Compared to the precise scientific orbit products,the 3D RMS of the orbit differences for the two Gravity Recovery and Climate Experiment Follow-on(GRACE-FO)satellites is below 1.5 cm by conducting Precise Point Positioning with Ambiguity Resolution(PPP-AR).In addition,a series of rapid data processing algorithms are developed,and the operation speed of the GSTAR software is 5.6 times faster than that of the Positioning and Navigation Data Analyst(PANDA)software for the quad-system precise orbit determination procedure.

Principle and performance of BDSBAS and PPP-B2b of BDS-3

Within the framework of diferential augmentation,this paper introduces the basic technical framework and performance of the BeiDou Global Navigation Satellite System(BDS-3)Satellite-Based Augmentation System(BDSBAS),including orbit products,satellite clock ofset products,ionosphere and its integrity performance.The basic principle of BDS-3 Precise Point Positioning(PPP-B2b)is expounded,the similarities and diferences between the PPP service provided by BDS-3 and International Global Navigation Satellite System(GNSS)Service(IGS)are discussed,and the limitations of PPP-B2b are analyzed.Since both the BDSBAS and PPP-B2b utilize a ground monitoring station network to determine the satellite orbits and clock ofset corrections,and broadcast diferential corrections through the three Geostationary Orbit(GEO)satellites of BDS-3,the feasibility of the co-construction of BDSBAS and PPP-B2b is analyzed,strategies for the infrastructure sharing and correction broadcasting are presented,and the infuences of BDSBAS correction broadcasting strategy adjustment are evaluated.In addition,it assesses the possibility of broadcasting diferential corrections through the Inclined Geosynchronous Orbit(IGSO)satellites of BDS-3,and the feasibility of augmenting satellite navigation with Low Earth Orbit(LEO)satellites.

Multi-GNSS products and services at iGMAS Wuhan Innovation Application Center:strategy and evaluation

Over the past years the International Global Navigation Satellite System(GNSS)Monitoring and Assessment System(iGMAS)Wuhan Innovation Application Center(IAC)dedicated to exploring the potential of multi-GNSS signals and providing a set of products and services.This contribution summarizes the strategies,achievements,and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC.Both the precise products and Real-Time Services(RTS)are evaluated and discussed.The precise orbit and clock products have comparable accuracy with the precise products of the International GNSS Service(IGS)and iGMAS.The multi-frequency code and phase bias products for Global Positioning System(GPS),BeiDou Navigation Satellite System(BDS),Galileo navigation satellite system(Galileo),and GLObal NAvigation Satellite System(GLONASS)are provided to support multi-GNSS and multi-frequency Precise Point Positioning(PPP)Ambiguity Resolution(AR).Compared with dual-frequency PPP AR,the time to first fix of triple-frequency solution is improved by 30%.For RTS,the proposed orbit prediction strategy improves the three dimensional accuracy of predicted orbit by 1 cm.The multi-thread strategy and high-performance matrix library are employed to accelerate the real-time orbit and clock determination.The results with respect to the IGS precise products show the high accuracy of RTS orbits and clocks,4–9 cm and 0.1–0.2 ns,respectively.Using real-time satellite corrections,real-time PPP solutions achieve satisfactory performance with horizontal and vertical positioning errors within 2 and 4 cm,respectively,and convergence time of 16.97 min.

Closely interleaved self-comparison method applied to precise measurement

A self-comparison method with closely interleaved switching states is analyzed and used to evaluate some type-B uncertainties of an ^87Rb atomic fountain clock. Free from additional frequency reference, the method can be applied to a running fountain to reach a precision beyond its uncertainty. A verification experiment proves an uncertainty of 9.2 × 10^-16 at an averaging time of 242500 s. Further, the method is applied to measure light shift, and no visible relative frequency shift is found in the fountain within the uncertainty of 2.1 × 10^-15. When applied to the evaluation of a cold collisional shift, the result gives a -2.2 × 10^-15 shift with a 9.5 × 10^-16 uncertainty.