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。     

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.     

几何精度因子对GRACE卫星几何轨道精度影响分析

分析了GDOP值与GRACE卫星几何轨道精度之间的关系,发现定轨精度较差的历元其GDOP值普遍较大甚至异常,进一步研究发现GDOP值异常现象是因剔除个别含有粗差的卫星而导致的,进而通过设置GDOP值阈值的方式剔除发生GDOP值异常的历元。实验结果表明,GDOP值阈值设置为50,将大于该阈值的历元剔除,能够有效抑制个别历元精度较差的情况,最终的RMS在地固系X,Y,Z3个方向分别为0.029m,0.043m,0.029m,实现了几何法厘米级精密定轨的目标。     

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.     

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。     

A closed-form formula to calculate geometric dilution of precision (GDOP) for multi-GNSS constellations

With the future global navigation satellite system (GNSS), the multi-GNSS constellations, which are composed of various single systems, will be the main navigation method in future. For the multi-GNSS constellations, the geometric dilution of precision (GDOP) is an important parameter used for satellite selection and the evaluation of positioning accuracy. However, the calculation of GDOP is a time-consuming and power-consuming task. Using Schur complement, we present a closed-form formula to calculate GDOP for multi-GNSS constellations. The formula can be applied to multi-GNSS constellations that include two, three or four different single systems. Furthermore, a closed-form formula for the case of exactly five satellites is also derived. Compared with the conventional numerical methods, the formula can reduce the amounts of multiplication and addition effectively. Numerical experiments validate the effectiveness and feasibility of the closed-form formula.     

Satellite selection with an end-to-end deep learning network

Benefiting from multi-constellation Global Navigation Satellite Systems (GNSS), more and more visible satellites can be used to improve user positioning performance. However, due to limited tracking receiver channels and power consumption, and other issues, it may be not possible, or desirable, to use all satellites in view for positioning. The optimal subset is generally selected from all possible satellite combinations to minimize either Geometric Dilution of Precision (GDOP) or weighted GDOP (WGDOP). However, this brute force approach is difficult to implement in real-time applications due to the time- and power-consuming calculation of the DOP values. As an alternative to a brute force satellite selection procedure, the authors propose an end-to-end deep learning network for satellite selection based on the PointNet and VoxelNet networks. The satellite selection is converted to a satellite segmentation problem, with specified input channel for each satellite and two class labels, one for selected satellites and the other for those not selected. The aim of the satellite segmentation is that a fixed number of satellites with the minimum GDOP/WGDOP value can be segmented from any feeding order of input satellites. To validate the proposed satellite segmentation network, training and test data from 220 IGS stations tracking GPS and GLONASS satellites were used. The segmentation performance using different architectures and representations of input channels, including receiver-to-satellite unit vector and elevation and azimuth, were compared. It was found that the input channel with elevation and azimuth can achieve better performance than using the receiver-to-satellite unit vector, and an architecture with stacked feature encoding (FE) layers has better satellite segmentation performance than one without stacked FE layers. In addition, the models with GDOP and WGDOP criteria for selecting 9 and 12 satellites were trained. It was demonstrated that the satellite segmentation network was about 90 times faster than using the brute force approach. Furthermore, all the trained models can effectively select the satellites making the most contribution to the desired GDOP/WGDOP value. Approximately 99% of the tests had GDOP and WGDOP value differences smaller than 0.03 and 0.2, respectively, between the predicted subset and the optimal subset.     

