BDS/GPS融合精密定位理论与算法研究

正北斗卫星导航系统是首个异构星座,是目前完全运行的唯一的三频导航系统,集导航定位、授时、用户监测、短报文通信于一体。BDS具有的独特优势,有利于改善DOP(dilution of precision)值、削弱大气误差、缩短模糊度初始化时间等。BDS与GPS融合卫星资源的利用,将成为BDS逐步走向国际卫星导航领域的一个过程。本文分析BDS与GPS在时空参考框架、星座结构、信号内容、数据质量等方面的差异性,研究BDS/GPS融合高精度相对定位关键技术。提出了一套BDS/GPS静态与动态相对定位算法,并开展了大量的试验研究,如铁路CPI控制网静态数据处理,基于相对定位精度因子RPDOP(relative positioning dilution of precision)分析的快速静态定位,不同范围与挑战性环境下RTK(real time kinematic)定位等,验证本文理论算法研究的正确性。本文主要内容如下。     

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.     

COMBINED GPS/GLONASS PRECISE POSITIONING FOR LONG-DISTANCE BASELINES

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｍｂｉｎｅｄＧＰＳ/ＧＬＯＮＡＳＳｏｆｆｅｒｓｍａｎｙａｄ ｖａｎｔａｇｅｓｃｏｍｐａｒｅｄｗｉｔｈＧＰＳ＿ｏｎｌｙｕｓｅｆｏｒｐｏｓｉｔｉｏｎ ｉｎｇａｐｐｌｉｃａｔｉｏｎｓｅｓｐｅｃｉａｌｌｙｉｎａｒｅａｓｗｈｅｒｅｔｈｅｎｕｍ ｂｅｒｏｆｖｉｓｉｂｌｅｓａｔｅｌｌｉｔｅｓｉｓｌｉｍｉｔｅｄ .ＴｈｅｉｎｃｌｕｓｉｏｎｏｆｔｈｅＧＬＯＮＡＳＳｓｉｇｎａｌｓｃａｎｉｎｃｒｅａｓｅｔｈｅａｃｃｕｒａｃｙｏｆｐｏｓｉｔｉｏｎｉｎｇａｓｗｅｌｌａｓｔｈｅａｖａｉｌａｂ…     

Combined GPS/GLONASS precise positioning for long-distance baselines

Combined GPS/GLONASS can increase the accuracy and reliability of positioning especially in some applications with many impediments. Due to the atmosphere delay, the commonly used methods for processing short distance baselines can not be implemented in long distance baselines. In this paper, a new data processing strategy for long distance baselines is proposed, which uses the properties of some combination observables of combined GPS/GLONASS and distance baselines may come to the order of 10?8 and combined GPS/GLONASS improves the accuracy over that of GPS-only positioning, which brings benefit to crust deformation monitoring and research on geodynamics.     

GPS/GLONASS组合精密单点定位性能分析

本文利用IGS 5个站的观测数据分7个时段进行了GPS/GLONASS组合精密单点定位计算,与单独GPS精密单点定位的结果在精度和收敛时间方面进行了性能比较.结果表明,在当前GPS卫星数量充足的情况下,增加少量的GLONASS卫星对定位精度的提高帮助不大,但能显著改善滤波收敛的时间.     

Modeling and assessment of combined GPS/GLONASS precise point positioning

A combination of GPS and GLONASS observations can offer improved reliability, availability and accuracy for precise point positioning (PPP). We present and analyze a combined GPS/GLONASS PPP model, including both functional and stochastic components. Numerical comparison and analysis are conducted with respect to PPP based on only GPS or GLONASS observations to demonstrate the benefits of the combined GPS/GLONASS PPP. The observation residuals are analyzed for more appropriate stochastic modeling for observations from different navigation systems. An analysis is also made using different precise orbit and clock products. The performance of the combined GPS/GLONASS PPP is assessed using both static and kinematic data. The results indicate that the convergence time can be significantly reduced with the addition of GLONASS data. The positioning accuracy, however, is not significantly improved by adding GLONASS data if there is a sufficient number of GPS satellites with good geometry.     

Improving BeiDou real-time precise point positioning with numerical weather models

Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.     

