Galileo系统与GPS卫星定位系统相位组合观测值的模型研究

在介绍Galileo系统空间信号的基础上,以模糊度保持整数为前提,给出了Galileo系统的4个频率载波与GPS L2载波的组合相位观测值的定义,并对有关误差影响加以分析,最后根据一定的组合标准论述了具有相应特性的组合观测值,并给出一些典型的组合.      

Galileo/GPS载波相位组合观测值可匹配的研究

详细讨论了Galileo系统的4种载波与GPS L2载波的相位组合观测值的可匹配问题.在模糊度保持为整数的前提下,给出了Galileo/GPS载波相位组合观测值的定义,并对包括系统噪声和观测噪声在内的有关误差影响加以分析,最后给出了组合观测值可匹配的定义和判断可匹配的充要条件.      

脉冲星导航的整周模糊度解算方法研究

脉冲相位是X射线脉冲星导航方法的基本观测量,在测量的脉冲相位与预报相位比对的过程中存在整周期模糊度问题．借鉴GPS载波相位模糊度的解算方法,提出了单差搜索法、最小二乘搜索法和模糊度函数法3种空间搜索方法用以解算脉冲星导航系统的整周模糊度,并针对地球卫星完全迷失的情况进行了搜索仿真验证．结果表明,这3种方法都能够准确地解算出整周模糊度,均可用于脉冲星导航系统的在轨解算．其中最小二乘搜索法的性能稳定,搜索速度快;模糊度函数法搜索速度慢,但适用于装配单X射线探测器的脉冲星导航系统．     

基于DSP＋LAMBDA算法的GPS实时定位技术研究

主要分析了GPS载波相位整周模糊度LAMBDA求解算法,通过数据模拟测试来验证该算法在DSP上的工作状况。仿真计算证明,在DSP上实现LAMBDA算法可以满足GPS实时动态定位的要求。     

北斗三频相位观测值线性组合研究

以北斗三频数据为基础,给出了北斗三频组合观测值的数学模型并系统分析了组合后的波长、电离层误差以及观测噪声误差;在保持整周模糊度整数特性的前提下,以整数线性变换法为基础,通过Matlab编程实现组合系数的优化选取。通过将不同组合系数应用于伪距相位法三频数据周跳探测中,发现组合系数之和不为0的组合周跳探测值均在0.5周以上,且组合系数之和越大,波动越大;通过将不同组合系数应用于无几何CIR法三频数据模糊度解算中,发现系数之和不为0,但波长较长的组合求得的模糊度残差值大致在0.6周,通过合适的模糊度搜索方法可以得到正确的模糊度固定解,在短基线模糊度解算中可以考虑使用。     

新的GPS单频单历元定姿算法

LAMBDA算法依赖于初始的模糊度浮点解,但仅用载波相位观测方程需要多个历元才能获得浮点解,将导致初始化时间过长.针对这一问题,对GPS(Global Positioning System)单历元的载波相位单差方程进行特殊变换,将未知的整周模糊度看成噪声,从而构造出新的观测方程,和原始的观测方程进行组合求解,克服了仅用载波相位双差观测方程因为亏秩而无法在单历元获得浮点解的缺点,解决了初始化时间的问题.通过深入研究浮点解和固定解之间的关系,提出一种将低精度浮点解映射到固定解的方法,降低了LAMBDA算法对高精度浮点解的依赖性,避免了用多个历元获取浮点解的高精度,从而实现了单频、单历元的整周模糊度估计.通过实际测试,该算法成功率高于97%,能够有效地用于实时动态姿态解算.      

