New characteristics of weighted GDOP in multi-GNSS positioning

In positioning, navigation and timing applications of multi-GNSS (global navigation satellite system) constellations, the geometric dilution of precision (GDOP) offers an important index for selecting satellites and evaluating positioning accuracy. However, GDOP assumes that the measurement errors of all the tracked satellites are independent and have the same accuracy level, which is impossible in practice, especially when the tracked satellites are from various constellations. Through introducing a weighted matrix describing the measurement errors of different satellites into a common GDOP, we focus on new characteristics of weighted GDOP (WGDOP) in two aspects. First, we compare the sizes of WGDOP and the common GDOP based on the range of the weights of different satellites, i.e., the diagonal elements of the weighted matrix. In addition, when the weights of different satellites increase, the change of WGDOP with the weights is also derived. Moreover, a closed-form formula for calculating WGDOP is also presented. The theoretical derivations demonstrate that the closed-form can reduce the computation burden effectively. Furthermore, numerical tests verify these analyses.     

BeiDou、Galileo、GLONASS、GPS多系统融合精密单点

随着中国BeiDou系统与欧盟Galileo系统的出现以及俄罗斯GLONASS系统的恢复完善,过去单一的GPS导航卫星系统时代已经逐步过渡为多系统并存且相互兼容的全球性卫星导航系统(multi-constellation global navigation satellite systems,multi-GNSS)时代,多系统GNSS融合精密定位将成为未来GNSS精密定位技术的发展趋势。本文采用GPS、GLONASS、BeiDou、Galileo 4大卫星导航定位系统融合的精密单点定位(precise point positioning,PPP)实测数据,初步研究并分析了4系统融合PPP的定位性能。试验结果表明:在单系统观测几何构型不理想的区域,多系统融合能显著提高PPP的定位精度和收敛速度。4大系统融合的PPP收敛速度相对于单GNSS可提高30%~50%,定位精度可提高10%~30%,特别是对高程方向的贡献更为明显。此外,在卫星截止高度角大于30°的观测环境下,单系统由于可见卫星数不足导致无法连续定位,而多系统融合仍然可以获得PPP定位结果,尤其是水平方向具有较高的定位精度。这对于山区、城市以及遮挡严重的区域具有非常重要的应用价值。     

GPS,Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.     

基于组合卫星导航系统的编队卫星分析

针对编队飞行中星间相对定位的任务需求,分析了卫星导航系统对编队卫星的动态观测几何问题,引入了相对定位精度衰减因子(RDOP)描述,并讨论了其性质。在对编队中单颗低轨卫星进行导航卫星GDOP分析的基础上,研究了不同编队宽度下编队集合的共视卫星和共视时段,仿真了一定场景下的编队卫星RDOP,并比较了与PDOP的大小关系。接收机的截止高度角对于导航卫星GDOP影响较大;编队宽度会影响到共视卫星的选择;而与采用单个GPS系统相比,采用GPS-Galileo组合卫星导航系统对编队卫星进行相对定位,RDOP数值明显减小,从而有利于高精度的星间位置确定。     

单频到五频多系统GNSS精密单点定位参数估计与应用

全球导航卫星系统(GNSS)已发展至多频多系统时代,特别以我国北斗卫星导航系统(BDS)为代表的四大全球导航卫星系统可全天时、全天候播发十几个频率的伪距、相位和多普勒等观测信息。多频多系统GNSS为用户提供更多的观测数据和组合选择,为精密定位、导航和授时(PNT)应用带来了新的机遇,如高精度位置服务、大地测量、空间天气和灾害监测等。但多频多系统GNSS观测为精密单点定位(PPP)组合模型和系统偏差及大气延迟估计等带来诸多问题和挑战。本文给出了单频到五频多系统GNSS精密单点定位(PPP)模型,估计和评估了单频到五频多系统GNSS PPP定位精度、接收机钟差、对流层延迟、卫星和接收机硬件延迟,以及频间偏差。给出了GNSS PPP最新应用进展,包括GNSS气象学、电离层模拟、时间频率传递、建筑物安全和地震监测及其应用。结果表明,多频多系统极大地提高了GNSS PPP参数估计的精度和可靠性,具有重要的应用价值。最后给出了多频多系统GNSS PPP应用前景与展望。     

A closed-form formula for GPS GDOP computation

Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision. An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that increasing the number of satellites for positioning will always reduce the GDOP. Since most GPS receivers today can receive signals from more than four satellites, it is desirable to compute GDOP efficiently for the general case. Previous studies have partially solved this problem with artificial neural network (ANN). Though ANN is a powerful function approximation technique, it needs costly training and the trained model may not be applicable to data deviating too much from the training data. Using Newton’s identities from the theory of symmetric polynomials, this paper presents a simple closed-form formula for computing GDOP with the inputs used in previous studies. These inputs include traces of the measurement matrix and its second and third powers, and the determinant of the matrix.     

