长距离网络RTK参考站间双差模糊度快速解算算法

提出了一种长距离网络RTK参考站间双差整周模糊度快速解算方法,该方法利用双频载波相位模糊度间的线性关系确定宽巷模糊度,然后选取双频载波相位的备选模糊度组合,通过计算参考站间对流层误差和轨道误差等非色散误差,对双频载波相位整周模糊度进行搜索。实验结果表明,此方法能够快速、可靠地解算长距离参考站间的双差整周模糊度。     

Triple-frequency GPS precise point positioning with rapid ambiguity resolution

At present, reliable ambiguity resolution in real-time GPS precise point positioning (PPP) can only be achieved after an initial observation period of a few tens of minutes. In this study, we propose a method where the incoming triple-frequency GPS signals are exploited to enable rapid convergences to ambiguity-fixed solutions in real-time PPP. Specifically, extra-wide-lane ambiguity resolution can be first achieved almost instantaneously with the Melbourne-Wübbena combination observable on L2 and L5. Then the resultant unambiguous extra-wide-lane carrier-phase is combined with the wide-lane carrier-phase on L1 and L2 to form an ionosphere-free observable with a wavelength of about 3.4 m. Although the noise of this observable is around 100 times the raw carrier-phase noise, its wide-lane ambiguity can still be resolved very efficiently, and the resultant ambiguity-fixed observable can assist much better than pseudorange in speeding up succeeding narrow-lane ambiguity resolution. To validate this method, we use an advanced hardware simulator to generate triple-frequency signals and a high-grade receiver to collect 1-Hz data. When the carrier-phase precisions on L1, L2 and L5 are as poor as 1.5, 6.3 and 1.5 mm, respectively, wide-lane ambiguity resolution can still reach a correctness rate of over 99 % within 20 s. As a result, the correctness rate of narrow-lane ambiguity resolution achieves 99 % within 65 s, in contrast to only 64 % within 150 s in dual-frequency PPP. In addition, we also simulate a multipath-contaminated data set and introduce new ambiguities for all satellites every 120 s. We find that when multipath effects are strong, ambiguity-fixed solutions are achieved at 78 % of all epochs in triple-frequency PPP whilst almost no ambiguities are resolved in dual-frequency PPP. Therefore, we demonstrate that triple-frequency PPP has the potential to achieve ambiguity-fixed solutions within a few minutes, or even shorter if raw carrier-phase precisions are around 1 mm. In either case, we conclude that the efficiency of ambiguity resolution in triple-frequency PPP is much higher than that in dual-frequency PPP.     

Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization

Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.     

模糊度线性约束的消电离层多频模糊度解算

针对传统多频模糊度解算方法受到电离层延迟影响造成窄巷模糊度解算可靠性降低的问题,提出一种基于模糊度线性约束的消电离层MCAR方法。该方法通过模型等价性原理构建了基于几何相关-消电离层组合模型,并凭借能够可靠解算的超宽巷/宽巷模糊度值形成线性约束,进而构造窄巷模糊度解算模型,最终求解窄巷模糊度及精密定位结果。多组北斗三频实际数据测试结果表明,即使双差电离层延迟达到73.2 cm,所提出方法也可实现模糊度解算成功率高于96%,定位精度优于15 cm。     

基于北斗三频的短基线单历元模糊度固定

采用三频观测值能组成更多波长更长、噪声较小的观测值;通过依次固定超宽巷、宽巷、窄巷模糊度,可以实现模糊度的快速固定。目前以TCAR、CIR为代表的方法均是基于无几何模型的方法,通过伪距直接求解相位模糊度;由于不同卫星模糊度各自单独求解,没有综合利用所有卫星的观测值信息。基于有几何模型,使用LAMBDA方法进行逐级模糊度固定,依次固定超宽巷、两个宽巷、两个无电离层组合窄巷模糊度,最后使用模糊度固定的两个无电离层组合进行最终基线解算。北斗实测数据验证表明,针对10km的短基线数据,采用本文方法可以实现100%的单历元模糊度固定的成功率。     

