利用卡尔曼滤波估计导航信号电离层差分改正

针对星基增强系统中估计电离层延迟改正数的问题,提出了利用卡尔曼滤波估计导航信号电离层延迟的方法。将电离层格网点处的电离层垂直延迟及其变化率作为状态变量进行滤波估计,根据电离层的时域缓变特性建立了状态模型,基于星基增强系统中使用的格网模型建立了观测模型。仿真结果表明,与传统的电离层延迟校正方法相比,该方法具有更高的估计精度。     

三频电离层延迟改正中多路径误差和观测噪声的削弱算法

多频测距系统可以借助多频观测数据削弱电离层延迟的影响,但多频改正算法在改正电离层延迟项的同时会不同程度地放大多路径误差、观测噪声等伪距误差的影响。其中利用三频数据可以将电离层延迟改正至二阶项,也可以只改正至一阶项,分别称为三频二阶改正和三频一阶改正。首次推导了利用三频观测数据削弱伪距中多路径效应和观测噪声等误差的算法,使三频电离层延迟改正中伪距误差的影响大大减小。通过对三频实测数据的处理和分析验证了算法的有效性并给出了一些有益的结论和建议:在利用三频观测数据进行电离层改正时,首先改正伪距中的多路径误差和观测噪声,然后采用三频二阶改正算法将电离层延迟改正至二阶项,将有效提高伪距改正精度。如果不能有效削弱这些误差的影响,宜采用三频一阶改正或双频改正。     

基于残差统计特性的中国区域格网电离层GIVE算法优化

北斗星基增强(BDSBAS)系统播发格网电离层改正数和格网电离层完好性参数GIVE,用以提升GNSS系统的服务精度并实现区域电离层活动完好性监视,以满足精密进近(GLS PA)需求.本文在实现BDSBAS格网电离层粗差剔除与改正数计算的基础上,提出了一种电离层完好性参数GIVE的优化方法,进而评估了BDSBAS格网电离层的应用精度.BDSBA S格网电离层格网点延迟估计采用平面拟合算法计算,异常数据剔除采用稳健的中值容错算法,GIVE的估计考虑了电离层残差分布的偏度与峰度统计特性,能够实现对电离层异常活动的及时响应.2020年1月实测数据分析结果表明,BDSBAS格网电离层修正精度(RMSE)为2～3 TECU,改正百分比达到75％ ～79％,GIVE包络率优于99.9％.修正格网电离层后可提升GPS定位精度20％ ～40％.     

GPS现代化后电离层折射误差高阶项的三频改正方法

研究了电离层对GPS观测信号的主要影响及电离层折射误差模型,总结了电离层双频改正模型。针对GPS现代化中增加的第三频率,系统推导了三个频率的电离层改正模型及相位观测值无电离层组合(LC组合)模型。该模型将电离层折射误差模型改正至二阶项,可进一步提高GPS定位精度,同时,为GPS定位中其他误差的改正及分离、周跳的探测等提供了有力的技术手段。     

Galileo电离层折射误差高阶项的四频改正方法

研究了电离层对Galileo观测信号的主要影响及电离层折射误差模型。针对Galileo中的四个频率,系统推导了四个频率的电离层改正模型及相位观测值无电离层组合(LC组合)模型。该模型将电离层折射误差模型改正至三阶项,可进一步提高Galileo定位精度,同时,为Galileo定位提供了有力的技术手段。     

网络RTK基准站间的模糊度及空间相关误差解算

利用载波相位双差观测值的宽巷和无电离层组合固定部分模糊度参数,并采用Kalman滤波算法估计残余的对流层延迟;然后对观测值进行改正,剔除对流层延迟误差,从而提高剩余模糊度参数的固定率;最后估计双差电离层延迟。文中采用美国CORS网的GPS数据进行实验,实验结果表明,自适应滤波算法可明显提高残余对流层延迟的解算精度和模糊度的解算效率;固定模糊度并改正对流层和电离层延迟,差分定位精度得到很大提高。     