BDS/GPS/GLONASS组合单历元姿态测量性能对比分析

相比于单一卫星导航系统,多卫星导航系统组合具有显著增加可用卫星数目、改善卫星空间几何结构等优点,因而多卫星导航系统组合应用成为近年来关注的热点。在复杂观测条件下,利用BDS/GPS/GLONASS组合进行载体姿态测量具有单系统无法比拟的优势。首先阐述了BDS/GPS/GLONASS组合超短基线解算的双差模型以及姿态测量基本原理;然后分析了BDS/GPS/GLONASS组合多频单历元姿态测量性能。通过实测静态数据设置不同高度截止角进行分析表明:相比于单系统及双系统组合的姿态测量,BDS/GPS/GLONASS组合能够有效地提高姿态测量的精度、稳定性和可用性。当运动载体处于高楼、峡谷等受遮挡严重的复杂环境时,BDS/GPS/GLONASS组合单历元姿态测量更具有应用价值。     

QZSS/IRNSS对BDS在中国定位性能增强的评估

通过STK软件对BDS、QZSS、IRNSS卫星星座结构仿真的基础上,选择BDS、BDS/QZSS、BDS/IRNSS、BDS/QZSS/IRNSS、QZSS/IRNSS等定位方式对中国大陆单观测站与整体范围最小可见卫星数、GDOP值、定位误差进行覆盖分析,确定了QZSS与IRNSS在我国的覆盖范围及对BDS定位性能增强作用的评估。结果表明,BDS/QZSS/IRNSS组合在我国的最小可见卫星数可达16~21颗,GDOP值在1.4~1.7之间,定位误差达5.5~7.5m,相比单BDS定位最小可见卫星数增加了6~8颗,GDOP值减小了0.3~0.5,定位精度提升了2.0~3.0m,对华南地区的定位性能有明显提升,而对东北等地区定位性能的提升较小。     

A computationally efficient approach for estimating high-rate satellite clock corrections in realtime

Realtime satellite clock corrections are usually estimated using undifferenced phase and range observations from a global network. Because a large number of ambiguity parameters must be estimated, the computation is time-consuming. Consequently, only a sparse global network of limited number of stations is processed by most IGS Realtime Analysis Centers with an update rate of 5 s. In addition, it is very desirable to build the capability to simultaneously estimate clock corrections for multi-GNSS constellations. Although the estimation can be sped up by epoch-differenced observations that eliminate ambiguities, the derived clocks can contain a satellite-specific bias that diminishes the contribution of range observations. We introduce a computationally efficient approach for realtime clock estimation. Both the epoch-differenced phase and undifferenced range observations are used together to estimate the epoch-differenced satellite clocks and the initial clock bias for each satellite and receiver. The biased clock corrections accumulated from the estimated epoch-differenced clocks are then aligned with the estimated clock biases and provided as the final clock corrections to users. The algorithm is incorporated into the EPOS-RT software developed at GFZ (GeoForschungsZentrum) and experimentally validated with the IGS global network. The comparison with the GFZ rapid products shows that the accuracy of the clock estimation with the new approach is comparable with that of the undifferenced approach, whereas the computation time is reduced to one-tenth. As a result, estimation of high-rate satellite clocks from a large reference network and tracking satellites of multi-GNSS constellations becomes achievable.     

GPS/BDS/GLONASS/Galileo多系统融合在中国区域的仿真分析

通过STK软件对GPS、BDS、GLONASS、Galileo四个系统的星座结构进行仿真,并选择单系统与多系统组合定位的方式对中国区域内的可见卫星数、GDOP值和定位精度进行覆盖分析。结果表明,GPS/BDS/GLONASS/Galileo四系统组合定位在我国的GDOP值可达0.7~0.8,定位精度可达3~4m,优于其他方式的组合定位;同时四系统组合定位下的GDOP值降低,定位精度更好,GDOP值与定位精度的波动异常得到了抑制,导航定位的性能与稳定性也得到了相应的提升。     

卫星导航中几何精度衰减因子最小值分析及应用

DOP是评估卫星导航定位性能的重要手段之一。在分析GDOP的数学意义和测量意义的基础上,提出两种GDOP最小值的求解方法,并对最小值进行理论分析。结果表明,传统场合中认为DOP为"精度衰减"因子是有局限性的;随着卫星与用户几何关系的改变,包括GDOP在内的所有DOP完全可以小于1,从而具有一定的精度增强作用。在此基础上,提出一种评价星座空间分布均匀程度的星座几何构型品质因数,并以GPS和Galileo星座为例进行试验,结果表明该因数可以较好地评价星座的空间分布均匀程度。基于GPS星座在近地空间内导航精度性能的试验结果很好地证明了DOP具有精度增强的属性。     

北斗伪距单点定位的随机模型影响评估

北斗卫星导航系统包含3种不同类型的空间星座,相对应卫星的高度角存在一定的差异,对北斗卫星单点定位的影响也不同。针对这一问题,研究了等权模型、基于卫星高度角和信噪比的北斗卫星观测量随机模型确定方法。利用MGEX站提供的观测数据,通过比较不同模型的实验结果表明:相对于等权模型,基于卫星高度角和信噪比定权模型可以提高单点定位的精度,并且信噪比模型优于高度角模型;在基于信噪比确定权阵的随机模型中,选择不同的参数,对解算结果精度会产生相应的影响。     