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。     

PPP网解UPD模糊度固定的无基站差分大型CORS站整网快速精密解算

本文利用“国家基准一期工程”和上千全国部分省市CORS站的GNSS观测资料,基于PPP网解UPD模糊度固定技术实现了区域内无基站差分毫米级定位以及上千全国CORS站整网一次快速精密解算,这对于保障国家应急测绘快速响应、实现灾区基准快速建立以及快速获取和恢复国家统一坐标框架基准站坐标等具有重要的实用价值意义。首先,选取2015年8月1—31日198个国家GNSS连续运行基准站计算卫星端的宽巷、窄巷UPD,采用PPP网解UPD模糊度固定技术,对这些GNSS测站的载波相位进行模糊度固定:宽巷模糊度31 d固定率平均值在80%以上的测站共有193个;窄巷模糊度31 d固定率平均值在60%以上的测站共有165个。其次,对PPP整网一次快速解算定位结果进行统计分析,结果表明:31 d整网解算在NEU 3个方向的RMS分别为2.8、3.9、5.3 mm;标准差分别为2.1、3.2、6.7 mm。再者,使用中国区域内5个IGS观测站进行无基站差分精密定位,与SOPAC单天解ITRF2008框架下历元坐标的对比分析表明,31 d单日解外符合精度水平及高程方向均相差在毫米量级。最后,利用上述GNSS基准站解算出来的卫星端的宽、窄巷UPD(31 d),依次对2015年8月1—31日全国及部分省市1195个CORS站观测数据进行载波相位模糊度固定,得到无模糊度的精确相位观测值,从而使法方程中待估模糊度参数减少,克服了基准站网规模和测站个数的限制,实现了上千CORS站整网一次快速解算,对31 d月平均解与国际知名软件GAMIT/GLOBK的双差月解结果(2015年国家基础测绘任务成果)进行比较,结果显示,NEU 3个方向上差异在1 cm以内的测站分别为99.92%、99.33%、79.83%,其中U方向相差在1.5 cm为93.22%。综上所述,PPP网解UPD模糊度固定技术的方法,确保了区域内无基站精密定位、大网快速解算的精度和效率,能够满足灾区及国家坐标框架基准站坐标快速解算与恢复的迫切需求。     

GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers

Integer ambiguity resolution (IAR) appreciably improves the position accuracy and shortens the convergence time of precise point positioning (PPP). However, while many studies are limited to GPS, there is a need to investigate the performance of GLONASS PPP ambiguity resolution. Unfortunately, because of the frequency-division multiple-access strategy of GLONASS, GLONASS PPP IAR faces two obstacles. First, simultaneously observed satellites operate at different wavelengths. Second and most importantly, distinct inter-frequency bias (IFB) exists between different satellites. For the former, we adopt an undifferenced method for uncalibrated phase delay (UPD) estimation and proposed an undifferenced PPP IAR strategy. We select a set of homogeneous receivers with identical receiver IFB to perform UPD estimation and PPP IAR. The code and carrier phase IFBs can be absorbed by satellite wide-lane and narrow-lane UPDs, respectively, which is in turn consistent with PPP IAR using the same type of receivers. In order to verify the method, we used 50 stations to generate satellite UPDs and another 12 stations selected as users to perform PPP IAR. We found that the GLONASS satellite UPDs are stable in time and space and can be estimated with high accuracy and reliability. After applying UPD correction, 91 % of wide-lane ambiguities and 99 % of narrow-lane ambiguities are within (?0.15, +0.15) cycles of the nearest integer. After ambiguity resolution, the 2-hour static PPP accuracy improves from (0.66, 1.42, 1.55) cm to (0.38, 0.39, 1.39) cm for the north, east, and up components, respectively.     

BDS网络RTK中距离参考站整周模糊度单历元解算方法

提出了一种BDS网络RTK中距离(50~100 km)参考站间的双频载波相位整周模糊度单历元解算方法。该方法首先利用B1、B2载波相位整周模糊度间的线性关系选取B1、B2载波相位整周模糊度备选值。利用双频载波相位整周模糊度备选值计算双差电离层延迟误差,根据参考站各卫星电离层延迟误差间的空间关系,使用双差电离层延迟误差构建双差电离层延迟误差的线性计算模型。通过双差电离层延迟误差线性计算模型的建立搜索和确定B1、B2载波相位的整周模糊度。经CORS网实测数据试验算例的验证,该方法只需一个历元的观测数据即可确定参考站间双差B1、B2载波相位整周模糊度,且不受周跳影响。     

GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals

This paper presents a general modeling strategy for ambiguity resolution (AR) and position estimation (PE) using three or more phase-based ranging signals from a global navigation satellite system (GNSS). The proposed strategy will identify three best “virtual” signals to allow for more reliable AR under certain observational conditions characterized by ionospheric and tropospheric delay variability, level of phase noise and orbit accuracy. The selected virtual signals suffer from minimal or relatively low ionospheric effects, and thus are known as ionosphere-reduced virtual signals. As a result, the ionospheric parameters in the geometry-based observational models can be eliminated for long baselines, typically those of length tens to hundreds of kilometres. The proposed modeling comprises three major steps. Step 1 is the geometry-free determination of the extra-widelane (EWL) formed between the two closest L-band carrier measurements, directly from the two corresponding code measurements. Step 2 forms the second EWL signal and resolves the integer ambiguity with a geometry-based estimator alone or together with the first EWL. This is followed by a procedure to correct for the first-order ionospheric delay using the two ambiguity-fixed widelane (WL) signals derived from the integer-fixed EWL signals. Step 3 finds an independent narrow-lane (NL) signal, which is used together with a refined WL to resolve NL ambiguity with geometry-based integer estimation and search algorithms. As a result, the above two AR processes performed with WL/NL and EWL/WL signals respectively, either in sequence or in parallel, can support real time kinematic (RTK) positioning over baselines of tens to hundreds of kilometres, thus enabling centimetre-to-decimentre positioning at the local, regional and even global scales in the future.     

