3种PPP模型的统一模糊度固定方法

精密单点定位(PPP)的模糊度经未校准硬件延迟小数部分(FCB)产品改正后,可恢复整周特性,能够显著缩短PPP的初始化时间。然而由于用户端模糊度固定模型需与服务端FCB产品保持一致,不仅造成了用户端面临不同FCB产品无法使用的问题,而且加重了服务端的链路传输压力。本文提出一种基于用户端3种PPP模型(消电离层组合、无电离层约束的非组合以及先验电离层约束的非组合模型)的统一模糊度固定方法,不同用户端可采用同一种FCB产品实现模糊度的快速固定。选取全球116个MGEX测站作为服务端生成3种FCB产品,选取未参与服务端解算的50个测站作为用户端进行验证。试验结果表明,本文方法解决了用户端面临不同FCB产品的PPP模糊度固定问题,在定位精度、收敛时间、固定率方面与传统方法保持一致。     

BDS-3新频点PPP模糊度固定研究

针对BDS-3新频点在精密单点定位解算中的模糊度固定问题，该文采用绝对信号偏差(OSB)改正的方法，对B2a频点在精密单点定位方面的性能进行了研究。首先通过与整数钟差法进行对比实验，验证OSB改正法在模糊度固定方面的可靠性，之后采用该方法对B2a频点构建的双频无电离层组合进行精密单点定位-模糊度固定(PPP-AR)实验，与B1I/B3I的PPP-AR结果进行比较，评估定位精度。结果表明，OSB改正原始观测值的模糊度固定方法有较好的可靠性，收敛速度提升20%,模糊度固定成功率在90%以上；新频点B2a的精密单点定位性能较好，收敛速度和定位精度与B1I、B3I频点相当，采用B2a频点得到的双频无电离层组合在PPP-AR解算时能完成模糊度的快速固定，收敛时间在25 min以内，收敛后误差小于2 cm, B2a频点可用于PPP-AR解算。     

一种加快BDS精密单点定位初始化的方法

由于BDS卫星的星座特性及卫星的轨道和钟差的精度影响,使得传统消电离层组合精密单点定位(PPP)的初始化时间较长。针对上述问题,文中对附加电离层约束的非组合精密单点定位算法进行研究。首先介绍非组合PPP算法,分析其与传统PPP的差异;其次分别利用CODE电离层格网产品,以反距离加权算法计算的站星电离层延迟、低阶球谐函数建立的区域电离层产品等作为先验信息对非组合PPP进行约束。通过MGEX观测网实测数据静态和仿动态计算表明,相比传统消电离层组合PPP,附加电离层约束的非组合PPP能够有效缩短初始化时间,同时能够获得高精度的定位结果。     

不同函数模型的精密单点定位性能分析

针对精密单点定位常用的无电离层组合模型、非组合模型和Uofc函数模型的静态和仿动态精密单点定位定位性能问题,该文利用2015年10月27日MGEX 94个跟踪站点的静态观测数据,分别从观测残差、收敛时间和定位精度3个方面对其进行了对比分析。实验结果表明:(1)非组合的观测残差最小,内符合精度最高,收敛时间最长;(2)无电离层组合观测残差最大,内符合精度最差,收敛时间最短。3种函数模型无论是静态还是仿动态精密单点定位,都具有相当的定位精度,静态精密单点定位在水平方向的定位精度优于1cm,高程方向的偏差优于3cm;仿动态精密单点定位在水平方向的定位精度优于1.5cm,高程方向优于4cm。     

精密单点定位中附加先验电离层改正的内插方法研究

在精密单点定位技术中,外部提供给接收机更多的先验信息能使其定位精度和实时性得到提高。依靠增强站网内插出流动站的电离层延迟进行非差非组合精密单点定位时,其提供的改正达到精度要求势必使待估参数减少,模型强度变强,定位精度高。本文对比了内插电离层改正的精度,探讨了内插模型,提出了平面双样条内插模型。实验结果表明:在内插模型合适的情况下,电离层延迟精度可达到精密单点定位的要求。      

非差增强信息与差分虚拟观测数据的等价变换理论

针对目前非差精密单点定位增强信息无法直接用于RTK（real time kinematic）相对定位的问题，研究了基于附加坐标约束的参考站非差精密单点模糊度固定解提取非差改正信息的方法，并建立了非差增强信息与虚拟参考站观测信息等价变换模型，重点论述了空间状态域信息（state space representation，SSR）在等价变换中的区别应用。根据RTK模糊度部分固定技术，利用实测数据设计实验证明了算法的正确性与可用性。结果表明，虚拟零基线可获得与网络RTK同等精度的定位效果，从而实现了区域增强系统在非差与差分模式上的高度统一。     

