Instantaneous BeiDou–GPS attitude determination: A performance analysis

The advent of modernized and new global navigation satellite systems (GNSS) has enhanced the availability of satellite based positioning, navigation, and timing (PNT) solutions. Specifically, it increases redundancy and yields operational back-up or independence in case of failure or unavailability of one system. Among existing GNSS, the Chinese BeiDou system (BDS) is being developed and will consist of geostationary (GEO) satellites, inclined geosynchronous orbit (IGSO) satellites, and medium-Earth-orbit (MEO) satellites. In this contribution, a BeiDou–GPS robustness analysis is carried out for instantaneous, unaided attitude determination.     

Determination of station positions and velocities from laser ranging observations to Ajisai,Starlette and Stella satellites

The positions and velocities of the four Satellite Laser Ranging (SLR) stations: Yarragadee (7090), Greenbelt (7105), Graz (7839) and Herstmonceux (7840) from 5-year (2001–2005) SLR data of low orbiting satellites (LEO): Ajisai, Starlette and Stella were determined. The orbits of these satellites were computed from the data provided by 20 SLR stations. All orbital computations were performed by means of NASA Goddard’s GEODYN-II program. The geocentric coordinates were transformed to the topocentric North–South, East–West and Vertical components in reference to ITRF2005. The influence of the number of normal points per orbital arc and the empirical acceleration coefficients on the quality of station coordinates was studied. To get standard deviation of the coordinates determination lower than 1 cm, the number of the normal points per site had to be greater than 50. The computed positions and velocities were compared to those derived from LAGEOS-1/LAGEOS-2 data. Three parameters were used for this comparison: station coordinates stability, differences from ITRF2005 positions and velocities. The stability of coordinates of LEO satellites is significantly worse (17.8 mm) than those of LAGEOS (7.6 mm), the better results are for Ajisai (15.4 mm) than for Starlette/Stella (20.4 mm). The difference in positions between the computed values and ITRF2005 were little bit worse for Starlette/Stella (6.6 mm) than for LAGEOS (4.6 mm), the results for Ajisai were five times worse (29.7 mm) probably due to center of mass correction of this satellite. The station velocities with some exceptions were on the same level (≈1 mm/year) for all satellites. The results presented in this work show that results from Starlette/Stella are better than those from Ajisai for station coordinates determination. We can applied the data from LEO satellites, especially Starlette and Stella for determination of the SLR station coordinates but with two times lower accuracy than when using LAGEOS data.     

基于GNSS的高轨卫星定位技术研究

利用全球卫星导航系统(GNSS)进行导航定位具有全球、全天候、实时和高精度的优点,应用于高地球轨道(HEO)卫星的定位,能够提供精确的轨道和姿态确定,并且可以克服目前主要利用地面测控系统对HEO卫星进行定位的设备复杂、投资高等缺点,使得自主导航成为可能.本文对利用GNSS的高轨卫星定位相关技术进行了研究,分析了单一GNSS系统和多个GNSS组合系统的卫星可见性、动态性和几何精度因子(GDOP).通过仿真分析表明,利用组合GNSS系统并通过提高GNSS接收机灵敏度的方法,可以解决GNSS进行HEO卫星定位的相关问题,并能保证HEO卫星定位精度的要求.      

Iridium/ORBCOMM机会信号融合定位技术

在全球导航卫星系统(GNSS)不可用情况下，低地球轨道(LEO)卫星机会信号(SOP)定位技术是一种有效的导航定位解决方案。单LEO星座机会信号定位技术面临星座构型不足或可见卫星偏少等问题，多LEO星座机会信号融合定位技术可有效解决该问题。通过分析瞬时多普勒定位原理，建立了Iridium/ORBCOMM机会信号融合定位模型，引入基于Helmert方差估计的加权最小二乘算法进一步提高定位精度。实测数据表明:基于Helmert方差估计的Iridium/ORBCOMM机会信号融合定位精度优于70 m，验证了多LEO星座机会信号融合定位的可行性和有效性。      