联合CDGPS技术和星间相对测量进行编队星座状态确定

以空间圆3星编队星座为对象,建立了联合GPS载波相位差分(Carrier phase Differential GPS,CDGPS)和星间相对测量进行编队星座状态确定的数学模型;利用高精度的星间相对测量信息给星间公里级基线提供厘米级约束,极大地缩小了星间单差模糊度的搜索空间,进而在卫星无需机动的情况下采用Bayes最小二乘法快速解算出星间GPS载波相位单差整周模糊度;最后数学仿真证明了方法的有效性,结果表明卫星间相对位詈确定精度达10^-2m．卫星姿态确定精度达10^-3rad．     

基于MLAMBDA的BDS/GPS单频RTK性能分析

GNSS RTK技术以其高精度、高效率、实时性的优点，被广泛应用于航空航天等领域.目前双频RTK技术已非常成熟并且应用较广.相比于双频，单频GNSS RTK在数据质量控制、定位误差处理等方面存在难点.因此单频RTK服务精度可能会受到限制，其定位性能有待研究.本文基于扩展卡尔曼滤波模型，通过MLAMBDA模糊度搜索方法和Ratio检验法，结合实测数据，对比分析BDS，GPS，BDS/GPS三种模式下的单频RTK定位性能.实验证明在静态场景下，三种模式的单频RTK定位精度都在厘米级，可满足高精度定位需求；动态场景下三种模式的模糊度固定率都在70%以上，可满足日常定位需求.在静态及动态应用场景下，北斗的模糊度固定率最高，模糊度解算所用时间短，能实现快速RTK定位.      

附加Doppler预报坐标约束的模糊度 动态解算新方法

利用GPS(Global Positioning System)相位观测进行动态定位的主要困难就是法方程不适定问题(秩亏或病态问题),导致模糊度浮动解及其协方差阵不准,以此构造的模糊度搜索范围比较大,使得模糊度的搜索非常困难.提出利用Doppler高精度测速预报近似坐标并对其附加约束,解决法方程求逆中的不适定问题,提高模糊度浮动解及其方差阵的准确性,缩小模糊度的搜索范围,提高模糊度搜索的成功率.结果表明,短基线情况,新方法在模糊度动态解算中取得了明显效果.      

单频GPS动态相对定位的模糊度逼近/搜索解法

针对目前实时动态定位(RTK)中常用搜索解法可靠度不高的缺点,利用各历元诸双差方程所形成的法方程,对其进行解耦处理以便于实时计算.在此基础上综合了逼近、搜索两种解法各自的局部优势,构成了逼近/搜索的联合解法.实际测试表明,该算法在单频全球定位系统(GPS)载波相位差分的动态相对定位过程中,用2～3min的时间即可可靠地在航解算出整周模糊度.     

Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals

GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galileo signals will come available, the number of observations at the L1 frequency will increase as we will have a GPS and Galileo multi-constellation. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS and this, combined with the increased number of observations, will result in a stronger model for single frequency relative positioning. In this contribution we will develop an even stronger model by combining the attitude determination problem with relative positioning. The attitude determination problem will be solved by the recently developed Multivariate Constrained (MC-) LAMBDA method. We will do this for each spacecraft and use the outcome for an ambiguity constrained solution on the baseline between the spacecraft. In this way the solution for the unconstrained baseline is bootstrapped from the MC-LAMBDA solutions of each spacecraft in what is called: multivariate bootstrapped relative positioning. The developed approach will be compared in simulations with relative positioning using a single antenna at each spacecraft (standard LAMBDA) and a vectorial bootstrapping approach. In the simulations we will analyze single epoch, single frequency success rates as the most challenging application. The difference in performance for the approaches for single epoch solutions, is a good indication of the strength of the underlying models. As the multivariate bootstrapping approach has a stronger model by applying information on the geometry of the constrained baselines, for applications with large observation noise and limited number of observations this will result in a better performance compared to the vectorial bootstrapping approach. Compared with standard LAMBDA, it can reach a 59% higher success rate for ambiguity resolution. The higher success rate on the unconstrained baseline between the platforms comes without extra computational load as the constrained baseline(s) problem has to be solved for attitude determination and this information can be applied for relative positioning.     

Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

GNSS carrier phase ambiguity resolution based on integrity restriction in ambiguity domain

Carrier phase ambiguity resolution of Global Navigation Satellite System (GNSS) is a key technology for high-precision navigation and positioning, and it is a challenge for applications which require both high accuracy and high integrity. This paper proposes efficient ambiguity resolution methods based on integrity restriction using Fixed Failure rate Ratio Test (FF-RT) and Doubly Non-central F-distribution Ratio Test (DNF-RT), and derives the related processing models and numerical algorithms compared with the traditional Ratio Test (RT) method. Firstly, the integer ambiguity resolution and validation procedures, especially the Least squares AMBiguity Decorrelation Adjustment (LAMBDA) estimation and RT validation are analyzed. Then the quality evaluation using success rate, the FF-RT method using Integer Aperture (IA) estimation and the NDF-RT method are proposed. Lastly, the simulation and analysis for LAMBDA using RT, FF-RT and DNF-RT methods are performed. Simulation results show that in case of unbiased scenario FF-RT and DNF-RT have similar performances, which are significantly better than RT. In case of biased scenario it is difficult for FF-RT to predict the biased success rate thus it should not be used for bias detection, while DNF-RT can detect biases in most cases except for the biases are approximate or equal to integer, which has the important benefit for early detection of potential threat to the position solution.     

软件GNSS信号模拟器架构与中频信号生成

软件GNSS(Global Navigation Satellite Systems)信号模拟器对于GNSS接收机的高效研发将做出重要贡献,因其结构灵活、开放性以及低成本.以GPS/Galileo组合系统为例,讨论了软件GNSS中频信号模拟器的架构,主要功能模块包括卫星星座仿真、接收机轨迹生成、传播通道特性仿真(包括电离层模型、对流层模型、多径模型等)、数字中频信号生成.在此基础上,着重阐述了数字中频信号生成模块的实现,功率谱图及分析结果验证了所生成的信号,包括GPS L1 C/A,Galileo E1 CBOC(Composite Binary Offset Carrier),Galileo E5a和E5b信号.     

Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.     

基于代价函数的组合导航系统地图匹配算法

研究了地图匹配技术在GPS(Global Positioning System)/DR(Dead Reckoning)组合导航系统中的应用,建立了GPS/DR/地图匹配组合导航系统模型,给出了一种基于代价函数和概率统计准则的地图匹配算法,通过合理地定义代价函数有效消除了存在于匹配路段挑选过程中的模糊性问题.对实际跑车数据的仿真处理结果表明,应用该算法可以为组合导航系统的定位精度带来明显的改善.     

Estimating inter-system biases for tightly combined Galileo/BDS/GPS RTK

The overlapping carrier frequencies L1/E1, L5/E5a and B2/E5b from GPS/Galileo/BDS allow inter-system double-differencing of observations, which shows a clear advantage over differencing of the observations of each constellation independently. However, the inter-system biases destroy the integer nature of the inter-system double-differencing ambiguities. Two methods of direct rounding and parameter estimation are used to determine the ISB value. By analyzing data collected from Curtin University from 2015 to 2018, the phase and code inter-system bias (ISB) are related to the receiver type, firmware version and the selected overlapping frequency. Upgrade of receiver firmware version results in changes of ISB values. For example, the upgrade of Javad firmware in Dec, 15, 2017 causes the difference of 0.5 cycles ISB between BDS GEO and non-GEO satellites. By comparing the three dynamic models which include white noise process, random walk process, and random constant in the parameter estimation method, the ISB determined by the random constant model is consistent with the value obtained by the direct rounding method. After the calibration of ISBs, the performances of tightly combined positioning are assessed. The success rate of ambiguity resolution and accuracy of positioning for the tight combination (TC) are significantly improved in comparison with that for the loose combination (LC) over short baselines. For L5/E5a, on which only few satellites can be observed, the maximum increase in success rates of ambiguity resolution can reach 31.7%, i.e., from 54.9% of LC to larger than 86.6% of TC, and the positioning accuracies can even be increased by 0.13 m, i.e., from 0.208 of LC to 0.074 m of TC in East direction for the mix-receiver TRIMBLE NETR9-SEPT POLARX4 in 2018.