电离层时变特性约束的BDS长距离RTK定位算法

电离层误差是影响长距离GNSS定位性能的主要因素,通常采用无电离层组合消除电离层误差的影响,但无电离层组合存在观测噪声放大、在多系统多频数据时无法对单个频率的观测值进行单独处理,直接消除电离层参数使得无法对电离层参数施加约束,而电离层的先验信息,时空约束信息更易获得,为此本文对非组合定位模型中电离层误差的时变特性进行研究。在非组合定位模型中电离层参数常被估计为随机游走,功率谱密度决定了随机游走的过程,也表达了电离层误差的时变特性,通过对功率谱密度的研究,对电离层参数进行合理的约束来改善定位的性能。不需要经验模型及人为的给予电离层参数时变约束信息,而是通过顾及电离层实时特性的电离层观测值确定功率谱密度值,提供了简单实用的电离层时变约束方法。通过试验验证采用Vondrak平滑方法进行电离层延迟的最佳平滑,能在削弱观测噪声的同时反映电离层实时变化,求得的电离层功率谱密度能显著提升整周模糊度收敛时间,使定位性能达到最优。对电离层时变约束的BDS三频观测数据长距离RTK定位试验表明：静态和动态定位模式下均能实现模糊度的快速固定,可满足高精度实时定位的需求。     

多系统非差非组合精密单点定位电离层延迟约束权阵的确定

非差非组合精密单点定位需要估计电离层延迟参数,采用电离层先验改正模型约束可以辅助电离层参数解算。针对先验电离层改正量与实际观测量之间权比关系难以确定的问题,本文提出一种电离层约束权因子搜索算法,采用权因子对先验电离层改正量的方差进行调整,根据验后残差加权平方和最小原则通过搜索找出较优的权因子,利用验后残差动态调整先验电离层改正量的方差从而达到改善定位结果的目的。采用8个MGEX跟踪站的GPS/BDS观测数据对该算法进行验证。静态结果表明：对比传统约束方法,采用搜索算法后平均三维定位精度由3.96 cm提高到3.40 cm,平均收敛时间由76.3 min缩短为59.9 min。     

非差非组合PPP的广域星间单差天顶电离层模型及其验证

高精度电离层修正是非差非组合精密单点定位(precise point positioning, PPP)加速收敛的重要前提。首先基于参考站网台站观测数据,以非差非组合精密单点定位提取的电离层延迟作为建模数据源,提出一种基于多项式模型的估计天顶电离层延迟参数以及卫星硬件延迟的单差电离层模型。然后开发了服务端和用户端相应软件系统,服务端提取电离层延迟和进行单差建模,并将模型参数播发给用户端作为电离层约束进行非差非组合精密单点定位。最后在欧洲地区通过PPP提取电离层进行拟合实验,结果表明,广域地区GPS和俄罗斯GLONASS(global navigation satellite system)单系统电离层模型内外符合精度分别为1 TECu(total electron content unit)和3 TECu。采用电离层约束的非差非组合动态精密单点定位,统计136个1 h时段的定位结果,发现在附加电离层约束PPP实验中,78个时段(57.35%)收敛时间在5 min内,97个时段(71.32%)在10 min内,122个时段(89.7%)在15 min内,132个时段(97.06%)在25 min内;在无约束PPP实验中,上述收敛时间内结果分别为15个(11.03%)、64个(47.06%)、91个(66.91%)、110个(80.88%)。     

一种改进的GPS/GLONASS组合精密单点定位算法研究

讨论了GPS精密单点定位的数学模型。提出了一种改进的GPS精密单点定位算法,该算法是把电离层延迟分为一阶电离层延迟和二阶电离层延迟的方法。分别对各阶电离层进行研究:一阶电离层采用线性组合的方式消除,二阶电离层延迟采用模型估计方法进行消除,最终达到消除电离层影响的目的。最后把该算法应用于GPS/GLONASS组合精密单点定位中,分别从E、N、U 3个定位方向上比较了GPS和GPS/GLONASS组合精密单点定位的定位结果,计算结果表明,该算法在一定程度上提高了定位的精度。较单系统GPS精密单点定位,它能够加快定位的收敛速度,保证定位的连续性。     

基于CORS的区域大气增强产品对实时PPP的影响

精密单点定位（precise point positioning，PPP）的初始化速度是制约PPP实时应用的主要因素。基于连续运行参考系统（continuously operating reference system，CORS）获取大气改正产品可以改善非组合PPP收敛时间，同时可定量探究各类大气产品对实时PPP浮点解的影响，并评估产品的精度与有效性。实时PPP实验结果表明，相对于传统PPP模式，引入电离层产品使PPP东方向收敛时间显著改善，北方向与高程方向次之，且基于非组合PPP方法获取的区域PPP电离层产品（分别改善85%、61%、18%）优于无几何距离组合相位平滑伪距方法获取的区域平滑电离层产品；引入对流层产品对高程方向的收敛时间有显著改善（52%）。而相较于单一产品和其他产品组合约束，区域PPP电离层产品和区域对流层产品组合约束PPP拥有更好的性能，对东、北、高程方向分别改善85%、63%、69%。     