区域卫星导航系统覆盖性能分析

北斗卫星导航系统已完成区域系统的建设任务。相比GPS而言,由于其星座结构的特殊性,目前仅对部分地区提供可用服务。本文以STK软件为基础,仿真计算了当前北斗导航星座对中国地区单一测站的卫星可视情况和GDOP变化情况,并计算了全球范围内7天观测周期内的平均GDOP分布情况。结果表明,当前星座的北斗卫星导航系统能够完成对中国及周边大部分地区的覆盖。     

水下声纳定位浮标阵列解析优化

全球导航卫星系统（global navigation satellite system,GNSS）/声纳水下定位精度主要取决于GNSS浮标阵列构型和声学测距精度。优化水面浮标阵列是提高水下定位精度的重要途径。探讨了GNSS浮标阵列解析优化方法,算例以5枚和6枚浮标布设为例,应用所提方法给出了最优浮标阵列解。基于几何精度因子（geometric dilution of precision,GDOP）最小构型解析方法,通过考虑水下定位GNSS浮标位于水面和存在高度角限制这一约束条件,对水下定位浮标阵列进行了解析优化。由于浮标进行水下定位时是范围性的,还基于区域GDOP均值和方差两个指标对GNSS浮标阵优化问题进行了探讨,并采用数值方法设计了区域GDOP均值最小构型搜索算法。研究表明,虽然存在高度角约束条件,最优浮标阵列几何结构并不唯一,若在此基础上进一步考虑区域GDOP均值和方差最小的目标,则最终可获得唯一的区域均值浮标阵列结构。     

GPS/GALILEO组合系统可见卫星与GDOP的区域和时序分析

卫星星座方案的选择对导航定位精度具有很大影响。本文根据GALILEO系统的设计轨道参数模拟得到的GALILEO系统的卫星位置,分别计算了GPS系统、GALILEO系统和GPS/GALILEO组合系统在不同卫星截止高度角的情况下,全国范围内可见卫星和GDOP值的分布情况,并选择了北京、武汉和乌鲁木齐三个城市,连续观测24小时,分析了各城市的可见卫星和GDOP值随时间的变化规律。     

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。     

“一带一路”沿线及周边地区BDS定位性能动态分析

本文通过STK软件对BDS全球组网时至当前的星座结构进行了动态仿真,确定了“一带一路”沿线及周边地区最小可见卫星数、GDOP值以及定位误差的动态变化过程。结果表明,当前BDS已实现“一带一路”沿线大部分地区的覆盖,中国大陆、东南亚、南亚等地区的定位精度优于13 m,但北欧、东欧、西亚等小部分地区的定位精度仍有待提高;MEO卫星较GEO／IGSO卫星对“一带一路”沿线及周边地区定位精度的提升作用要大;同时发现,随着可见卫星数的增加,GDOP值逐渐减小,但当可见卫星数达到一定值时,随着可见卫星数的增加,GDOP值的减小幅度不明显,说明单纯增加可见卫星数有时并不完全能提高定位精度。      

一种顾及几何精度因子的GNSS控制网构型选站方法CSCD

在相对定位基线解算过程中,控制网约束点坐标位置的选取对数据解算精度有一定的影响.讨论了顾及最小几何精度因子(GDOP)值控制网构型选站方法,对全球MGEX(Multi-GNSS Experiment)测站进行6个约束点基准站的选择,利用北斗二号/北斗三号(BDS2/BDS-3)的实测数据,对全球18个连续监测评估系统(iGMAS)观测站的站坐标进行解算,并与全球格网化随机选站法选站结果的解算精度进行对比.实验结果表明:相较于格网化随机选站法,采用顾及GDOP值选站法进行相对定位基线解算时,6000 km以上的基线长度标准差值能够提高约7 mm;长基线在东(E)、北(N)、天顶(U)三方向的标准差值精度提升约5 mm;待定点的点位精度能够提升约40%.可以看出采用GDOP法选站可以提高BDS-2/BDS-3相对定位解算精度.     

