Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals

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

Testing the no-hair theorem with observations of black holes in the electromagnetic spectrum

According to the no-hair theorem, astrophysical black holes are uniquely described by their mass and spin. In this paper, we review a new framework for testing the no-hair hypothesis with observations in the electromagnetic spectrum. The approach is formulated in terms of a Kerr-like spacetime containing a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation from the Kerr metric quadrupole has to be zero. We show how upcoming VLBI imaging observations of Sgr A∗ as well as spectroscopic observations of iron lines from accreting black holes with IXO may lead to the first astrophysical test of the no-hair theorem.     

A novel predictive algorithm for double difference observations of obstructed BeiDou geostationary earth orbit (GEO) satellites

Transmission link disturbances and device failure cause global navigation satellite system (GNSS) receivers to miss observations, leading to poor accuracy in real-time kinematic (RTK) positioning. Previously described solutions for this problem are influenced by the length of the prediction period, or are unable to account for changes in receiver state because they use information from previous epochs to make predictions. We propose an algorithm for predicting double difference (DD) observations of obstructed BeiDou navigation system (BDS) GEO satellites. Our approach adopts the first-degree polynomial function for predicting missing observations. We introduce a Douglas-Peucker algorithm to judge the state of the rover receiver to reduce the impact of predictive biases. Static and kinematic experiments were carried out on BDS observations to evaluate the proposed algorithm. The results of our navigation experiment demonstrate that RTK positioning accuracy is improved from meter to decimeter level with fixed ambiguity (horizontal?<?2?cm, vertical?<?18?cm). Horizontal accuracy is improved by over 50%, and the vertical accuracies of the results of the static and kinematic experiments are increased by 47% and 27% respectively, compared with the results produced by the classical approach. Though as the baseline becomes longer, the accuracy is weakened, our predictive algorithm is an improvement over existing approaches to overcome the issue of missing data.     

Beyond Einstein: scientific goals and missions

A century ago, Albert Einstein began creating his theory of relativity, the ideas we use to understand space, time, and gravity, and he took some of the first steps towards the theory of quantum mechanics, the ideas we use to understand matter and energy. Time magazine named Einstein the “Person of the Century” because his ideas transformed civilization. But his work is not finished: spacetime is not yet reconciled with the quantum. Einstein’s general theory of relativity opened possibilities for the formation and structure of the Universe that seemed unbelievable even to Einstein himself but which have all been subsequently confirmed: that the whole Universe began in a hot, dense Big Bang from which all of space expanded; that dense matter could tie spacetime into tangled knots called black holes; and that “empty” space might contain energy with repulsive gravity. Despite these discoveries, we still do not understand conditions at the beginning of the Universe, how space and time behave at the edge of a black hole, or why distant galaxies are accelerating away from us. These phenomena represent the most extreme interactions of matter and energy with space and time. They are the places to look for clues to the next fundamental revolution in understanding – Beyond Einstein.     

Network based real-time precise point positioning

Network based real-time precise point positioning system includes two stages, i.e. real-time estimation of satellite clocks based on a reference network and real-time precise point positioning thereafter. In this paper, a satellite- and epoch-differenced approach, adopted from what is introduced by Han et al. (2001), is presented for the determination of satellite clocks and for the precise point positioning. One important refinement of our approach is the implementation of the robust clock estimation. A prototype software system is developed, and data from the European Reference Frame Permanent Network on September 19, 2009 is used to evaluate the approach. Results show that our approach is 3 times and 90 times faster than the epoch-difference approach and the zero-difference approach, respectively, which demonstrates a significant improvement in the computation efficiency. The RMS of the estimated clocks is at the level of 0.1 ns (3 cm) compared to the IGS final clocks. The clocks estimates are then applied to the precise point positioning in both kinematic and static mode. In static mode, the 2-h estimated coordinates have a mean accuracy of 3.08, 5.79, 6.32 cm in the North, East and Up directions. In kinematic mode, the mean kinematic coordinates accuracy is of 4.63, 5.82, 9.20 cm.     