基于部分整周模糊度固定的非差GPS精密单点定位方法

近年来,精密单点定位(PPP)模糊度固定技术不断发展,模糊度正确固定后可以提高短时间的定位精度。然而固定错误的模糊度,将引起严重的定位偏差,因此对PPP模糊度固定的成功率和可靠性进行研究很有必要。本文探讨了采用非差小数偏差(FCBs)改正的PPP模糊度固定方法;同时提出了一种分步质量控制的PPP部分模糊度固定(PAR)策略。通过欧洲CORS数据对该方法进行验证,结果表明:PPP模糊度固定可以提高小时解静态PPP定位精度。同时,采用部分模糊度固定策略,能够有效控制未收敛模糊度影响,提高用户端PPP模糊度固定成功率。     

整数相位钟法精密单点定位模糊度固定模型及效果分析

精密单点定位(PPP)模糊度固定方法有3种:星间单差法、整数相位钟法和钟差解耦法,但目前仅法国CNES公开发布用于整数相位钟法PPP模糊度固定的产品,因此研究基于整数相位钟法的用户端PPP模糊度固定模型很有必要.本文分析了整数相位钟法PPP模糊度固定模型,着重指出该模型与传统浮点解PPP模型的区别;提出一种顾及质量控制的逐级模糊度固定策略用于具体实施PPP模糊度固定.大量动态PPP解算试验表明:与浮点解PPP相比,固定解PPP具有更快的收敛速度且定位精度和稳定性更好.     

Assessment of correct fixing rate for precise point positioning ambiguity resolution on a global scale

Ambiguity resolution (AR) for a single receiver has been a popular topic in Global Positioning System (GPS) recently. Ambiguity-resolution methods for precise point positioning (PPP) have been well documented in recent years, demonstrating that it can improve the accuracy of PPP. However, users are often concerned about the reliability of ambiguity-fixed PPP solution in practical applications. If ambiguities are fixed to wrong integers, large errors would be introduced into position estimates. In this paper, we aim to assess the correct fixing rate (CFR), i.e., number of ambiguities correctly fixing to the total number of ambiguities correctly and incorrectly fixing, for PPP user ambiguity resolution on a global scale. A practical procedure is presented to evaluate the CFR of PPP user ambiguity resolution. GPS data of the first 3 days in each month of 2010 from about 390 IGS stations are used for experiments. Firstly, we use GPS data collected from about 320 IGS stations to estimate global single-differenced (SD) wide-lane and narrow-lane satellite uncalibrated phase delays (UPDs). The quality of UPDs is evaluated. We found that wide-lane UPD estimates have a rather small standard deviation (Std) between 0.003 and 0.004 cycles while most of Std of narrow-lane estimates are from 0.01 to 0.02 cycles. Secondly, many experiments have been conducted to investigate the CFR of integer ambiguity resolution we can achieve under different conditions, including reference station density, observation session length and the ionospheric activity. The results show that the CFR of PPP can exceed 98.0 % with only 1 h of observations for most user stations. No obvious correlation between the CFR and the reference station density is found. Therefore, nearly homogeneous CFR can be achieved in PPP AR for global users. At user end, higher CFR could be achieved with longer observations. The average CFR for 30-min, 1-h, 2-h and 4-h observation is 92.3, 98.2, 99.5 and 99.7 %, respectively. In order to get acceptable CFR, 1 h is a recommended minimum observation time. Furthermore, the CFR of PPP can be affected by diurnal variation and geomagnetic latitude variation in the ionosphere. During one day at the hours when rapid ionospheric variations occur or in low geomagnetic latitude regions where equatorial electron density irregularities are produced relatively frequently, a significant degradation of the CFR is demonstrated.     

Regional reference network augmented precise point positioning for instantaneous ambiguity resolution

Integer ambiguity fixing can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP), but it still takes approximate 15 min of time to achieve reliable integer ambiguity solutions. In this contribution, we present a new strategy to augment PPP estimation with a regional reference network, so that instantaneous ambiguity fixing is achievable for users within the network coverage. In the proposed method, precise zero-differenced atmospheric delays are derived from the PPP fixed solution of the reference stations, which are disseminated to, and interpolated at user stations to correct for L1, L2 phase observations or their combinations. With the corrected observations, instantaneous ambiguity resolution can be carried out within the user PPP software, thus achieving the position solutions equivalent to the network real-time kinematic positioning (NRTK). The strategy is validated experimentally. The derived atmospheric delays and the interpolated corrections are investigated. The ambiguity fixing performance and the resulted position accuracy are assessed. The validation confirms that the new strategy can provide comparable service with NRTK. Therefore, with this new processing strategy, it is possible to integrate PPP and NRTK into a seamless positioning service, which can provide an accuracy of about 10 cm anywhere, and upgrade to a few centimeters within a regional network.     

