北斗三频整系数线性组合优化模型

针对北斗三频观测量的应用需求,该文在对北斗三频载波相位线性组合观测模型进行误差分析的基础上,从几何的角度对削弱或消除误差的实系数无电离层组合、无对流层组合和最小噪声组合进行空间分析,更为直观地描述了无电离层平面、无对流层平面和最小噪声线的关系。在此基础之上,引出北斗整系数线性组合,并对长波长组合、弱电离层组合和弱观测噪声组合进行分析,以巷数、电离层延迟系数和噪声放大系数作为三频最优整系数线性组合的判断指标,得到了以(-1,-5,6)、(0,-1,1)和(1,4,-5)为代表的几组具有不同特性的最优三频整系数线性组合,并得出三频整系数优选线性组合模型的系数之和一般为S=0或者S=±1。     

BDS三频信号最优组合的模糊聚类分析法

针对如何优选出三频BDS最优载波相位线性组合观测量的问题,基于三频GNSS载波相位组合观测量理论,本文提出最优组合观测量选取的模糊聚类分析法。首先构建满足超宽巷组合和窄巷组合条件,且具有不同巷数、电离层数及噪声放大因子的三频BDS组合观测量,并假定各参数均为最优值的理论最优组合观测量;然后对满足条件的超宽巷组合和窄巷组合用模糊聚类分析法进行聚类排序;最后根据各组合观测量与假定的最优组合观测量聚为一类的先后顺序,确定三频BDS最优组合观测量的选取顺序。结果表明:模糊聚类分析法通过组合观测量的聚类排序,实现了最优组合观测量的筛选。无几何TCAR算法也验证了模糊聚类分析结果的正确性。     

中长基线的BDS三频线性组合观测量优化

基于几何无关（geometry-free,GF）和电离层无关（ionosphere-free,IF）的三频原始载波线性组合观测量,由于消除了一阶电离层延迟项以及同卫星与测站间几何距离相关误差项的影响,可有效应用于中长基线模糊度解算。对适用于北斗卫星导航系统（BDS）中长基线模糊度解算的GF和IF线性组合观测量进行了研究和优化,通过对载波观测量与伪距观测量组合,得到噪声最小且基于GF和IF的宽巷组合观测量,然后将模糊度得到固定的两个载波组合观测量与原始载波观测量进行最优线性组合,得到具有最低噪声的基于GF和IF的窄巷组合观测量。该方法充分利用了所有载波及伪距观测量信息,并根据其噪声水平进行了加权优化,公式推导具有普遍性和代表性。通过三频实测基线数据进行了论证分析。结果表明,经过一段时间的平滑之后,宽巷和窄巷模糊度浮点解的偏差能收敛到0.5周以内,从而实现模糊度的快速准确固定。     

三频精密单点定位观测模型初探

三频观测值为导航定位提供了更多的观测值组合选择。在利用载波相位三频线性组合消除一阶电离层误差的基础上,对组合模糊度为实数和整数两种情况下的二阶电离层误差及观测噪声水平进行了分析,获得了几种适用于精密单点定位的三频观测值组合。     

一种改进的基于 BDS 三频非差观测的周跳实时探测与修复模型

BDS三频观测条件下可以组合得到具有优良特性的虚拟载波观测量,有利于改善非差观测数据的周跳实时探测与修复。文中提出一种基于BDS三频非差数据的周跳实时探测与修复模型:首先,采用消电离层无几何HMW组合观测量探测和修复EWL周跳;然后,将经过修复的EWL观测量与WL组合消除几何相关项,忽略电离层延迟残差进而确定WL周跳;最后采用经过修复的WL观测量与NL组合形成无几何观测量,并通过优化载波相位组合确定电离层延迟的变化量以探测和计算NL周跳,并通过简单变换得到原始载波观测量的周跳值。通过实测BDS三频数据对模型可行性进行验证分析,结果表明,即使在30s的采样率以及电离层活动活跃条件下,该模型都可有效实时探测和修复各类周跳。     

GPS三频载波相位组合误差分析及选择方法

本文首先从GPS双差模型出发，给出了三频载波组合的基本形式，依据该形式，得到了组合波长表达式，并分析了电离层误差和观测噪声对三频组合的影响。由这些误差特性，给出了三频线性组合系数的选取方法，并给出了一些常用的线性组合形式，分析了它们的优缺点。最后，简单介绍了目前主要的三频模糊度解算方法CIR和TCAR。     

基于北斗三号三频数据的周跳探测与修复

针对载波相位观测值中出现周跳的问题及北斗三号系统(BDS-3)将至少有B_(1I),B_(1C),B_(2a)和B_(3I) 4个信号提供全球公开服务的现状,研究北斗三号系统的周跳探测与修复。提出优化三频相位电离层残差二阶历元差分组合和三频无几何无电离层相位组合的信号排列顺序,可进一步削弱组合观测量的电离层延迟影响和噪声影响,并基于北斗三号的实测数据,联合STPIR法、MW法和无几何无电离层相位组合法进行周跳探测与修复实验。实验结果表明,组合观测量信号的优化排列,削弱组合观测量的电离层延迟影响和噪声影响,且所选的3个组合观测量可以准确探测所有周跳,并有效地修复。     

