近年来我国GNSS电离层延迟精确建模及修正研究进展

空间电离层是影响全球卫星导航系统(GNSS)应用服务性能最棘手的误差源之一。近几十年来,随着地基/空基GNSS数据的日益丰富,国内外学者发展并提出了多种重要技术措施修正、削弱电离层延迟对各类GNSS用户导航定位的影响,取得了重要进展和成果。本文在系统总结GNSS空间电离层延迟影响修正研究成果的基础上,从电离层延迟信息精确提取、建模及误差分析、实时改正方法等几个方面,重点介绍了近年来我国在这一领域的主要研究进展情况。     

Mitigation of higher order ionospheric effects on GNSS users in Europe

Current dual-frequency GPS measurements can only eliminate the first-order ionospheric term and may cause a higher-order range bias of several centimeters. This research investigates the second-order ionospheric effect for GNSS users in Europe. In comparison to previous studies, the electron density profiles of the ionosphere/plasmasphere are modeled as the sum of three Chapman layers describing electron densities of the ionospheric F₂, F₁ and E layers and a superposed exponential decay function describing the plasmasphere. The International Geomagnetic Reference Field model is used to calculate the geomagnetic field vectors at numerous points along the incoming ray paths. Based on extended simulation studies, we derive a correction formula to compute the average value of the longitudinal component of the earth’s magnetic field along the line-of-sight as a function of geographic latitude and longitude, and geometrical parameters such as elevation and azimuth angles. Using our correction formula in conjunction with the total electron content (TEC) along the line-of-sight, the second-order ionospheric term can be corrected to the millimeter level for a vertical TEC level of 10¹⁸ electrons/m².     

Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.     

Application of SWACI products as ionospheric correction for single-point positioning: a comparative study

In Global Navigation Satellite Systems (GNSS) using L-band frequencies, the ionosphere causes signal delays that correspond with link related range errors of up to 100 m. In a first order approximation the range error is proportional to the total electron content (TEC) of the ionosphere. Whereas this first order range error can be corrected in dual-frequency measurements by a linear combination of carrier phase- or code-ranges of both frequencies, single-frequency users need additional information to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by ionospheric models. In this paper we discuss and compare different ionospheric correction methods for single-frequency users. The focus is on the comparison of the positioning quality using dual-frequency measurements, the Klobuchar model, the NeQuick model, the IGS TEC maps, the Neustrelitz TEC Model (NTCM-GL) and the reconstructed NTCM-GL TEC maps both provided via the ionosphere data service SWACI (http://swaciweb.dlr.de) in near real-time. For that purpose, data from different locations covering several days in 2011 and 2012 are investigated, including periods of quiet and disturbed ionospheric conditions. In applying the NTCM-GL based corrections instead of the Klobuchar model, positioning accuracy improvements up to several meters have been found for the European region in dependence on the ionospheric conditions. Further in mid- and low-latitudes the NTCM-GL model provides results comparable to NeQuick during the considered time periods. Moreover, in regions with a dense GNSS ground station network the reconstructed NTCM-GL TEC maps are partly at the same level as the final IGS TEC maps.     

面向北斗单历元分米级定位的ARAIM保护水平计算方法CSCD

精密定位的质量控制和完好性评估是实时全球卫星导航系统(GNSS)导航应用不可或缺的环节,尤其是在GNSS易受损害的城市峡谷等场景下,这种需求更加迫切.广域精密单点定位(PPP)瞬时分米级定位,利用GNSS三频信号形成的两个宽巷观测值可以实现单点单历元分米级定位.然而,在城市复杂环境中,反射信号、严重多路径以及其他信号干扰对定位造成的影响无法准确评估与识别,限制了PPP瞬时分米级单点定位的应用.完好性概念中的高级接收机自主完好性监测(ARAIM)可以计算用户定位误差最小置信区间的上限保护水平(PL)以评估定位有效性,可经过一定改进用于PPP瞬时定位的质量控制.针对当前ARAIM中计算PL的误差模型难以适应高精度定位需求的问题,提出了一种改进的ARAIM PL算法,称其为BARAIM(Back Advanced Receiver Autonomous Integrity Monitoring).使用PPP三频组合观测值残差对ARAIM权与误差模型进行修正以计算PL.基于不同复杂程度的环境下采集的车载数据对算法进行了验证,对PL的改进情况以及导航的可用性提升情况进行评估.结果表明:在不同环境下,基于改进的B-ARAIM算法得到的PL,相比传统方法得到的PL更符合城市定位的需要,将PL降低了30%~70%.此方法有助于将ARAIM算法应用在高精度GNSS定位领域.     