GLONASS pseudorange inter-channel biases and their effects on combined GPS/GLONASS precise point positioning

Combined GPS/GLONASS precise point positioning (PPP) can obtain a more precise and reliable position than GPS PPP. However, because of frequency division multiple access, GLONASS carrier phase and pseudorange observations suffer from inter-channel biases (ICBs) which will influence the accuracy and convergence speed of combined GPS/GLONASS PPP. With clear understanding of the characteristics of carrier phase ICBs, we estimated undifferenced GLONASS pseudorange ICBs for 133 receivers from five manufacturers and analyzed their characteristics. In general, pseudorange ICBs corresponding to the same firmware have strong correlations. The ICB values of two receivers with the same firmware may be different because of different antenna types, and their differences are closely related to frequency. Pseudorange ICBs should be provided for each satellite to obtain more precise ICBs as the pseudorange ICBs may vary even on the same frequency. For the solutions of standard point positioning (SPP), after pseudorange ICB calibration, the mean root mean square (RMS) improvements of GLONASS SPP reach up to 57, 48, and 53 % for the East, North, and Up components, while combined GPS/GLONASS SPP reach up to 27, 17, and 23 %, respectively. The combined GPS/GLONASS PPP after pseudorange ICB calibration evidently improved the convergence speed, and the mean RMS of PPP improved by almost 50 % during the convergence period.     

GPS、BDS、GPS+BDS精密单点定位精度评估

由于北斗系统卫星正式完成组网,因此有必要对BDS系统性能进行精度评估与分析.本文选取了MGEX网所采集的31 d观测数据,对比分析了GPS、BDS、GPS+BDS不同情况下静态与动态精密单点定位精度.试验结果表明,GPS和BDS单系统静态PPP在N、E、U方向上的精度分别优于4、4、7 cm;GPS+BDS组合系统静态...     

Helmert方差分量估计在GPS/GLONASS/BDS/Galileo组合精密单点定位权比确定中的应用CSCD

多星座组合定位可以提升导航定位性能,但不同星座观测量组合时需要考虑合适的随机模型.传统方法是根据经验直接设定各系统的等价权重,但会导致随机模型确定不精确,从而影响组合系统的性能提升.将Helmert方差分量估计方法应用于GPS/GLONASS/BDS/Galileo组合精密单点定位(PPP)中,以自适应确定各系统间权比.采用国际GNSS服务(IGS)MGEX(Multi-GNSS Experiment)观测网的10个测站一周的观测数据进行静态和仿动态试验.结果表明:采用Helmert方差分量估计定权方法可显著提高GPS/GLONASS/BDS/Galileo组合PPP的收敛速度,与等权定权方案比较,静态模式下平均提高52%,仿动态模式下平均提高64%.因定位精度主要由载波相位观测值精度和误差修正水平决定,在静态和仿动态测试中Helmert方差分量估计方法对定位精度没有明显改善.     

GPS静态精密单点定位算法精度分析

采用精密轨道和钟差,利用Bernese软件解算得到亚洲地区13个IGS跟踪站的站坐标、对流层ZTD和接收机钟差,将解算的结果与CODE发布的结果对比发现：静态PPP算法解算的N方向收敛精度明显优于E方向和U方向,4~6 h后,坐标偏差在1 cm左右;NEU RMS均值分别为0.45、0.29、0.69 cm,ZTD RMS均值为0.85 cm,接收机钟差RMS均值为0.14 ns。试验表明：精密单点定位算法具有较高的精度和可靠性,可为实际工程测量及相关地球物理信号研究提供理论依据。     

GPS/BDS/Galileo三频精密单点定位模型及性能分析

在精细考虑伪距和载波相位硬件偏差时变特性的基础上,导出了更为严谨的非差非组合观测方程,并给出了非组合模式下两类GNSS偏差的数学表达形式.基于此,本文详细研究了3种常用的三频精密单点定位(PPP),即无电离层两两组合IF1213、单个无电离层组合IF123与非组合UC123函数模型的独立参数化方法,系统分析了3种PPP...     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

GPS/Galileo精密单点定位模糊度解算与实验分析

针对提高多频模糊度固定解的GNSS精密单点定位的可靠性与稳定性的问题,该文基于实时非组合相位偏差产品,对三频非差非组合GPS/Galileo PPP的浮点解、固定解模型进行深入研究,并设计了3种定位策略,选取了17个MGEX跟踪站7d的实测数据,分析了三频非差模糊度固定解对静态、仿动态PPP定位精度与滤波收敛时间的影响。结果表明,滤波收敛后,与浮点解策略相比较,固定三频模糊度对高程、水平方向定位精度均有提高,在静态定位模式中提升幅度分别约为20.45%和37.50%,在仿动态定位模式中提升幅度分别约为22.41%和33.33%。在滤波收敛时间方面,相较于浮点解策略的收敛时间,静态与仿动态定位中模糊度固定策略的收敛时间分别提升了约12.57%和6.41%。     

