卫星钟差解算及其星间单差模糊度固定

整数相位模糊度解算可以显著提高GNSS精密单点定位（PPP）的精度。本文提出一种解算卫星钟差的方法,通过固定星间单差模糊度恢复出能够支持单台接收机进行整数模糊度解算的卫星钟差,即所谓的“整数”钟差。为了实现星间单差模糊度固定,分别通过卫星端宽巷FCB解算和模糊度基准的选择与固定恢复出宽巷和窄巷模糊度的整数性质。为了证明本文方法的可行性,采用IGS测站的GPS数据进行卫星钟差解算试验。结果表明,在解算钟差时,星间单差模糊度固定的平均成功率为73%。得到的卫星钟差与IGS最终钟差产品相比,平均的RMS和STD分别为0.170和0.012 ns。448个IGS测站的星间单差宽巷和窄巷模糊度小数部分的分布表明本文得到的卫星钟差和FCB产品具备支持PPP用户进行模糊度固定的能力。基于以上产品开展了模拟动态PPP定位试验,结果表明模糊度固定之后,N、E、U和3D的定位精度（RMS）分别达到0.009、0.010、0.023和0.027 m,与不固定模糊度或采用IGS钟差的结果相比,分别提高了30.8%、61.5%、23.3%和37.2%。     

GBM快速轨道产品及非差模糊度固定对其精度的改进

GNSS是实时定位导航最重要的方法,精密卫星轨道钟差产品是GNSS高精度服务的前提。国际GNSS服务中心(IGS)及其分析中心长期致力于GNSS数据处理的研究及高精度轨道和钟差产品的提供。GFZ作为分析中心之一,提供GBM多系统快速产品。本文基于2015—2021年GBM提供的精密轨道产品,阐述了数据处理策略,分析了轨道的精度,介绍了非差模糊度固定的原理和对精密定轨的影响。结果表明:GBM快速产品中的GPS轨道精度与IGS后处理精密轨道相比的精度约为11~13 mm,轨道6 h预报精度约为6 cm;GLONASS预报精度约为12 cm,Galileo在该时期的精度均值为10 cm,但是在2016年底以后精度提升到5 cm左右;北斗系统的中轨卫星(medium earth orbit,MEO)在2020年以后预报精度约为10 cm;北斗的静止轨道卫星(geostationary earth orbit,GEO)卫星和QZSS卫星的预报精度在米级;卫星激光测距检核表明,Galileo、GLONASS、BDS-3 MEO卫星轨道精度分别为23、41、47 mm;此外,采用150 d观测值的试验结果表明,采用非差模糊度固定能显著改善MEO卫星轨道精度,对GPS、GLONASS、Galileo、BDS-2和BDS-3的MEO卫星的6 h时预报精度改善率分别为9%~15%、15%~18%、11%~13%、6%~17%和14%~25%。     

基于等价观测方程的GPS/GLONASS组合多基线解算方法

进行独立参数化时,GNSS观测方程的双差、单差与非差观测方程理论上是等价的。利用按高度角定权的模型以及不同测站跟踪不同数量卫星的等价观测方程,实现基于简化等价观测方程的GPS/GLONASS组合多基线解算,包括多基线模糊度的固定、基线向量的解算与精度分析,并用多个测站的GPS/GLONASS同步实测载波相位和码伪距观测数据完成多基线解算分析。计算结果表明,由于多个测站的同时作用导致几何强度增强,降低模糊度间的相关性,有利于模糊度的快速解算;同时简化等价观测方程,提高法方程的形成速度,解算的基线精度也优于单基线解算模式。     

非差模糊度固定北斗三号实时滤波精密定轨

模糊度固定是全球导航卫星系统（global navigation satellite system,GNSS）高精度数据处理的关键。不同于传统的双差模糊度固定,非差模糊度固定无需构建双差模糊度,更为简单高效。将非差模糊度固定引入北斗三号全球卫星导航系统(BeiDou-3 global navigation satellite system,BDS-3)中地球轨道卫星实时滤波定轨,分析非差模糊度固定对实时滤波轨道收敛速度及精度的影响。利用国际GNSS服务组织全球测站网观测数据进行实时滤波精密定轨实验,以德国地学研究中心的事后快速轨道为参考评定精度。结果表明：非差模糊度固定对收敛速度影响很小,但可以有效提升轨道切向、法向精度;相比浮点解轨道,固定解轨道径向、切向、法向精度分别提高1.0%、18.5%、19.5%,误差均方根分别达到6.0、7.4、6.2 cm;受切向、法向影响,中国空间技术研究院类型卫星轨道精度优于上海微小卫星工程中心类型卫星轨道;顾及窄巷固定率与轨道精度的相关性,窄巷固定率可以作为实时轨道质量的重要指标之一。实时滤波轨道精度的进一步提升有赖于BDS-3数据处理模型的持续精...     