GPS三频组合观测量的特征及应用研究

介绍了GPS载波相位双差观测方程以及误差影响因素,给出GPS三频组合观测量的一般表达式并分析影响组合观测量的主要误差因素,研究了电离层无关线性组合的构建方法及其性能,详细分析几种特殊的线性组合形式及特点,总结了GPS三频组合观测值在电离层误差改正、周跳探测与修复、整周模糊度解算以及精密定位等方面的应用前景。     

BDS三频双差载波相位组合平滑伪距算法

针对现有的载波相位平滑伪距算法多基于GNSS双频观测值且在伪距平滑过程中易受电离层延迟累积干扰的问题,提出一种基于北斗三频观测值的载波相位平滑伪距算法。首先通过构建北斗三频优选线性组合,进一步削弱双差载波相位观测值的电离层延迟以及观测噪声;接着通过经典Hatch滤波平滑器,用优选三频双差载波相位观测值代替原始载波相位观测值对组合伪距观测值进行平滑,得到最终伪距平滑解用于伪距定位。最后采用0.004、14.4、61.7和131.6 km这4组不同基线长度的北斗三频实测数据对算法进行验证,给出了平滑前后伪距历元差对比图及算法对4组基线观测值的平滑率。结果表明,所提算法对短基线和中长基线三频观测值的平滑率均能达到90%以上。通过对4组基线条件下平滑效果进行比较分析,验证了本文中的理论推导及算法的有效性。     

基于伪距相位和STPIR组合的北斗三频周跳探测与修复

GNSS周跳探测中,电离层残差法的适用性受数据采样间隔的影响较大,同时联合其它组合观测量进行周跳修复时,周跳修复方程组易出现病态解。针对这些问题,文中提出一种可靠的北斗三频周跳探测与修复算法,通过构造北斗三频电离层残差组合观测量,进行二阶历元间差分,基于三频伪距相位组合优选理论,选取适用于北斗三频数据的伪距相位组合,结合两种组合观测量,优选条件数较小的组合系数矩阵进行周跳修复,最后通过北斗三频实测数据验证,结果表明:在数据采样间隔较大的情况下,利用构建的三个组合观测量可以探测出北斗三频原始数据中的所有周跳,具有很好的修复效果。     

A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS

The upcoming modernization of the GPS signals will allow for measurements on an additional third frequency L5 located at 1176.45 MHz. To take advantage of carrier-phase measurements on this new signal, the strategies for integer ambiguity resolution, required for centimeter-level accuracy, may need to be revised. The Least-squares Ambiguity Decorrelation Adjustment method remains perhaps the most powerful tool for finding the best combinations based on a complete decorrelation of the variance–covariance matrix related to the ambiguities. However, the computational load of that method plus the opportunity to comprehensively study the interaction of multiple frequencies suggest a reconsideration of approaches using predefined combinations between frequencies is not out of place. In this paper a systematic investigation is made of all possible triple-frequency geometry-free carrier-phase combinations which retain the integer nature of the ambiguities. The concept of the lane-number is presented to unambiguously describe the wavelength of a particular combination. The propagation of the observation noise and of the ionospheric bias on these combinations is presented. These noise and ionospheric amplification factors are analysed with respect to the resulting wavelength, in an effort to highlight optimal combinations characterized by a long wavelength, low noise and limited ionospheric impact.     

Optimal linear combinations of triple frequency carrier phase data from future global navigation satellite systems

With the introduction of a third frequency on GPS Block IIF satellites and the implementation of Galileo, there will be three freely available carrier phase measurements transmitted from each system. This change in satellite navigation infrastructure will enable the use of linear combinations of the original measurements that are not currently available. As a result, it is conceivable that there may be an optimal choice of combination coefficients for a given positioning campaign. This article outlines some of the motivations of using linear combinations of Global Navigation Satellite System (GNSS) data. For example, linear combinations can be used to eliminate or mitigate individual sources of error, they can be used to alleviate excessive computational burdens, and they can be used to reduce the necessary bandwidth in communication systems. Upon establishing the motivations for using linear combinations of data, the mathematical theory involved in creating linear combinations is given. The variance of the combined signal is shown to be a weighted sum of the variances of the error sources in the untransformed signals. The weights depend on the choice of combination coefficients and the nominal frequencies of the carrier signals. As a result, there are certain choices of combination coefficients that eliminate or mitigate individual sources of error. Three categories of combinations are developed: those that eliminate the ionospheric effect, those that mitigate the effects of thermal noise and multipath, and those that mitigate the tropospheric effects. The relationships between these various categories of linear combinations are shown geometrically and the concept of optimal linear combinations of data is discussed. Finally, experimental results using optimal linear combinations of data are shown. The results are obtained using a commercially available software simulator and a GNSS processing engine from the Mobile Multi-Sensor Research Group in the Geomatics Engineering Department of the University of Calgary. It is shown that there indeed exist combinations that produce approximately the same ambiguity estimation accuracy as the pure L1 (or E1) signals, but that deliver far better baseline precision results. However, like the pure L1 (or E1) signals, instantaneously resolving integer ambiguities with these combinations will be impossible for baselines longer than about 15 km depending on the existing ionospheric conditions.     