全球电离层TEC格网时空变化特性分析

卫星导航定位中,电离层延迟是影响用户实时定位精度的重要因素之一。利用全球电离层格网(global ionosphere maps,GIM)提供电离层延迟改正是较为常用的方法,而GIM格网的精度受限于地面GNSS(global navigation satellite system)跟踪站的分布密度。利用区域内少量或1个GNSS跟踪站建立实时区域电离层总电子含量(total electron content,TEC)模型,生成高精度的实时区域电离层格网,为用户提供区域电离层延迟改正显得尤为重要。基于CODE(Center for Orbit Determination in Europe)分析中心2016—2018年995 d的GIM格网数据,分析了相邻格网点TEC的变化范围以及不同时间间隔同一格网点TEC的变化范围。结果表明,GIM在经度方向上分辨率为5°变化的均值范围为0.2～1.0 TECU,在纬度方向上分辨率为2.5°变化的均值范围为0.4～1.4 TECU,在经度和纬度分辨率均小于1°时,电离层TEC的变化小于1.0 TECU;1 h内同一格网点电离层TEC的变化均值约为1.28 TECU,30 min内同一格网点电离层TEC的变化小于1.0 TECU。该研究为小范围内(半径小于100 km)实时区域电离层TEC模型的建立及电离层格网的时间适用范围提供了有效的数据支撑和理论验证,同时对区域电离层TEC时空变化的研究、电离层TEC预报、电离层异常监测和磁暴监测等具有一定的参考意义。     

GPS+BDS中长距离RTK定位算法及结果分析

GPS/BDS中长距离RTK定位因为电离层和对流层残余误差的影响,其性能相对于常规RTK有所降低。将GPS/BDS卫星双差电离层误差和对流层误差作为参数,采用卡尔曼滤波进行实时估计。为了验证算法的有效性,利用武汉地区103 km静态基线24 h双频观测数据,分析了GPS和BDS单系统以及二者组合双系统中长距离RTK定位性能。实验结果表明,精确估计的双差电离层残余误差达到米级、对流层误差达到分米级;经过改正后,GPS/BDS单系统的定位精度在1 cm左右,组合双系统则实现了中长距离基线毫米级的高精度定位。     

BDS中长距离非差实时动态厘米级定位算法

针对BDS常规实时动态定位(RTK)中,随着流动站与参考站间的距离增加,大气延迟误差的空间相关性大大降低,影响了整周模糊度的快速解算和流动站位置信息的解算精度问题。该文研究了一种基于非差观测误差的BDS中长距离常规RTK定位算法,采用非差误差改正方法为流动站提供误差改正,利用参考站的非差误差改正数以单颗卫星为对象进行误差改正。对电离层延迟误差和相对天顶对流层延迟误差进行参数估计,处理电离层延迟误差和对流层延迟误差的影响。最后通过BDS实测数据对该算法进行了算法验证和结果分析。实验结果表明,该算法可以实现BDS中长距离常规RTK的快速定位,并获得厘米级定位精度。     

Galileo改正电离层折射误差高阶项的方法

在研究电离层折射对Galileo测量的影响及电离层折射误差模型的基础上,针对Galileo系统中的4个频率,提出运用四频观测值将电离层折射误差改正至三阶项的方法,并推导了四频载波相位观测值无电离层折射组合方程,从而进一步提高了Galileo的定位精度。     

Preliminary analysis of grid ionospheric vertical error for GAGAN

The inverse distance weighted model (IDWM) represents a geo-spatial interpolation technique used for estimation of ionospheric vertical delays at the ionospheric grid points (IGPs) and user ionospheric pierce points (IPPs). The GPS Aided Geo Augmented Navigation (GAGAN) system is planned for air-navigation over the Indian service region using a space based augmentation. One of the main needs for GAGAN is to develop a suitable grid-based ionospheric model for estimating the vertical delay and its error bound, i.e., grid ionospheric vertical error (GIVE) at all the IGPs covering the Indian subcontinent. Dual frequency GPS receiver data obtained from 17 total electron content (TEC) stations are considered in the analysis. For a typical IGP (25°N, 75°E), variations in the GIVE for a few days of quiet ionosphere are presented. For a quiet and magnetically moderate day, the mean and standard deviations of the user IPP (UIPP) estimation error and the mean GIVE are presented using the IDWM with Klobuchar, Junkins and bilinear models.     