长基线GLONASS模糊度固定方法及实验分析

格洛纳斯（Global Navigation Satellite System,GLONASS）采用了频分多址技术,接收机在接收不同卫星信号时会产生频间偏差,阻碍了GLONASS长基线模糊度固定,限制了其定位定轨的精度。提出了一种新的GLONASS模糊度固定方法。该方法基于全球电离层格网产品,根据频间偏差率的变化范围,采用搜索的方法和线性模型去除相位频间偏差对宽窄巷模糊度的影响,实现了GLONASS无电离层组合模糊度固定。利用平均基线长度为763 km的全球卫星导航系统（Global Navigation Satellite System,GNSS）服务站实验网数据对该方法进行分析,结果表明:连续30 d内,模糊度固定成功率最高为95.4%,最低为88.8%,平均为93.45%;模糊度固定后,北（north,N）、东（east,E）、高（up,U）各分量重复性和均方根误差（root mean square er-ror,RMSE）值均得到不同程度的改善,E分量重复性和RMSE值分别改善了20%和14%,改善效果最为明显。     

Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm

GPS Single-epoch Real-Time Kinematic positioning is immune to cycle slips and can be immediately re-initialized after loss-of-lock, providing high availability. This technique requires reliable ambiguity resolution: incorrect ambiguities can cause position errors of several meters, and failed ambiguity resolution reduces availability. However, a bias or inaccuracy in a single phase observation can prevent successful resolution of the whole set of ambiguities. Partial ambiguity resolution allows a subset of ambiguities to be resolved with greater probability of success than the full set. A new algorithm for resolving a subset of ambiguities with validation from previous epochs is described. If normal ambiguity resolution fails, all ambiguity subsets are generated and ordered with the best subsets first. Each subset is then resolved in turn. Fixed subsets are validated against values from previous epochs; this validation procedure greatly reduces the proportion of epochs with incorrect ambiguities. An additional algorithm is described that uses the fixed ambiguities as precise ranges to resolve the remaining unfixed ambiguities. In order to test these new algorithms, GPS data were collected from static and ship-based GPS receivers around Harwich harbor and processed from reference stations at distances up to 111 km. In the static tests the distance over which a 90% ambiguity resolution success rate for dual-frequency data was achieved was increased from 15 to 76 km. However, in some cases, the processing time was too long for this algorithm to be practical without a time-based cut-off. There is also a risk of incorrect ambiguities being propagated, particularly for single-frequency processing. In a ship-based test, the distance over which sufficient availability to support harbor navigation was achieved using single-epoch dual-frequency RTK was increased from 1 to 66 km.     

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%。     

A comparison of P code and high performance C/A code GPS receivers for on the fly ambiguity resolution

Carrier phase ambiguity resolution on the fly is investigated using two receiver technologies, namely dual-frequency P code and high performance, single frequency, C/A code receivers. Both receiver types were used simultaneously in a series of land kinematic trials. A least-squares search technique is used to find the correct double difference carrier phase ambiguities. Both C/A and single frequency P code technologies are found to be equivalent and capable of resolving the integer ambiguities on the fly using some 30 to 200 seconds of data under benign multipath conditions. Successful ambiguity resolution on the fly results in cm-level accuracy kinematic positioning. The ambiguity resolution time required and success rate are however found to be strongly dependent on the level of carrier phase multipath and, as a consequence, on the error variance assigned to the carrier phase measurements. The use of widelaning with the dual frequency P code results in ambiguity resolution in seconds. The performance of widelaning is also superior in a comparatively high carrier phase multipath environment.     

长距离GPS/BDS双系统网络RTK方法

基于区域参考站网的网络实时动态定位(real-time kinematic,RTK)方法是实现全球定位系统(global positioning system,GPS)、北斗卫星导航系统(BeiDou satellite navigation system,BDS)高精度定位的主要手段.研究了一种长距离GPS/BDS双...     