基于伪卫星的改善GPS几何精度因子的研究

随着人们活动范围的日益扩大和周边环境的日益复杂,高精度GPS导航技术逐渐成为国内外研究的重点。GPS系统的定位精度在很大程度上取决于参与定位卫星的数目和几何布局,而几何精度因子(GDOP)正是衡量定位卫星几何布局优劣的量度。文章从几何精度因子着手,从理论上证明了伪卫星对GPS系统GDOP的改善,分析了伪卫星数量对GPS系统定位精度的影响。借助于仿真实验,结果表明,在GPS导航定位中,伪卫星能够显著增强卫星几何图形结构、提高测量精度、改善精度因子从而提高定位精度。     

低轨卫星增强载波相位差分定位

针对低轨卫星快速空间几何变化和抗干扰能力强等特征,该文基于卫星工具包软件对全球导航定位系统和铱星系统星座进行了仿真,并假定铱星具有导航卫星的功能,分析铱星对GPS定位的增强作用。首先对GPS和铱星增强星座的可见卫星数量和几何精度因子值进行了分析,然后通过对不同的误差值建模,对GPS系统和铱星系统的观测值进行了仿真,分析了低轨卫星对双差定位浮点解和模糊度固定的增强作用,结果表明:低轨卫星的加入增加了可见卫星数量,几何精度因子也优于单GPS系统。单频双差模糊度浮点解的RMS值优于1周,双频双差模糊度浮点解的RMS值优于0.5周,与单GPS相比有了较明显的提高,同时,低轨卫星的加入更有利于单频短基线的模糊度固定。     

应用StarReport星历预报软件提高测量工作效率

GPS测量中经常出现开机后卫星数不够或PDOP几何精度因子超限等问题,接收GPS导航电文中星历预报文件,提前预测测区卫星分布情况卫星出入地平时刻、卫星进退观测允许高度角时刻及可见卫星的高度角辅方位角等,对于合理选择观测时间,提高作业效率具有很重要的作用。本文介绍了如何应用StarReport星历预报软件获取和解算GPS星历文件的方法。     

几何精度因子的算法研究及矩阵病态性探讨

针对GPS定位中的影响定位精度的几何精度因子（GDOP）的传统矩阵求逆算法和基于矩阵QR分解法进行了叙述,并对两种方法进行了比较分析,结果表明：后者具有数值稳定性好,计算效率高等优点。最后对其矩阵病态性进行了讨论。     

一种基于观测方程GDOP值的优化选站模型

针对GNSS（global navigation satellite system）数据分析中心对快速、超快速轨道产品精度及时效性的要求以及全球跟踪站分布不均匀性的现状,本文提出一种基于观测方程GDOP（geometric dilution of precision）值的优化选站SSS（selected step by step）模型。从理论上推导出精密定轨最小地面跟踪站数与地面最优跟踪站数的计算方法,分别通过s°×s°和k°×k°带全球网格划分,筛选最小跟踪站全球分布,以定轨观测方程GDOP值最小为准则,逐步累加筛选定轨全球跟踪站最优分布。连续6 d的数据分析结果表明,本文提出的优化选站模型,在相同数据处理能力条件下,定轨精度可达整体处理的90%,处理时间缩短50%以上;与一般策略对比表明,SSS模型计算出的轨道精度相当,时间节约20%左右;此模型所选跟踪站为最优或次优,提高了分析中心数据处理效率。     

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。     

Neural network-based GPS GDOP approximation and classification

In this paper, the neural network (NN)-based navigation satellite subset selection is presented. The approach is based on approximation or classification of the satellite geometry dilution of precision (GDOP) factors utilizing the NN approach. Without matrix inversion required, the NN-based approach is capable of evaluating all subsets of satellites and hence reduces the computational burden. This would enable the use of a high-integrity navigation solution without the delay required for many matrix inversions. For overcoming the problem of slow learning in the BPNN, three other NNs that feature very fast learning speed, including the optimal interpolative (OI) Net, probabilistic neural network (PNN) and general regression neural network (GRNN), are employed. The network performance and computational expense on NN-based GDOP approximation and classification are explored. All the networks are able to provide sufficiently good accuracy, given enough time (for BPNN) or enough training data (for the other three networks).