基于帝国竞争优化的双目标综合决策选星算法

全球卫星导航系统（GNSS）的应用前景已经得到世界各国的普遍承认,其应用领域也趋于多样化,在此背景下,卫星接收机也要求其具有更快的解算速度和可靠的精度。针对目前多数接收机的选星算法都是固定选星数目从而限制算法机动性的问题,提出基于帝国竞争优化算法（ICA）的双目标综合决策选星算法。为了更好获取几何构型较好的卫星星座,引入可见卫星的卫星仰角和方向角先验信息,进行先验性约束,通过构建几何精度因子（GDOP）以及选星数目2个目标,进行综合决策的快速选星,提高了选星的灵活度,并且在满足用户精度的要求下减轻了多星座卫星接收机的计算负担。通过仿真实验和实测数据对双目标综合决策选星算法验证的结果表明:所提算法在高度截止角5°下引入先验性约束条件后平均选星数目在仿真数据和实测数据中缩减率分别为51.8%和45.4%,平均GDOP值较无约束下分别减少0.209 2和0.248 4。同时,所提算法单次选星平均耗时分别为0.168 4 s和0.303 1 s,与遍历法的选星耗时4 s相比,提高了95.79%和92.42%。      

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.     

Analysis of GNSS clock prediction performance with different interrupt intervals and application to real-time kinematic precise point positioning

Continuous and timely real-time satellite orbit and clock products are mandatory for real-time precise point positioning (RT-PPP). Real-time high-precision satellite orbit and clock products should be predicted within a short time in case of communication delay or connection breakdown in practical applications. For prediction, historical data describing the characteristics of the real-time orbit and clock can be used as the basis for performing the prediction. When historical data are scarce, it is difficult for many existing models to perform precise predictions. In this paper, a linear regression model is used to predict clock products. Seven-day GeoForschungsZentrum (GFZ) final clock products sampled at 30 s are used to analyze the characteristics of GNSS clocks. It is shown that the linear regression model can be used as the prediction model for the satellite clock products. In addition, the accuracy of the clock prediction for different satellites are analyzed using historical data with different periods (such as 2 and 10 epochs). Experimental results show that the accuracy of the clock with the linear regression prediction model using historical data with 10 epochs is 1.0 ns within 900 s. This is higher accuracy than that achieved using historical data of 2 epochs. Finally, the performance analysis for real-time kinematic precise point positioning (PPP) is provided using GFZ final clock prediction results and state space representation (SSR) clock prediction results when communication delay or connection breakdown occur. Experimental results show that the positioning accuracy without prediction is better than that with prediction in general, whether using the final clock product or the SSR clock product. For the final clock product, the positioning accuracy in the north (N), east (E), and up (U) directions is better than 10.0 cm with all visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 15.0 cm to 7.0 cm. For the SSR clock product, the positioning accuracy of N, E, and U directions is better than 12.0 cm with visible GNSS satellites with prediction. In comparison, the 3D positioning accuracy of N, E, and U directions with visible GNSS satellites whose prediction accuracy is better than 0.1 ns using historical data of 10 epochs is improved from 12.0 cm to 9.0 cm.     

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.     

关于北斗卫星导航系统的被动式定位算法比较研究

我国北斗卫星导航系统空间卫星共有2或3颗,无法单独满足被动导航定位的要求．针对这种卫星稀少的情况提出了3种被动式定位算法: 2星定位算法、 3星3参数定位算法和3星4参数定位算法, 这些算法分别采用气压测高方法增加观测数据和采用数学模型描述接收机钟差的方法减少定位方程求解的未知数;探讨了北斗卫星导航系统备份星的可用性和对导航定位精度的贡献;还提出了准差分修正技术,提高了定位精度．实验证明, 3种算法都取得了100m以内的定位结果,可以满足一般用户定位需求．     

Evaluation of COMPASS ionospheric model in GNSS positioning

As important products of GNSS navigation message, ionospheric delay model parameters are broadcasted for single-frequency users to improve their positioning accuracy. GPS provides daily Klobuchar ionospheric model parameters based on geomagnetic reference frame, while the regional satellite navigation system of China’s COMPASS broadcasts an eight-parameter ionospheric model, COMPASS Ionospheric Model(CIM), which was generated by processing data from continuous monitoring stations, with updating the parameters every 2 h. To evaluate its performance, CIM predictions are compared to ionospheric delay measurements, along with GPS positioning accuracy comparisons. Real observed data analysis indicates that CIM provides higher correction precision in middle-latitude regions, but relatively lower correction precision for low-latitude regions where the ionosphere has much higher variability. CIM errors for some users show a common bias for in-coming COMPASS signals from different satellites, and hence ionospheric model errors are somehow translated into the receivers’ clock error estimation. In addition, the CIM from the China regional monitoring network are further evaluated for global ionospheric corrections. Results show that in the Northern Hemisphere areas including Asia, Europe and North America, the three-dimensional positioning accuracy using the CIM for ionospheric delay corrections is improved by 7.8%–35.3% when compared to GPS single-frequency positioning ionospheric delay corrections using the Klobuchar model. However, the positioning accuracy in the Southern Hemisphere is degraded due apparently to the lack of monitoring stations there.     