A preliminary evaluation of the performance of multiple ionospheric models in low- and mid-latitude regions of China in 2010–2011

Ionospheric delay is a dominant error source in Global Navigation Satellite System (GNSS). Single-frequency GNSS applications require ionospheric correction of signal delay caused by the charged particles in the earth’s ionosphere. The Chinese Beidou system is developing its own ionospheric model for single-frequency users. The number of single-frequency GNSS users and applications is expected to grow fast in the next years in China. Thus, developing an appropriate ionospheric model is crucially important for the Chinese Beidou system and worldwide single-frequency Beidou users. We study the performance of five globally accessible ionospheric models Global Ionospheric Map (GIM), International Reference Ionosphere (IRI), Parameterized Ionospheric Model (PIM), Klobuchar and NeQuick in low- and mid-latitude regions of China under mid-solar activity condition. Generally, all ionospheric models can reproduce the trend of diurnal ionosphere variations. It is found that all the models have better performances in mid-latitude than in low-latitude regions. When all the models are compared to the observed total electron content (TEC) data derived from GIM model, the IRI model (2012 version) has the best agreement with GIM model and the NeQuick has the poorest agreement. The RMS errors of the IRI model using the GIM TEC as reference truth are about 3.0–10.0 TECU in low-latitude regions and 3.0–8.0 TECU in mid-latitude regions, as observed during a period of 1 year with medium level of solar activity. When all the ionospheric models are ingested into single-frequency precise point positioning (PPP) to correct the ionospheric delays in GPS observations, the PIM model performs the best in both low and mid-latitudes in China. In mid-latitude, the daily single-frequency PPP accuracy using PIM model is ~10 cm in horizontal and ~20 cm in up direction. At low-latitude regions, the PPP error using PIM model is 10–20 cm in north, 30–40 cm in east and ~60 cm in up component. The single-frequency PPP solutions indicate that NeQuick model has the lowest accuracy among all the models in both low- and mid-latitude regions of China. This study suggests that the PIM model may be considered for single-frequency GNSS users in China to achieve a good positioning accuracy in both low- and mid-latitude regions.     

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.     

顾及卫星姿态的多系统精密钟差产品综合

国际GNSS服务(IGS)提供的GPS综合产品被广泛应用于各种高精度科学研究中. 随着各国卫星导航系统的发展,亟需研究针对多系统全球卫星导航系统(GNSS)产品的综合策略. 由于卫星姿态与钟差相互耦合,综合钟差时额外考虑姿态改正将进一步提高综合产品精度,因此研究了一种顾及卫星姿态的GNSS钟差综合策略,改正姿态后GPS综合残差最大可减小80%. 对142个IGS测站进行精密单点定位(PPP)解算发现,综合产品比单个分析中心产品更加稳定,东(E)、北(N)、高(U)方向的动态定位精度最大可提升22.7%、16.7%和18.3%. 相对于未顾及姿态改正的综合产品,顾及姿态改正的综合产品的动态定位精度最大可提升65.3%.      

谷歌Nexus 9智能终端原始GNSS观测值的质量分析

从信噪比、伪距残差、相位残差等方面对开阔环境下的静态谷歌Nexus 9智能平板终端的原始全球导航卫星系统（Global Navigation Satellite System,GNSS）观测数据质量进行了分析评估,结果表明,Nexus 9平板的全球定位系统（Global Positioning System,GPS）、GLONASS观测值的信噪比比测量型接收机低10 dBHz左右;伪距精度分别为5.43 m、11.39 m,相位精度分别为4.44 mm、4.99 mm;相对于高度角来说,信噪比与伪距残差的相关性更强,更能反映观测数据的质量。在此基础上给出了信噪比定权的随机模型,并进行了开阔环境下的伪距单点定位测试。实验结果表明,基于信噪比定权的单点定位平面精度为2.74 m,高程精度为4.56m,比高度角定权精度提高了约26%。     

Ionospheric effects on relative positioning within a dense GPS network

Local variability in total electron content can seriously affect the accuracy of GNSS real-time applications. We have developed software to compute the positioning error due to the ionosphere for all baselines of the Belgian GPS network, called the Active Geodetic Network (AGN). In a first step, a reference day has been chosen to validate the methodology by comparing results with the nominal accuracy of relative positioning at centimeter level. Then, the effects of two types of ionospheric disturbances on the positioning error have been analyzed: (1) Traveling ionospheric disturbances (TIDs) and (2) noise-like variability due to geomagnetic storms. The influence of baseline length on positioning error has been analyzed for these three cases. The analysis shows that geomagnetic storms induce the largest positioning error (more than 2 m for a 20 km baseline) and that the positioning error depends on the baseline orientation. Baselines oriented parallel to the propagation direction of the ionospheric disturbances are more affected than others. The positioning error due to ionospheric small-scale structures can be so identified by our method, which is not always the case with the modern ionosphere mitigation techniques. In the future, this ionospheric impact formulation could be considered in the development of an integrity monitoring service for GNSS relative positioning users.     