顾及电离层改正精度信息的高精度单频单点定位方法研究

提出了将电离层改正量作为虚拟观测值,参数估计随机模型顾及电离层改正量先验信息的高精度单频单点定位新方法,并推导出该方法的数学模型。实测数据解算定位结果表明,新方法能够实现中国高、中、低纬区域的无初始化高精度单频单点定位,其平面精度为0.1~0.2 m,高程精度为0.3~0.5 m。     

基于L5的GPS电离层折射误差改正

在分析电离层折射误差模型以及双频改正模型的基础上,在原有的双频数据处理方法之下,利用GPS现代化中新增的L5频率与原有的L1、L2频率进行新的双频组合,再利用双频组合解算来得出电离层折射误差,以取得双频最优改正值,进而即可对GPS的电离层折射误差进行有效的改正。同时,简单介绍利用三频观测值改正电离层折射误差二阶项的方法。这些方法的使用均可提高GPS电离层折射误差的改正精度,从而提高GPS的定位精度,扩大其应用的深度与广度。     

Higher order ionospheric effects in precise GNSS positioning

With the increasing number of precise navigation and positioning applications using Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS), higher order ionospheric effects and their correction become more and more important. Whereas the first-order error can be completely eliminated by a linear combination of dual- frequency measurements, the second- and third-order residual effects remain uncorrected in this approach. To quantify the second-order residual effect, a simple formula has been derived for GNSS users in Germany. Our proposed correction algorithm reduces the second-order effects to a residual error of fractions of 1 mm up to 2 mm at a vertical total electron content level of 10¹⁸ electrons/m² (100 TECU), depending on satellite azimuth and elevation angles. The correction formula can be implemented in real-time applications as it does not require the knowledge of the geomagnetic field or the electron density distribution in the ionosphere along the signal path. It is expected that the correction will enable more accurate positioning using the line-of-sight carrier-phase measurements.     

电离层延迟对单频GPS点的影响及改正方法研究

电离层延迟是单频GPS地面沉降监测点的最主要误差源,如何削弱该误差的影响是提高单双频混合地面沉降监测系统精度的关键。采用中国广州南沙单双频混合GPS地面沉降监测网数据进行处理分析,结果表明,在低纬度地区即使基线较短,电离层延迟对单频GPS监测精度影响仍然较大,影响程度随基线长度增加而增大,而且在时间域上有明显的季节性变化规律:2、3月份与8、9月份电离层影响较为显著。利用双频点数据从观测值域对单频点电离层延迟误差进行改正,监测精度提高了57%,改善效果明显。     

广域差分的全矢量法

针对广域差分改正矢量的组成元素集之一的电离层模型参数集,分别用Klobuchar模型和Georgiadou模型进行了分析和比较,详细推演了广域差分改正矢量估计的全矢量法.在统一的数学模型中给出了统一解算卫星星历误差、卫星钟差和广域差分基准站时钟误差的计算公式;对理想状态下的模型参数、基准站和跟踪的卫星的数量关系进行了探讨.     

Application of the TaiWan Ionospheric Model to single-frequency ionospheric delay corrections for GPS positioning