Demonstration of a high sensitivity GNSS software receiver for indoor positioning

Advances in signal processing techniques contributed to the significant improvements of GNSS receiver performance in dense multipath environments and created the opportunities for a new category of high-sensitivity GNSS (HS-GNSS) receivers that can provide GNSS location services in indoor environments. The difficulties in improving the availability, reliability, and accuracy of these indoor capable GNSS receivers exceed those of the receivers designed for the most hostile urban canyon environments. The authors of this paper identified the vector tracking schemes, signal propagation statistics, and parallel processing techniques that are critical to a robust HS-GNSS receiver for indoor environments and successfully incorporated them into a fully functional high-sensitivity software receiver. A flexible vector-based receiver architecture is introduced to combine these key indoor signal processing technologies into GSNRx-hs™ – the high sensitivity software navigation receiver developed at the University of Calgary. The resulting receiver can perform multi-mode vector tracking in indoor environment at various levels of location and timing uncertainties. In addition to the obvious improvements in time-to-first-fix (TTFF) and signal sensitivity, the field test results in indoor environments surrounded by wood, glass, and concrete showed that the new techniques effectively improved the performance of indoor GNSS positioning. With fine GNSS timing, the proposed receiver can consistently deliver indoor navigation solution with the horizontal accuracy of 2–15 m depending on the satellite geometry and the indoor environments. If only the coarse GNSS timing is available, the horizontal accuracy of the indoor navigation solution from the proposed receiver is around 30 m depending on the coarse timing accuracy, the satellite geometry, and the indoor environments. From the preliminary field test results, it has been observed that the signal processing sensitivity is the dominant factor on the availability of the indoor navigation solution, while the GNSS timing accuracy is the dominant factor on the accuracy of the indoor navigation solution.     

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.     

A null frame for spacetime positioning by means of pulsating sources

We introduce an operational approach to the use of pulsating sources, located at spatial infinity, for defining a relativistic positioning and navigation system, based on the use of four-dimensional bases of null four-vectors, in flat spacetime. As a prototypical case, we show how pulsars can be used to define such a positioning system. The reception of the pulses for a set of different sources whose positions in the sky and periods are assumed to be known allows the determination of the user’s coordinates and spacetime trajectory, in the reference frame where the sources are at rest. We describe our approach in flat Minkowski spacetime, and discuss the validity of this and other approximations we have considered.     

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.     

Stochastic modelling considering ionospheric scintillation effects on GNSS relative and point positioning

Global Navigation Satellite Systems (GNSS), in particular the Global Positioning System (GPS), have been widely used for high accuracy geodetic positioning. The Least Squares functional models related to the GNSS observables have been more extensively studied than the corresponding stochastic models, given that the development of the latter is significantly more complex. As a result, a simplified stochastic model is often used in GNSS positioning, which assumes that all the GNSS observables are statistically independent and of the same quality, i.e. a similar variance is assigned indiscriminately to all of the measurements. However, the definition of the stochastic model may be approached from a more detailed perspective, considering specific effects affecting each observable individually, as for example the effects of ionospheric scintillation. These effects relate to phase and amplitude fluctuations in the satellites signals that occur due to diffraction on electron density irregularities in the ionosphere and are particularly relevant at equatorial and high latitude regions, especially during periods of high solar activity. As a consequence, degraded measurement quality and poorer positioning accuracy may result.     