Ionospheric correction using NTCM driven by GPS Klobuchar coefficients for GNSS applications

Global Navigation Satellite Systems (GNSS) require mitigation of ionospheric propagation errors because the ionospheric range errors might be larger than tens of meters at the zenith direction. Taking advantage of the frequency-dispersive property of ionospheric refractivity, the ionospheric range errors can be mitigated in dual-frequency applications to a great extent by a linear combination of carrier phases or pseudoranges. However, single-frequency GNSS operations require additional ionospheric information to apply signal delay or range error corrections. To aid single-frequency operations, the global positioning system (GPS) broadcasts 8 coefficients as part of the navigation message to drive the ionospheric correction algorithm (ICA) also known as Klobuchar model. We presented here an ionospheric correction algorithm called Neustrelitz TEC model (NTCM) which can be used as complementary to the GPS ICA. Our investigation shows that the NTCM can be driven by Klobuchar model parameters to achieve a significantly better performance than obtained by the mother ICA algorithm. Our research, using post-processed reference total electron content (TEC) data from more than one solar cycle, shows that on average the RMS modeled TEC errors are up to 40% less for the proposed NTCM model compared to the Klobuchar model during high solar activity period, and about 10% less during low solar activity period. Such an approach does not require major technology changes for GPS users rather requires only introducing the NTCM approach a complement to the existing ICA algorithm while maintaining the simplicity of ionospheric range error mitigation with an improved model performance.     

顾及有色噪声的卡尔曼滤波在多路径误差削弱中的应用

多路径误差为一时空环境效应,难以构建准确数学模型消除其影响,且该误差在基线两端不具有空间相关性,运用现有差分技术也无法很好消除,是高精度短基线测量中主要误差之一.为进一步削弱多路径误差,本文以监测站坐标时间序列中多路径误差为研究对象,根据多路径误差在历元间的时变特性,建立多路径误差状态空间模型,采用标准卡尔曼滤波和顾及有色噪声的卡尔曼滤波从监测站第一天双差固定解坐标残差序列中估计多路径误差改正序列,并根据多路径误差的周日重复特性,利用第一天得到的多路径误差改正序列对之后各天坐标序列进行改正.最后通过实验分析,得出顾及有色噪声的卡尔曼滤波估计方法优于标准卡尔曼滤波的结论.研究方法对提高GNSS定位精度具有重要实用价值.     

GNSS‐声学海底定位的声速误差处理方法综述

全球导航卫星系统（global navigation satellite system,GNSS）‐声学海底定位是面向海底俯冲带板块形变监测需求提出的一种定位技术,也是建设海洋时空基准网的一种重要技术,有着广阔的应用前景。虽然目前GNSS‐声学海底定位技术的研究成果还不能满足海洋时空基准网的建设需求,但其数据处理方法尤其是声速误差精细处理方法,对海洋时空基准网海底部分（海底大地基准）的建设具有重要借鉴意义。介绍了GNSS‐声学海底定位技术的起源,并将其分为静态测量和动态测量两类,同时将声速误差处理方法作为该技术的发展脉络进行梳理,提炼了该技术的3个发展阶段:仅假设海洋声速垂向分层、考虑声速的时域变化、考虑声速的水平梯度。对于仅假设海洋声速垂向分层的阶段,国外学者采用几何结构对称的方式来削弱声速误差的影响;国内学者则主要对声速以外误差源（杆臂矢量误差、时标偏差、姿态角误差等）进行了研究,并用优化随机模型的方式削弱系统误差对定位的影响。对于考虑声速时域变化的阶段,国外学者利用拟合方法（多项式拟合或三次样条拟合）结合参数平滑约束来解算声速的时域变化量,提高定位的稳定性;国内学者基于此细化了参数拟合的方法（考虑参数长周期项的变化特征）,并创新性地提出了水下差分定位算法。对于考虑声速水平梯度的阶段,国内外学者在GNSS‐声学海底定位中解算了声速水平梯度参数,提高了水平方向定位的稳定性,并利用海洋数值模型验证了结果的可靠性。展望了将GNSS‐声学海底定位高精度数据处理方法应用于海底大地基准建设的前景,并引入了小时空尺度声速层析的概念（基于海洋时空基准网的声速误差处理方法）,以期解决数值预报模型不能提供小时空尺度产品的问题,进而为水下潜器提供更高精度的声速误差改正服务。     

苏州3D连续运行卫星定位服务系统平面精度检测与分析

对SZ-GNSS CORS覆盖范围内的定位精度进行检测,可确定系统设计是否达标,使各类卫星定位作业模式的针对性更强,经济效益更高.本文对SZ-GNSS CORS的平面定位精度检测方法和检测精度进行分析,结果表明,在SZ-GNSS CORS中RTK观测模式下X和y方向的内附合中误差为5mm左右,外附合中误差为11 mm左右;动态规则几何轨迹的检测结果良好.平面定位精度达到设计要求,在很大程度上能够满足苏州城市建设和信息化建设对GNSS的需求.     

Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling

Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8 cm for the Global Positioning System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation, but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method will have important practical applications for correcting for multipath in well-constrained environments (such as at base stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.     

全球导航卫星系统反射测量(GNSS+R)最新进展与应用前景

全球导航卫星系统(GNSS)具有全天候、近实时、高精度的特点,可持续发射L波段信号,广泛应用于定位、导航和授时(PNT)。随着GNSS技术的发展,最近GNSS反射信号可探测地球表面特征,即GNSS反射测量(GNSS+R)。结合GNSS接收机天线位置和介质信息,利用延迟测量值可以确定表面粗糙度和表面特性。GNSS+R作为当前GNSS和遥感领域的研究热点,取得了一些研究进展和成果。本文详细介绍了GNSS+R原理和方法及其最新应用进展,包括各种GNSS+R技术手段和方法,以及海洋、陆地、水文、植被和冰雪等遥感应用,特别是最新BeiDou-R和TDS-1研究进展。最后给出了GNSS+R应用前景和展望,包括多GNSS系统、GNSS+R接收机、GNSS+R卫星计划和新兴应用等。     

基于北斗的精密单点定位估计对流层天顶延迟精度分析

通过全球导航卫星（GNSS）系统获取对流层天顶延迟对于气象和电波折射修正具有重要应用价值。利用自主研发的静态精密单点定位软件CRPPP,基于国际GNSS地球动力学服务局（IGS）发布的北斗系统（BDS）精密星历和精密钟差,给出了BDS估算天顶延迟结果。以IGS发布的全球定位系统（GPS）结果为参考对比,BDS估算天顶延迟结果平均偏差优于5mm,均方根误差（rms）优于2．3cm．同时,给出了西沙地区GPS与BDS估计结果,结果表明：利用北斗系统估计的对流层天顶延迟精度与GPS相当。     

智能手机RTK定位软件实现及应用试验

随着芯片技术的发展,智能手机已成为使用最普遍的一类全球卫星导航系统(GNSS)设备,其提供位置服务的能力逐步彰显.为探究将手机作为专业GNSS设备的可行性,利用谷歌开放Android智能终端GNSS原始观测数据这一契机,设计并实现一款手机实时动态(RTK)定位手机应用程序(APP),并基于该APP开展高精度定位应用试验.结果表明：在静态条件下,手机RTK定位精度约达1 dm;在行人和车载动态条件下,可达平面亚米级、高程1～2 m的精度水平,RTK定位精度远高于内置芯片解,但稳定性略差于芯片解.使用手机模拟RTK点测量,其平面精度约达1 m,基本满足地理信息采集和调查等亚米级到米级低精度专业应用的需求.     

INS/GNSS/ODO嵌入式系统的容错技术研究

车载低成本嵌入式组合导航系统的可靠性容易受到多种传感器故障和环境的影响,基于全球卫星导航系统(GNSS)状态的惯性导航系统(INS)/GNSS/里程计(ODO)抗差组合导航算法,提出了一种两级故障检测处理方法.其中,第一级检测使用了基于解析冗余的残差卡方检验法,第二级检测使用了改进的双状态传播卡方检验算法.利用自主研制...     

Using Allan variance to analyze the error characteristics of GNSS positioning

Currently, we evaluate the positioning accuracy of GNSS mainly by providing statistical values that can represent the overall error level, such as CEP, RMS, 2DRMS, and maximum error. These are solid indicators of the general performance of the GNSS positioning. But some applications like GNSS/INS integrated system require a detailed analysis of the error characteristics and knowledge of the precise error model. This requirement necessitates the modeling of the error components of the GNSS positioning solutions. In our research, the Allan variance method is proposed to analyze the GNSS positioning errors, describe the error characteristics, and build the corresponding error models. Based on our research, four dominant noise terms are identified in the GNSS positioning solutions, that is, 1st order Gauss-Markov process, Gaussian white noise, random walk noise, and flicker noise, which indicates that white noise is not always enough and appropriate to model GNSS positioning errors for some applications. The results show that the Allan variance is a feasible and effective way to analyze the error characteristics of the GNSS positioning solutions.