GNSS非组合PPP部分模糊度固定方法与结果分析

在精密单点定位(precise point positioning,PPP)技术中,模糊度固定错误将导致严重的定位偏差,为保证PPP模糊度实现更可靠的固定,需对模糊度子集的选取方式进行优化。提出了一种将质量控制与施密特正交化相结合的PPP部分模糊度固定方法。在全球导航卫星系统（global navigation satellite system,GNSS）多系统融合条件下, 选取多模GNSS实验数据,在非差非组合PPP模型中对比分析施密特正交化方法与高度角选星方法,并进行模糊度固定及定位性能验证。结果表明,施密特正交化方法相比高度角选星方法,各天与各站平均历元固定率在静态模式下分别提高了7.74%与11.46%,在仿动态模式下分别提高了7.90%与7.78%;各天与各站的首次固定时间在静态模式下分别提高了22.30%与25.42%,在仿动态模式下分别提高了20.44%与19.65%。在PPP模糊度固定和定位精度方面,多系统融合相比单BDS(BeiDou navigation satellite system)提升效果明显,在95%分位数条件下,水平和高程方向收敛时间分别平均减少20.00 min和19.00 min,水平和高程方向定位精度分别平均改善了1.50 cm和1.12 cm。在非差非组合PPP模型中,采用施密特正交化PPP部分模糊度固定方法可以显著提升模糊度固定性能,改善定位精度。     

Rapid PPP ambiguity resolution using GPS+GLONASS observations

Integer ambiguity resolution (IAR) in precise point positioning (PPP) using GPS observations has been well studied. The main challenge remaining is that the first ambiguity fixing takes about 30 min. This paper presents improvements made using GPS+GLONASS observations, especially improvements in the initial fixing time and correct fixing rate compared with GPS-only solutions. As a result of the frequency division multiple access strategy of GLONASS, there are two obstacles to GLONASS PPP-IAR: first and most importantly, there is distinct code inter-frequency bias (IFB) between satellites, and second, simultaneously observed satellites have different wavelengths. To overcome the problem resulting from GLONASS code IFB, we used a network of homogeneous receivers for GLONASS wide-lane fractional cycle bias (FCB) estimation and wide-lane ambiguity resolution. The integer satellite clock of the GPS and GLONASS was then estimated with the wide-lane FCB products. The effect of the different wavelengths on FCB estimation and PPP-IAR is discussed in detail. We used a 21-day data set of 67 stations, where data from 26 stations were processed to generate satellite wide-lane FCBs and integer clocks and the other 41 stations were selected as users to perform PPP-IAR. We found that GLONASS FCB estimates are qualitatively similar to GPS FCB estimates. Generally, 98.8% of a posteriori residuals of wide-lane ambiguities are within \(\pm 0.25\) cycles for GPS, and 96.6% for GLONASS. Meanwhile, 94.5 and 94.4% of narrow-lane residuals are within 0.1 cycles for GPS and GLONASS, respectively. For a critical value of 2.0, the correct fixing rate for kinematic PPP is only 75.2% for GPS alone and as large as 98.8% for GPS+GLONASS. The fixing percentage for GPS alone is only 11.70 and 46.80% within 5 and 10 min, respectively, and improves to 73.71 and 95.83% when adding GLONASS. Adding GLONASS thus improves the fixing percentage significantly for a short time span. We also used global ionosphere maps (GIMs) to assist the wide-lane carrier-phase combination to directly fix the wide-lane ambiguity. Employing this method, the effect of the code IFB is eliminated and numerical results show that GLONASS FCB estimation can be performed across heterogeneous receivers. However, because of the relatively low accuracy of GIMs, the fixing percentage of GIM-aided GPS+GLONASS PPP ambiguity resolution is very low. We expect better GIM accuracy to enable rapid GPS+GLONASS PPP-IAR with heterogeneous receivers.     

不同长度基线的电离层处理策略

针对不同长度的基线,受双差之后电离层延迟影响不同,提出一种新的电离层处理策略。对短、中、长基线处理分别采用3种不同的数学模型:电离层固定模型,电离层加权模型,电离层浮点模型。通过3组不同长度基线实测数据处理表明,对应不同长度的基线,文中策略可以有效地提高模糊度固定率及定位精度。