Particle filter-based real-time phase line bias estimation for GNSS-based attitude determination with common-clock receivers

Global navigation satellite system (GNSS)-based attitude determination has been widely adopted in a wide variety of terrestrial, sea, air, and space applications. Recently, the emergence of commercial multi-GNSS common-clock receivers has brought new opportunities for high-precision GNSS-based attitude determination with single-differenced (SD) model. However, the key requirement of using this approach is the accurate estimation of the troublesome line bias (LB) in real-time. In this contribution, we propose a particle filter-based real-time phase LB estimation approach that apply to SD model with single-system single-frequency observations from common-clock receiver. We first analyzed the relationship between the integer ambiguity ratio value and the phase LB. It is proved that the accuracy of a given phase LB value can be qualified by the related ambiguity resolution ratio value, and the normalized ratio value can therefore be used to represent the likelihood function of observations. Then, we presented the particle filter-based real-time phase LB estimation procedure, and assessed its performance using GPS L1/BDS B1I observations from two datasets collected with different types of common-clock receivers in terms of the accuracy and convergence time of phase LB estimation, the computation load, and the positioning and attitude determination accuracy with respect to the double-differenced (DD) model. Experimental results demonstrated that the phase LB could be accurately estimated with short convergence time (generally within 15 epochs). Moreover, compared with the classical DD approach, the particle filter-based SD approach delivers comparable positioning root-mean-square (RMS) errors in the North and East components but significantly smaller RMS errors in the Up component. Accordingly, the achievable yaw accuracy is comparable whereas the pitch accuracy is remarkably improved. The improvements of positioning accuracy in the Up component and pitch accuracy are approximately 35.7 % to 63.7 %, and 33.3 % to 63.1 %, respectively. Additionally, the single-epoch computation time with our particle filter-based SD approach is generally 0.08 s, which is obviously larger than the DD approach but could still meet the requirements of real-time applications below 10 Hz sampling.     

Millimeter observations of variable radio sources in the Galactic plane

We report on multi-epoch millimeter observations of variable radio sources that were identified through the 6-cm Galactic plane survey by Gregory and Taylor. Although the aim of the original survey was to search for exotic galactic radio sources such as Cyg X-3, our multifrequency study in the past suggested that the majority of these sources are extragalactic. To explore intrinsic variability of these sources, we carried out monitoring observations at short millimeter wavelengths where the interstellar scintillation effects become less significant and stronger intrinsic variability is expected as the millimeter emission arises from deeper in the cores. Most of the observed sources show moderate degrees of millimeter variability indicating they are intrinsically variable. The spectra for some observed sources are flat out to millimeter wavelengths — similar to that of blazars. Thus the survey sample is likely to contain many unidentified radio-loud AGN behind the Milky Way.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

The quantum temperature of accelerating cosmological models of an entangled Universe

Since the conception of quantum cosmology was introduced by Lemaitre in 1931, many authors have discussed the quantum nature of the Universe. Yet the most significant new feature of quantum physics, the notion of quantum nonlocality and its verification using Earth-based experiments, is never addressed by cosmologists because they basically do not know how to deal with it. In the spirit of making the transition “from quarks to cosmos” we will demonstrate how this is done. We show how to estimate the temperature of the flat Friedmann–Lemaitre–Robertson–Walker spacetime using a spherically symmetric approximation of the metric in conjunction with Lee’s theorem for scalar quantum fields on curved backgrounds. This temperature dependence is not the same as the classical Gamow temperature which follows from general relativity for the radiation-dominated era of the Big Bang model, and we relate this result to the question of decoherence in the very early Universe.     