The performance of a three-dimensional ionospheric electron density model derived from FormoSat3/COSMIC GPS Radio Occultation measurements, called the TaiWan Ionosphere Model (TWIM), in removing the ionospheric delays in single-frequency pseudorange observations is presented. Positioning results using TWIM have been compared with positioning results using other ionospheric models, such as the Klobuchar (KLOB) and the global ionospheric model (GIM). C/A code pseudoranges have been observed at three International GPS Service reference stations that are representative of mid-latitude (BOR1 and IRKJ) and low-latitude (TWTF) regions of the ionosphere. The observations took place during 27 geomagnetically quiet days from April 2010 to October 2011. We perform separate solutions using the TWIM, KLOB, GIM ionospheric models and carry out a solution applying no ionospheric correction at all. We compute the daily mean horizontal errors (DMEAN) and the daily RMS (DRMS) for these solutions with respect to the published reference station coordinates. It has demonstrated that TEC maps generate using the TWIM exhibit a detailed structure of the ionosphere, particularly at low-latitude region, whereas the Klobuchar and the GIM only provide the basic diurnal and geographic features of the ionosphere. Also, it is shown that even for lower satellite elevations, the TWIM provides better positioning than the Klobuchar and GIM models. Specifically, using TWIM, the difference of the uncorrected solution (no ionospheric correction), and the other solutions, relative to the uncorrected solution, is 45 % for the mean horizontal error (DMEAN) and 42 % for the horizontal root-mean-square error (DRMS). Using Klobuchar and GIM, the percent for DMEAN only reaches to about 12 % and 3 %, while the values for the DRMS are only 12 and 4 %, respectively. In the vertical direction, all models have a percentage of about 99 and 70 % for the mean vertical error (VMEAN) and vertical root-mean-square error (VRMS), respectively. These percentages show the greater impact of TWIM on the ionospheric correction compared to the other models. In at least 40 % of the observed days and across all stations, TWIM has the smallest DMEAN, VMEAN, DRMS, and VRMS daily values. These values reach 100 % at station TWTF. This shows the overall performance of TWIM is better than the Klobuchar and GIM.     

Contribution of ionospheric irregularities to the error of dual-frequency GNSS positioning

This paper investigates the third-order residual range error in the dual-frequency correction of ionospheric effects on satellite navigation. We solve the two-point trajectory problem using the perturbation method to derive second-approximation formulas for the phase path of the wave propagating through an inhomogeneous ionosphere. It is shown that these formulas are consistent with the results derived from applying perturbation theory directly to the eikonal equation. The resulting expression for the phase path is used in calculating the residual range error of dual-frequency global positioning system (GPS) observations, in view of second- and third-order terms. The third-order correction includes not only the quadratic correction of the refractive index but also the correction for ray bending in an inhomogeneous ionosphere. Our calculations took into consideration that the ionosphere has regular large-scale irregularities, as well as smaller-scale random irregularities. Numerical examples show that geomagnetic field effects, which constitute a second-order correction, typically exceed the effects of the quadratic correction and the regular ionospheric inhomogeneity. The contribution from random irregularities can compare with or exceed that made by the second-order correction. Therefore, random ionospheric irregularities can make a significant (sometimes dominant) contribution to the residual range error.     

利用 ARMA 模型短期预报北极地区电离层 T EC

北极地区电离层结构分布较为特殊,存在梯度变化。利用时间序列分析中的自回归移动平均模型(Autoregressive Moving Average,ARMA)对欧洲定轨中心(CODE)发布的北纬67.5°~87.5°以及利用反距离加权插值法得到的90°的格网数据逐点进行建模,分别利用7d、10d、20d、30d、40d、50d的电离层TEC值为样本数据采用线性最小方差法进行预报分析。结果表明:90%以上的预报绝对误差小于3TECU,预报精度随TEC样本序列长度的增加而提高,但样本序列增加到一定值后,相对精度提高不大;相同样本数据的预报精度随预报时间长度的增加而降低,起初不是很明显,超过20d后精度降低明显且波动幅度较大。尽管北极地区存在梯度变化,ARMA模型在北极地区具有较高的预报精度,是一种比较理想的预报方法。     

卫星摄影测量中偏流角修正余差改正技术

本文基于立体影像摄影机理,对偏流角修正的剩余误差导致的上下视差进行了分析,建立了立体相机偏流角余差改正的数学模型,推导出偏流角余差影响上下视差的误差方程,并重点从相机参数在轨标定和光束法平差中低频误差补偿两方面提出解决措施。理论分析与实际卫星影像试验表明,偏流角改正余差对上下视差影响较大,必须通过相机参数在轨标定和低频误差补偿两方面予以改正,才能保证全球范围无地面控制点目标定位精度的一致性。