北斗三号三频组合观测值特性分析研究

北斗三号卫星导航系统今年已步入全球组网阶段,预计到2018年底BDS-3的服务区域将覆盖“一带一路”国家及周边国家.目前BDS-3已发布B1I、B1C、B2a和B3I四个信号的用户接口控制文件,本文利用函数极值法给出了特定波长和电离层延迟影响系数下的噪声最优线性组合系数,分析得出BDS-3最优超宽巷组合为三频信号(B1C,B1I,B2a)和(B1C,B1I,B3I)中的线性组合(1,-1,0),最优宽巷组合为三频信号(B1I,B3I,B2a) 和(B1C,B3I,B2a)中的线性组合(1,-3,2),这三个组合也是BDS-3、BDS-2和GPS中的最优组合.利用北斗三号的实测数据进行长短基线下宽巷／超宽巷双差模糊度解算,验证了BDS-3最优宽巷与超宽巷组合的结论的同时,还得出三频信号(B1I,B3I,B2a)和(B1C,B3I,B2a)中的宽巷组合(1,-3,2)与超宽巷组合(1,-4,3)和(0,1,-1)在长／短基线情况下均适用,而筛选得到的较优三频信号(B1C,B1I,B2a)和(B1C,B1I,B3I)中的宽巷／超宽巷组合仅在短基线场景下均适用.      

一种适于Compass周跳探测的三频数据优化组合

根据多频数据组合原理,推导了组合观测值电离层比例因子与噪声比例因子的关系,分析了Compass码和相位的多种可能组合,从中选取3种线性无关的优化组合作为周跳检验量。所选检验量保持了周跳的整数特性,便于准确估计与修复周跳。利用Compass-M1实测数据进行的实验表明,基于优化组合可以探测出1周以上的所有周跳,在缺失历元较少和无电离层异常时可以准确估计与修复基本频率的周跳。     

三种电离层延迟多频修正算法的比较

电离层延迟多频修正算法在修正电离层延迟的同时会放大观测噪声等伪距误差的影响。分析了电离层延迟双频修正、三频一阶修正和三频二阶修正三种修正算法及观测噪声的影响。以Galileo系统的四个载波频率为例,对不同频率组合下三种修正算法进行了比较。结果表明电离层延迟多频修正中,并不是观测量的频点数越多或修正掉的高阶项越多修正精度越高,还与观测伪距噪声的大小以及采用的修正方法有关。为多频测距系统的电离层延迟修正算法和最佳频率组合设计提供了一种可行的分析方法。     

COMPASS三频数据线性组合优化选取分析

以北斗卫星1支路频点为例,从消除或减弱电离层影响、对流层影响和观测噪声与多路径误差3个方面分析COMPASS三频数据线性组合的优化选取问题,并通过MATLAB模拟,给出一些典型的组合,分析它们可能的应用,为COMPASS三频数据线性组合的优化选取提供一些借鉴。     

不同NeQuick电离层模型参数的应用精度分析

Galileo采用NeQuick作为全球广播电离层模型,其实际应用中以有效电离水平因子Az代替太阳活动指数作为NeQuick的输入参数,并利用二次多项式拟合得到广播星历中播发的3个电离层参数。本文在总结和讨论NeQuick模型参数估计方法及其变化特征的基础上,分别以全球电离层格网、GPS基准站及JASON-2测高卫星提供的电离层TEC为参考,分析不同NeQuick模型参数(包括以太阳活动参数F10.7为输入的NeQuick2、以本文解算参数为输入的NeQuickC和以Galileo广播电离层参数为输入的NeQuickG)在全球大陆及海洋地区的应用精度,并与GPS广播的Klobuchar模型对比。结果表明,NeQuickG在全球范围内的修正精度为54.2%~65.8%,NeQuickC的修正精度为71.1%~74.2%,NeQuick2的修正精度与NeQuickG相当,略优于GPS广播星历中播发的Klobuchar模型。     

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.     

GPS三频无几何相位组合周跳探测与修复

随着GPS现代化的实施和L5频率的开设,GPS进入了三频时代。相对于双频观测数据三频观测值线性组合可以形成更多长波长、弱电离层、低噪声的组合。本文分析了GPS三频无几何相位组合的特性,利用两个GPS三频无几何相位组合和一个三频伪距载波组合组成观测矩阵探测周跳,并采用搜索方法确保周跳修复的正确。最后利用模拟的L5观测数据进行验证,结果表明该算法可以有效地探测并修复周跳。