双星定位系统/SINS深组合导航系统研究

以卫星模拟器为基础，介绍了一种双星定位系统定姿的基本原理，解决了双星定位系统存在的位置滞后即定位实时性较差的缺陷，把双星定位系统的位置与姿态信息和捷联惯导系统的位置、姿态信息进行组合后，可有效地提高系统的精度．     

Numerical modeling of a Global Navigation Satellite System in a general relativistic framework

In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild space–time, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no a priori realization of a terrestrial reference frame. We perform a simulation of position determination and show that the determination of the four coordinates with a 25–32 digit accuracy takes only around 60 ms. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system. Effects of gravitational perturbations are omitted in this paper in order to make a clearer comparison between the relativistic and non-relativistic scheme, but they will be included in subsequent work. We believe that the final algorithm will be a serious alternative to the usual post-Newtonian scheme.     

NeQuick G model based scale factor determination for using SBAS ionosphere corrections at low earth orbit

A space-based augmentation system (SBAS) provides real-time correction data for global navigation satellite system (GNSS) users near ground. In order to use the SBAS ionosphere correction for low Earth orbit (LEO) satellites, the correction should be scaled down for the LEO altitude. This scale factor varies with ionosphere distribution and it is hard to determine the value at LEO in real time. We propose a real-time scale factor determination method by using Galileo GNSS’s NeQuick G model. A LEO satellite GPS data and SBAS data received on ground were used to evaluate the performance of the NeQuick G derived variable scale factor. The NeQuick G derived scale factor shows a significant accuracy improvement over NeQuick G model or pre-determined constant scale factor. It improves a vertical positioning accuracy of the LEO satellite. The error mean reductions of the vertical positioning over NeQuick G and the constant scale factor are 31.5% and 11.7%, respectively.     

基于ORBCOMM卫星机会信号的定位技术

为摆脱对全球导航卫星系统（GNSS）的依赖，克服其有意或无意干扰情况下无法工作等问题，可采用机会信号（SOP）实现定位，低轨卫星机会信号具备信号功率高、覆盖性广及无需增建基础设施等优点。提出了利用轨道通信卫星（ORBCOMM）系统实现天基机会信号定位。通过对ORBCOMM卫星机会信号的通信体制进行深入研究，实现了利用ORBCOMM卫星机会信号获取多普勒测量信息，建立了瞬时多普勒定位及其几何精度因子的数学模型，并采用卫星TLE数据结合轨道预测模型获得的卫星轨道信息实现ORBCOMM卫星机会信号定位。实测结果表明:利用ORBCOMM卫星机会信号可实现精度优于140 m的定位。研究成果对基于天基机会信号定位技术的理论研究及应用具有重要意义。      

GPS多径信号建模及接收机测试评估

多径信号误差是GPS(Global Positioning System)及其它卫星导航系统的重要误差源之一,有关多径建模与多径消除技术一直是卫星导航领域的研究热点.根据多径信号特性,推导了对GPS定位精度影响最大的镜面反射多径信号模型.基于这一多径模型,利用GPS软件接收机测试了多径对接收机伪距测量精度的影响.测试结果验证了所建立的多径模型的有效性,所获得的多径误差曲线为窄相关多径抑制技术提供了实验支持.     

机群组网定位的一种新途径

机群组网将成为体系对抗条件下空中行动的一种基本工作模式.提出的机群组网定位技术是基于飞行器相互测距信息优化惯导位置精度的一种新途径,可以明显提高网络节点间的时间同步水平.仿真结果表明:对一个由8架飞机组成的机群,当相互测距误差为20m(1 σ)时,经过1.5 min组网定位可将惯导水平位置误差校正到5m之内,同时将时间同步水平提高到1ms左右;经过15min组网定位可进一步估计每套惯导的误差模型参数,使纯惯导在校正后0.5 h内的定位精度提高约一个量级,达到30m(CEP,Circular Error Probability).周期性的组网定位不仅可以明显提高机群定位精度,还可识别出个别系统的软故障并加以隔离和重构.      