基于三频数据的北斗卫星导航系统DCB参数精度评估方法

差分码偏差（Differential Code Biases,DCB）参数作为导航电文中重要的一项,是影响用户PNT服务的主要误差源之一。北斗卫星导航系统（后文简称“北斗系统”）发射三个频点的导航信号,在导航电文中需要发播卫星的2个TGD（Timing Group Delay）参数。文章首先介绍了北斗系统卫星DCB参数最小二乘解算与形式误差评估;其次根据北斗系统三频特点,提出了不同频点组合计算垂直方向电离层电子总含量（VTEC）互差的DCB精度定量评估方法,并与IGS(International GNSS Service)提供的GPS卫星DCB精度进行比较;最后,详细分析了DCB参数精度对用户等效距离误差（UERE）计算和定位计算的影响,分别采用卫星出场标定DCB参数和经过解算DCB参数进行评估。实测数据分析结果表明,北斗系统卫星DCB参数解算形式误差与IGS解算GPS卫星DCB参数形式误差相当,但受卫星类型和解算测站的几何分布限制,北斗系统卫星DCB参数解算不确定度相比IGS略差,估计精度优于0.5ns,不同频率组合计算VTEC互差绝对值均值优于0.6TECU。相比采用卫星出场标定值,采用系统解算DCB参数后,双频用户三维位置误差改善13.80%～47.42%。     

Minimum of PDOP and its applications in inter-satellite links (ISL) establishment of Walker-δ constellation

Within the next decade, there will be a number of GNSS (Global Navigation Satellite System) available, i.e. modernized GPS, Galileo, restored GLONASS, BeiDou and many other regional GNSS augmentation systems. Thus, measurement redundancies and geometry of the satellites can be improved. GDOP (Geometric Dilution of Precision) and PDOP (Position Dilution of Precision) are associated with the constellation geometry of satellites, and they are the geometrically determined factors that describe the effect of geometry on the relationship between measurement error and position error. GDOP and PDOP are often used as standards for selecting good satellites to meet the desired positioning precision. In this paper, the related conclusions of minimum of GDOP which was discussed are given, and it is used to study the minimum of PDOP for two cases that the receiver is on the earth’s surface and the receiver is on satellite. The corresponding theorem and constructive solutions of minimum of PDOP are given. Then, the rationality of the ISL (inter-satellite link) establishment criteria in Walker-δ constellation is discussed by using the theory of minimum of PDOP. Finally, the minimum of PDOP is calculated when the number of satellites is 4–10, and these results are verified by using Monte Carlo method.     

Guidepost-based autonomous orbit determination method for GEO satellite

Guidepost-based navigation system is a novel autonomous orbit determination method for the GEO satellite. The system is achieved by using the camera imaging function to obtain the guidepost images and the GNSS signal receiver to obtain the pseudoranges between the GEO and the navigation satellites. Due to the high altitude of GEO satellite and the time-varying sunlight condition in the space environment, it may be difficult to obtain object image points and the distance measurements of GNSS because of the weak visibility of the guideposts. To deal with the problem, a novel integrated orbit determination system is presented. The Earth landmarks, the in-orbit spacecraft and GNSS navigation satellites whose line-of-sights and the distance can be easily obtained are used at the same time as information for the GEO satellite navigation based on the observability conditions analysis. The observability of the GEO satellite navigation system is analyzed through the physical observability, the mathematical observability and the engineering observability through the observing geometry, the rank of observability matrix and the Cramer-Rao lower bound (CRLB) respectively. Besides, the maximum correntropy unscented Kalman filter (MCUKF) algorithm is applied to improve the estimation stability of the system in the presence of non-Gaussian noises. The simulation indicates the feasibility of the proposed scheme.     

基于低轨稀疏星座的蓝绿激光对潜定位研究

潜艇只在必要时刻才浮出水面，对实时通信和导航定位造成极大制约。蓝绿激光具有深水穿透性高、衰减系数低等优势，已在机载和星载平台对潜艇通信中得到验证。借鉴GNSS导航信号产生原理，结合蓝绿激光通信测距一体化与低轨卫星自身精密定轨，提出了基于蓝绿激光通信的低轨卫星对潜定位算法。通过在激光通信中增加载波相位调制，实现潜艇激光接收器的伪距测量，联合其高程测量信息实现水下定位。以一带一路海域，特别是中国南海区域为服务对象，优化星座参数设计了3颗卫星组成的低轨稀疏星座。潜艇在星座覆盖区域内保持静态，间隔1~3min完成至少两次通信测距和导航电文接收，联合两组观测数据、精密星历及高程测量信息进行定位解算。仿真结果显示，在卫星过境期间，考虑卫星定轨精度，激光在空气、水下传播误差等因素，潜艇可在水下实现X、Z方向定位误差优于100m，Y方向误差约100~150m的高精度定位，对提升潜艇的战场作战能力具有意义。     

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.