双频BDS实时精密单点定位算法和精度分析

为了对BDS实时精密单点定位性能进行评估,该文提出了一种适用于BDS系统的实时精密单点定位算法。采用无电离组合模型作为双频实时精密单点定位的数学模型,采用电离层残差法和Melbourne-Wübbena组合实时探测相位周跳,进而单历元实时估计坐标、模糊度等参数,实现了BDS双频实时精密单点定位算法。基于此算法,采用轨道钟差产品和采样间隔为1s的观测数据,模拟实时BDS双频精密单点定位算法,并评估其定位精度。实验结果表明:BDS双频实时定位的平面精度和三维精度均为0.2m左右。     

PPPH: a MATLAB-based software for multi-GNSS precise point positioning analysis

The integration of different GNSS constellations offers considerable opportunities to improve Precise Point Positioning (PPP) performance. Being aware of the limited number of the alternatives that utilize the potential advantages of the multi-constellation and multi-frequency GNSS, we developed a MATLAB-based GNSS analysis software, named PPPH. PPPH is capable of processing GPS, GLONASS, Galileo and BeiDou data, and forming their different combinations depending on user’s preference. Thanks to its user-friendly graphical interface, PPPH allows users to determine a variety of processing options and parameters. In addition to an output file including the estimated parameters for every single epoch, PPPH also presents several analyzing and plotting tools for evaluating the results, such as positioning error, tropospheric zenith total delay, receiver clock estimation, satellite number, dilution of precisions. On the other hand, we conducted experimental tests to both validate the performance of PPPH and assess the potential benefits of multi-GNSS on PPP. The results indicate that PPPH provides comparable PPP solution with the general standards and also contributes to the improvement of PPP performance with the integration of multi-GNSS. Consequently, we introduce a GNSS analysis software that is easy to use, has a robust performance and is open to progress with its modular structure.     

GPS inter-frequency clock bias modeling and prediction for real-time precise point positioning

To ensure the consistent use of the current GPS precise satellite clock products, the inter-frequency clock bias (IFCB) should be carefully considered for triple-frequency precise point positioning (PPP). It is beneficial to investigate the modeling of the IFCB for multi-frequency PPP, especially for real-time users suffering from difficulties in real-time IFCB estimations. Our analysis is based on datasets from 129 stations spanning a whole year. A harmonic analysis is performed for all single-day IFCB time series, and periodic IFCB variations with periods of 12, 8, 6, 4.8, 4 and 3 h are identified. An empirical model composed of a sixth-order harmonic function and a linear function is presented to describe daily variations in the IFCB, and the modeling accuracy is 4 mm. A least squares fit is adopted to estimate the single-day harmonic coefficients phase and amplitude. The prediction accuracy of the IFCB models degrades from 7.2 to 12.3 mm when the time span of prediction is increased from a day to a week. When using IFCB models of the previous day to obtain the IFCB correction values, the positioning accuracy of triple-frequency PPP is improved by 21, 11 and 16% over the triple-frequency PPP neglecting the IFCB in the post-processing mode in the east, north and up directions, respectively. As to the real-time triple-frequency PPP, the corresponding accuracy improvement is 24, 9 and 10% in the three directions, respectively.     

不同卫星高度角对GPS/GLONASS/BDS/Galileo融合定位的影响

研究不同卫星高度角对GP S/GLONAS S/BDS/Galileo(G+R+B+E)融合定位的影响,并建立了相应的模型.采用MGEX(Multi-GNSS Experiment)提供的全球卫星导航系统(GNSS)数据,经理论分析和算例表明:G+R+B+E组合使得参与定位的有效卫星增多,在不同的卫星高度角下均能保证较...     

星基增强信号的GPS实时精密单点定位算法

针对现有基于网络和数据流量的实时精密单点定位应用中改正信息传播覆盖范围有限及信号延迟等问题,该文提出了一种新的基于GPS增强信号的实时精密单点定位算法。利用增强频段播发精密轨道、钟差产品有效地解决了传统改正信息传递过程中覆盖范围小与信号延迟的问题,极大地提高了实时改正产品的覆盖范围与时效性。基于亚太地区多个测站准实测数据的实验结果表明:基于LEX增强信息的实时动态和静态精密单点定位解算可分别实现分米级和厘米级的定位精度,显示了利用LEX增强信号进行实时高精度定位的可行性。