基于单差模糊度的 GPS／GLONASS 组合相对定位模型研究

采用频分多址技术(FDMA),GLONASS系统双差模糊度固定存在两个问题:不同卫星波长不一致,双差后不能保持模糊度整数特性;共视卫星频率不同,不同卫星之间存在大小不同的频间偏差(IFB)。传统的双差不能很好处理GLONASS相对定位模糊度固定问题。文中考虑将双差所涉及的两颗卫星的站间单差模糊度分别求解,不受共视卫星波长不一致的影响。同时采用参数估计法消除不同厂商接收机的频间偏差影响。试验结果表明采用文中方法可以正确固定GLONASS模糊度,并且达到与GPS相当的解算精度,GPS/GLONASS组合定位精度和可靠性也比GPS单系统有所提高。     

PPP网解UPD模糊度固定技术监测尼泊尔Ms8.1级地震对中国珠峰地区及周边地震同震位移

利用UPD模糊度固定技术无需顾及基线解算基站地震所带来的影响,可以进行高精度非差PPP解算,"真实"获取地震周边地区GNSS站点高精度同震位移变化。为此,本文利用"国家基准一期工程""中国大陆构造环境监测网络"以及国家测绘地理信息局在珠峰周边所观测的GNSS观测资料,基于UPD模糊度固定技术高精度非差解算2015年4月25日尼泊尔Ms8.1级地震对我国珠峰地区及周边地震同震位移影响。首先,本文选取全国及周边IGS均匀分布、站点稳定、远离震区的GNSS连续观测网络数据计算卫星端的宽、窄巷UPD,采用PPP网解UPD模糊度固定技术,对解算地震区域内的GNSS测站的载波相位模糊度进行固定,得到无模糊度的精确相位观测值,进行高精度非差PPP解算;通过对平静日IGS测站数据处理与ITRF2008历元坐标对比分析,验证了该方法的精确性;最后,对2015年4月25日、5月12日地震以及地震前后数据,进行了UPD模糊度固定技术的非差PPP解算,分析了中国珠峰地区及周边GNSS站的同震位移;同时也分析了中国珠峰地区在2005—2015年10年的位移变化情况。UPD模糊度固定技术整网解算的方法也证实了能够为GNSS用于监测地震同震位移等,提供了一种精确、可靠的技术手段。     

基于小波变换的单频GPS快速精密定位整周模糊度的解算

对于GPS短基线,载波相位双差观测量已基本消除了卫星轨道误差、钟差、大气折射误差等系统偏差的影响,主要包含距离观测量信息及随机测量误差,其中测量误差是高频的测量噪声,小波变换可将GPS载波相位双差观测量中的观测噪声(高频部分)分解出来。本文利用Coiflets小波基函数对GPS快速定位的原始载波相位双差观测量进行5层分解,通过重构第5层低频系数获得去除噪声的"干净"的载波相位双差观测量,然后利用"干净"的双差观测量进行最小二乘参数估计,以减小测量噪声对GPS快速定位病态方程解的扰动。计算结果表明该方法能够显著提高GPS快速定位中模糊度浮点解的精度,仅利用几个观测历元的数据就可以准确地固定模糊度。     

基于车载移动测量的GNSS定位方法

针对车载移动测量需要高频高精度的动态差分定位解算的问题,文中介绍利用GPS、北斗、GLONASS三个卫星导航系统进行载波相位动态差分的解算方法。首先利用双频观测值组成双差宽巷观测方程,利用M-W组合求出较高精度的宽巷模糊度浮点解,然后对宽巷模糊度进行搜索固定;接着对载波双差的基础模糊度进行搜索固定;最后将固定的模糊度代入载波相位双差观测方程,利用最小二乘求解测站坐标。文中使用该方法对车载GNSS实测数据进行解算,最终可得到厘米级别的定位结果。     