伪卫星改善DOP值的数学分析

在卫星导航系统中,DOP值是衡量卫星定位导航精度好坏的重要量度。在区域导航定位中,增设伪卫星可以很好地改善卫星分布的几何结构,降低DOP值,提高定位导航的精度。本文用矩阵分解的方法验证了在增设伪卫星后,GDOP必定会减小的结论,并且分析了仰角与VDOP之间的关系,利用伪卫星低仰角的特点例证了加入伪卫星后对系统DOP值的改善作用。     

多星座实时导航中一种快速次优的选星方法

随着各国卫星导航系统的建设与完善,同一历元的可见卫星数目逐渐增加,如何对众多卫星进行选择以优化利用现有资源便显得迫切而重要。本文以获得满足设计要求的GDOP为前提,根据各时刻可见卫星数量的大小,选择适合的遮蔽仰角,以卫星空间构型的体积与GDOP关系为依据,引入计算几何学中解决三维点集的凸壳问题的增量算法,并结合导航卫星星座的自身特点,提出了对卫星位置坐标直接进行选择的一种快速次优的选星算法。实验结果表明,在GDOP满足要求且选星数较少的情况下,相对传统GDOP选星法大大减小了计算量,该方法简洁快速,能有效满足选星求解的实时性和精度要求。     

An efficient solution of real-time data processing for multi-GNSS network

Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.     

北斗／GPS双模定位中快速选星算法研究

采用双系统组合定位模式,导航接收机能在同一时刻接收到超过20颗可见星,大大增加了可见星的数量,能提供十分精准的定位。但可见星数量大幅度增加带来定位精度提升的同时也带来了大量的计算量,加上实际作业中的一些问题,都大大增加了选星时间。本文从GDOP与星座几何布局的关系出发,结合实际应用场景,提出了基于仰角和方位角排序的选星算法。该方法以满足定位要求为前提,根据可见星仰角排序初筛卫星,对不同仰角卫星进行合理的顶星选择,以卫星均匀分布为原则,将在理想情况和实际情况下寻找有效定位平衡点,以规避无效选星并减少计算量,从而大大减少选星时间,有效实现了在北斗和GPS双模定位中的快速选星。      

北斗三号与超高频GNSS同震形变监测:以2021年青海玛多Mw 7.4地震为例

随着北斗三号完成全球组网以及硬件技术发展,地壳形变监测网络的全球导航卫星系统（global navigation satellite system, GNSS）接收机正朝着多系统、超高频（≥50 Hz）更新升级。基于陆态网络和中国青海省连续运行参考站的GNSS观测数据,获取2021年青海玛多Mw 7.4地震的同震位移波,并进行了震前精度统计和功率谱密度分析。结果表明,北斗三号在本次地震中的位移拾取精度比全球定位系统(global positioning system,GPS)更优;采样率提高到50 Hz对削弱位移时间序列混叠效应作用不显著,在10 Hz左右达到饱和;对50 Hz同震位移波差分获取到的速度和加速度序列噪声较大,难以利用。综合应用场景和成本考虑,GNSS地震监测的采样率最高设置在5~10 Hz即可。     

Positioning with two satellites and known receiver clock,barometric pressure and radar elevation

GPS Solutions - We investigate the feasibility of completing an aircraft precision approach using two global navigation satellite systems (GNSS) satellites from different constellations in...     

四大GNSS广播星历精度评估与对比分析

分析了 目前广播星历精度评估中存在的问题,详细论述了广播星历精度评估过程中对精密星历进行天线相位中心改正的取值方法,提出了利用单颗星单日钟差均值作二次差对广播星历钟差的系统性偏差进行改正的方法.选取2019-09-01-2019-11-01 共计62天的多模 GNSS 实验(multi-GNSS experiment,...     

全球导航卫星系统的进展及建设CORS的思考

介绍了GPS和GLONASS全球导航卫星系统的新进展，对GPS现代化的三个步骤作了简要介绍，对它和GLONASS的技术差异作了简评，对Galileo和北斗导航卫星系统的前景作了讨论。指出导航卫星系统将进入一个多系统近百颗卫星同时并存的新局面，用户将面临多系统导航卫星信号使用方面的组合、选用和最优化问题。讨论了全球导航卫星连续运行站网及其服务系统的构成和作用，及其在国内各地区各系统建设的概况。指出当前缺乏在国家级层面对全球导航卫星地面连续运行站系统的统一规划、设计、规范和标准。建议明确全球导航卫星系统的建设和管理的政府主管部门，建立全球导航卫星的国家级地面连续运行站系统，制定全球导航卫星地面连续运行站系统的国家级技术规范和标准，包括它的服务功能。