An improved approach to model regional ionosphere and accelerate convergence for precise point positioning

Given the severe effects of the ionosphere on global navigation satellite system (GNSS) signals, single-frequency (SF) precise point positioning (PPP) users can only achieve decimeter-level positioning results. Ionosphere-free combinations can eliminate the majority of ionospheric delay, but increase observation noise and slow down dual-frequency (DF) PPP convergence. In this paper, we develop a regional ionosphere modeling and rapid convergence approach to improve SF PPP (SFPPP) accuracy and accelerate DF PPP (DFPPP) convergence speed. Instead of area model, ionospheric delay is modeled for each satellite to be used as a priori correction. With the ionospheric, wide-lane uncalibrated phase delay (UPD) and residuals satellite DCBs product, the wide-lane observations for DF users change to be high-precision pseudorange observations. The validation of a continuously operating reference station (CORS) network was analyzed. The experimental results confirm that the approach considerably improves the accuracy of SFPPP. For DF users, convergence time is substantially reduced.     

Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.     

Near real-time PPP-based monitoring of the ionosphere using dual-frequency GPS/BDS/Galileo data

Ionosphere delay is very important to GNSS observations, since it is one of the main error sources which have to be mitigated even eliminated in order to determine reliable and precise positions. The ionosphere is a dispersive medium to radio signal, so the value of the group delay or phase advance of GNSS radio signal depends on the signal frequency. Ground-based GNSS stations have been used for ionosphere monitoring and modeling for a long time. In this paper we will introduce a novel approach suitable for single-receiver operation based on the precise point positioning (PPP) technique. One of the main characteristic is that only carrier-phase observations are used to avoid particular effects of pseudorange observations. The technique consists of introducing ionosphere ambiguity parameters obtained from PPP filter into the geometry-free combination of observations to estimate ionospheric delays. Observational data from stations that are capable of tracking the GPS/BDS/GALILEO from the International GNSS Service (IGS) Multi-GNSS Experiments (MGEX) network are processed. For the purpose of performance validation, ionospheric delays series derived from the novel approach are compared with the global ionospheric map (GIM) from Ionospheric Associate Analysis Centers (IAACs). The results are encouraging and offer potential solutions to the near real-time ionosphere monitoring.     

Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

Precise coseismic displacements from the GPS variometric approach using different precise products: Application to the 2008 MW 7.9 Wenchuan earthquake

The Global Positioning System (GPS) variometric approach has emerged as an attractive alternative to traditional well-developed positioning techniques including relative positioning and precise point positioning. Previous studies have demonstrated the capability of the variometric approach to retrieve coseismic displacements at centimeter-level precision, in a real-time manner using only readily available broadcast ephemeris. This study presents the first results comparing the performance of the variometric approach by using a variety of precise satellite orbit and clock products. Totally six kinds of products are included in our evaluation, namely the broadcast, IGS (International GNSS Service) ultra-rapid (predicted), ultra-rapid (observed), rapid, final (30-s clock) and CODE (Center for Orbit Determination in Europe) final (5-s clock) products. Static and dynamic experiments are conducted using 1-Hz GPS data covering a relatively large area in China during the 2008 Wenchuan M_W 7.9 earthquake. After removing the linear trend, the displacements using broadcast, ultra-rapid (predicted), ultra-rapid (observed) and rapid products reach nearly equivalent precisions at centimeter level. By using final and CODE final products, the precision of displacements can be significantly improved from 1.9–2.0 cm to 0.4–0.7 cm horizontally, and from 6.0–6.2 cm to 1.0–1.7 cm vertically for the dynamic experiments. The displacements using the CODE final products achieve the best precision, improved by more than 40% compared to those using the IGS final products. With the availability of IGS high-rate real-time precise products, this approach is promising to capture coseismic displacements more precisely in real time, which is crucial for earthquake and tsunami early warning.