单频RTK动态解算的卡尔曼滤波算法研究

本文针对单频RTK提出了一种快速动态定位卡尔曼滤波算法,该方法使用C码和L1观测值,用模型改正对流层干延迟,双差大气延迟分解为测站大气天顶延迟和投影函数,与流动站位置以及站间单差模糊度组成观测方程进行卡尔曼滤波,得到单差模糊度浮点解及方差阵,通过星间求差得到双差模糊度浮点解及方差阵,结合MLAMBDA方法实时动态确定模糊度。经实测数据和IGS站数据验证该算法具有较好定位结果。     

模糊度固定的北斗卫星多系统融合精密轨道确定

利用全球分布的IGS和MGEX站多模观测数据,研究了北斗卫星多系统融合双差动力学精密定轨方法,提出了适应北斗系统的双差模糊度固定策略。结合实测数据,对比了单系统与多系统融合、模糊度固定解与浮点解的定轨效果。结果表明：相比单系统定轨,多系统融合定轨能有效改进IGSO和MEO卫星轨道精度,但对于GEO卫星,多系统融合定轨并无优势;利用改进的模糊度固定策略对IGSO和MEO卫星双差模糊度进行固定,有效提高了长基线模糊度固定率,整体固定成功率由40%提高到60%以上;模糊度固定对定轨精度改进作用明显,IGSO和MEO卫星三维定轨精度分别提高了48%和36%,达到0.048 m和0.066 m。     

GNSS大网双差模型并行快速解算方法

针对GNSS大网数据采用双差模型解算时存在时效性差的问题,提出了一种改进的独立双差观测值构建与独立基线并行解算的方法,采用并行技术实现多核并行与网络多节点并行的双层自动快速解算策略。通过对约375个IGS站1周的观测数据进行处理,改进的独立双差观测值选取方法比传统路径最短方法所选的单天全网独立双差数据平均多了53万个,E、N、U方向坐标重复性平均提升了14.0%、12.9%和29.2%。采用不同解算策略的计算结果表明,4台普通计算机的并行计算比传统串行方案的计算效率提升了14倍左右,如375个测站采用改进观测值构建方法的4节点并行方案仅需要35.62min,显著提高了整网双差的解算效率。     

Improving carrier-phase ambiguity resolution in global GPS network solutions

Integer carrier-phase ambiguity resolution is one of the critical issues for precise GPS applications in geodesy and geodynamics. To resolve as many integer ambiguities as possible, the ‘most-easy-to-fix’ double-difference ambiguities have to be defined. For this purpose, several strategies are implemented in existing GPS software packages, such as choosing the ambiguities according to the baseline length or the variances of the estimated real-valued ambiguities. Although their efficiencies are demonstrated in practice, it is proven in this paper that they do not reflect all effects of varying data quality, because they are based on theoretical considerations of GPS data processing. Therefore, a new approach is presented, which selects the double-difference ambiguities according to their probability of being fixed to the nearest integer. The probability is computed from estimates and variances of wide-lane and narrow-lane ambiguities. Together with an optimized ambiguity fixing procedure, the new approach is implemented in the routine data processing for the International GPS Service (IGS) at GeoForschungsZentrum (GFZ) Potsdam. Within a sub-network of about 90 IGS stations, it is demonstrated that more than 97% of the independent ambiguities are fixed correctly compared to 75% by a commonly used method, and that the additionally fixed ambiguities improve the repeatability of the station coordinates by 10–26% in regions with sparse site distribution.     

Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations

Precise Point Positioning (PPP) has been demonstrated to be a powerful tool in geodetic and geodynamic applications. Although its accuracy is almost comparable with network solutions, the east component of the PPP results is still to be improved by integer ambiguity fixing, which is, up to now, prevented by the presence of the uncalibrated phase delays (UPD) originating in the receivers and satellites. In this paper, it is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network. An approach is implemented to estimate the fractional parts of the single-difference (SD) UPDs between satellites in wide- and narrow-lane from a global reference network. By applying the obtained SD-UPDs as corrections to the SD-ambiguities at a single station, the corrected SD-ambiguities have a naturally integer feature and can therefore be fixed to integer values as usually done for the double-difference ones in the network mode. With data collected at 450 stations of the International GNSS Service (IGS) through days 106 to 119 in 2006, the efficiency of the presented ambiguity-fixing strategy is validated using IGS Final products. On average, more than 80% of the independent ambiguities could be fixed reliably, which leads to an improvement of about 27% in the repeatability and 30% in the agreement with the IGS weekly solutions for the east component of station coordinates, compared with the real-valued solutions. An erratum to this article can be found at     

Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.     