北斗三号多频相位模糊度无几何单历元固定方法

北斗三号全球卫星导航系统目前已提供5个频率的观测数据,因此理论上可进行多频相位模糊度解算（MCAR）。本文系统研究了MCAR的基本理论和方法,包括三频（TCAR）、四频（FCAR）和五频（FiCAR）相位模糊度固定。首先,从线性组合角度出发,给出了TCAR、FCAR和FiCAR方法在内的基本数学模型。其次,探讨了高质量信号及在不同基线长度条件下的最优线性组合。此外,分析了利用无几何模型单历元模糊度固定的常用方法。最后,利用实测北斗三号五频观测数据进行了试验。结果表明,MCAR可有效进行单历元模糊度固定,同时频率数增加可显著提高模糊度固定成功率。     

北斗中长基线三频模糊度解算的自适应抗差滤波算法

针对经典TCAR(three carrier ambiguity resolution)算法受电离层延迟及测量噪声的影响,在中长基线下难以正确固定模糊度的问题,提出一种顾及电离层延迟影响并具有良好自适应抗差特性的改进TCAR算法。在无几何TCAR模型的基础上,通过对模糊度固定的超宽巷进行线性组合得到电离层延迟,再求解宽巷模糊度,通过构造最优组合观测量后用自适应抗差滤波求解窄巷模糊度,以提高窄巷模糊度固定正确率,减小粗差的不利影响。试验结果表明,改进TCAR算法可保证较高的宽巷模糊度固定正确率,有效提高了窄巷模糊度固定正确率,并具有良好抵抗粗差的能力。     

A modified geometry- and ionospheric-free combination for static three-carrier ambiguity resolution

The reliability of the classical geometry- and ionospheric-free (GIF) three-carrier ambiguity resolution (TCAR) degrades when applied to long baselines of hundreds of kilometers. To overcome this deficiency, we propose two new models, which are used sequentially to resolve wide-lane (WL) and narrow-lane (NL) ambiguities and form a stepwise ambiguity resolution (AR) strategy. In the first model, after a successful extra-wide-lane AR, the pseudorange and phase observations are combined to estimate WL ambiguities, in which the residual ionospheric delays and geometry effects are eliminated. In the second model, using the resolved ambiguities from the first step, the two WL ambiguities are combined to remove ionospheric and geometry effects. The unknown coefficients in the two models are determined in such that they minimize the formal errors in the ambiguity estimates to optimize the ambiguity estimation. Using experimental BeiDou triple-frequency observations, we evaluate our method and identify three advantages. First, the two models use double-differenced phase observations that are not differences across frequency. Second, the two models are entirely free from ionospheric delay and geometry effects. Third, the unknown estimates in the two models satisfy the minimum noise condition, which makes the formal errors in the float NL ambiguity estimates much lower than those obtained with common GIF TCAR methods, thereby directly and significantly increasing the success rate of AR compared to the cascaded integer resolution method and two other GIF combinations.     

BDS参考站三频整周模糊度单历元确定方法

参考站载波相位整周模糊度的准确确定是实现BDS网络RTK定位的关键。本文研究了BDS参考站三频载波相位整周模糊度单历元确定方法。首先推导了参考站三频载波相位整周模糊度之间的多个整数线性关系,根据双频载波相位整周模糊度的整数线性关系,以及B1载波相位整周模糊度备选值,确定B1/B2和B1/B3载波相位整周模糊度的备选组合。然后利用不受误差影响的三频载波相位整周模糊度间整数线性关系,对整周模糊度备选值进行约束和确定。根据大气误差的空间相关性,采用以卫星高度角和方位角为依据的基准卫星选择方法,降低了对流层延迟误差残差对多频载波相位整周模糊度之间线性关系约束能力的影响。试验结果表明,本文方法能够实现参考站三频载波相位整周模糊度的单历元准确确定,且计算效率高,算法简单。     

Ambiguity resolution strategies using the results of the International GPS Geodynamics Service (IGS)

Resolving the initial phase ambiguities of GPS carrier phase observations was always considered an important aspect of GPS processing techniques. Resolution of the so-called wide-lane ambiguities using a special linear combination of theL ₁ andL ₂ carrier and code observations has become standard. New aspects have to be considered today: (1) Soon AS, the so-called Anti-Spoofing, will be turned on for all Block II spacecrafts. This means that precise code observations will be no longer available, which in turn means that the mentioned approach to resolve the wide-lane ambiguities will fail. (2) Most encouraging is the establishment of the new International GPS Geodynamics Service (IGS), from where high quality orbits, earth rotation parameters, and eventually also ionospheric models will be available. We are reviewing the ambiguity resolution problem under these new aspects: We look for methods to resolve the initial phase ambiguities without using code observations but using high quality orbits and ionospheric models from IGS, and we study the resolution of the narrow-lane ambiguities (after wide-lane ambiguity resolution) using IGS orbits.