纳伪概率可控的四舍五入法及其在RTK模糊度固定中的应用

RTK模糊度固定通常采用序贯四舍五入方法,该方法只固定能可靠固定的部分模糊度,因此控制四舍五入的纳伪概率是实现RTK可靠性的关键。从含多个备选假设的假设检验理论出发,研究纳伪概率可控的四舍五入方法,根据风险水平和实数解的质量自适应地确定四舍五入取整区域,从而有效地控制整数固定的纳伪概率。并结合GNSS应用中两种特殊情况,发展两种简单实用的应用策略。采用基线长94.6 km的CORS站GPS双频数据进行网络RTK模糊度固定试验,分析本文纳伪概率可控的四舍五入方法的效果。结果表明,纳伪概率可控的四舍五入方法的固定率与传统四舍五入方法的固定率相当,且较传统方法更能有效地控制纳伪概率,提高整数解的可靠性。     

长距离GPS/BDS参考站网多频载波相位整周模糊度解算方法

长距离网络RTK是实现GPS/BDS高精度实时定位的主要手段之一,其核心是长距离参考站网GPS/BDS整周模糊度的快速准确确定。本文提出了一种长距离GPS/BDS参考站网载波相位整周模糊度解算方法,首先利用GPS双频观测数据计算和确定宽巷整周模糊度,同时利用BDS的B2、B3频率观测值确定超宽巷整周模糊度。然后建立GPS载波相位整周模糊度和大气延迟误差的参数估计模型,附加双差宽巷整周模糊度的约束,解算双差载波相位整周模糊度,并建立参考站网大气延迟误差的空间相关模型。根据B2、B3频率的超宽巷整周模糊度建立包含大气误差参数的载波相位整周模糊度解算模型,利用大气延迟误差空间相关模型约束BDS双差载波相位整周模糊度的解算。克服了传统的使用无电离层组合值解算整周模糊度的不利影响。采用实测长距离CORS网GPS、BDS多频观测数据进行算法验证,试验结果证明该方法可实现长距离参考站网GPS/BDS载波相位整周模糊度的准确固定。     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

FirCAR算法的OTF快速定位方法

根据GNSS不同频率间整周模糊度的约束关系,提出一种基于多频整周模糊度间关系约束的模糊度新算法(dual-frequency integer relationship constrained ambiguity resolution,FirCAR)。FirCAR可快速动态解算出高高度角卫星的整周模糊度,将已经固定的整周模糊度视为高精度的伪距观测值应用到下一步的浮点解重算中。结合模糊度搜索算法,如LAMBDA,在模糊度搜索方面的高效性,根据重算后的浮点解进一步解算其他未固定的模糊度解。模糊度固定成功后,即可实现OTF(on the fly)快速定位。实测数据表明,FirCAR算法在静态和动态观测条件下,模糊度初始化所用的平均观测历元数分别为1.04和1.10。与常规的模糊度搜索算法的对比试验表明,结合FirCAR算法模糊度固定所用的观测历元数分别减少了39%和18%。     

一种基于星间单差模糊度固定的载波伪距生成方法

随着测站和卫星数量的不断增加,大规模GNSS网的数据处理面临越来越大的挑战。将载波相位观测量转化为载波伪距是提高大规模GNSS网数据处理效率的有效方法。本文提出在精密单点定位基础上进行星间单差模糊度固定生成载波伪距的方法。采用中国大陆构造环境监测网络（陆态网）观测数据进行了验证。结果表明,对于包含252个测站的观测网,采用载波伪距进行整网解的处理时间不超过20 min。剔除异常测站后,240个陆态网测站的月坐标重复精度在N、E和U方向的均值分别为0.74、0.85和2.53 mm,略优于原始数据整网解的结果。本文还探讨了采用原始数据和载波伪距进行整网解的关系,利用带约束条件的观测模型对不同方法生成的载波伪距应用于整网解的原理进行统一解释,并指出了载波伪距整网解与原始数据整网解的理论等效性。