一个新的GNSS模糊度估计类

介绍了一类新的GNSS模糊度估计。因为该类遵循移去恢复原理,称之为整数等变估计类。本文将说明整数等变估计类较整数估计类和线性无偏估计类的范围要大,同时给出一个相当有用的整数等变估计类的表达式。这个表达式揭示了整数等变估计类的结构,并显示该表达式如何在浮点解的基础上实现整数等变估计。最后还提出最优整数估计。     

基于整数钟的PPP非差模糊度固定方法

非差模糊度固定能够有效提高精密单点定位(PPP)的定位精度和收敛速度,是国内外卫星导航定位领域的研究热点。基于整数钟实现了PPP非差模糊度固定,在非差模糊度逐级固定中分别估计接收机宽巷偏差和窄巷偏差;对宽巷和窄巷模糊度进行改正,从而消除了接收机硬件延迟对模糊度的影响;同时采用取整成功率检验和ratio值检验,保证模糊度固定的可靠性。将以上方法应用到动态精密单点定位中,实验结果表明:仿动态条件下,模糊度正确固定后,东、北向定位精度达到mm级、天向定位精度优于5 cm;动态解算条件下,采用1 s采样间隔数据16 min左右即可实现模糊度的首次固定。PPP固定解在东、北、天3个方向的定位精度分别为1.5、2.7和1.3 cm,相比于浮点解分别提升了61%、40%和38%。     

评价GPS相位模糊度整数解正确性的严密方法

针对如何评价模糊度整数解的正确性,指出了基于传统的假设检验理论的三步法存在的理论缺陷,介绍了模糊度归整域的概念和可容许整数估计的定义,并在Teunissen关于可容许整数估计原定义的基础上给出了更为严密的新定义。基于这个新定义,讨论了模糊度成功率的概念及其计算公式。     

时频传递的改进整数相位钟方法

整数相位钟法是精密单点定位（PPP）中应用最广泛的模糊度固定方法之一。利用整数相位钟法进行频率传递的稳定度优于传统PPP,但该方法的钟差计算结果包含系统性偏差,影响时间传递精度。本文介绍了整数相位钟法基本原理,分析了钟差计算结果所包含的系统性偏差成因,提出一种基于星间单差模糊度固定与原子钟精化模型的改进整数相位钟法,并检验改进整数相位钟法的模糊度固定性能与时频传递性能。试验结果表明,改进算法能够有效消除该系统性偏差,利用改进整数相位钟法进行时间传递精度能够达到0.1~0.2 ns,频率传递稳定度达到1.1×10^-15/d。     

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.     

一种整数相位钟法精密单点定位模糊度固定模型

星间单差法是常用的精密单点定位PPP模糊度固定方法,但是要面临基准星转换的问题。为此,提出了一种逐级模糊度固定模型,采用法国CNES发布的整数相位钟差产品,在PPP非差观测模型基础上逐一选取两颗卫星进行模糊度固定;得到多组单差模糊度固定解后,再以此构成约束条件进行滤波得到其他参数。实验选取了8个IGS站共48个观测时段进行模糊度固定实验。结果表明,模糊度成功固定后,位置三维误差平均值由5.60 cm减小到2.72 cm;位置误差标准差由3.64 cm减小到1.50 cm。仿动态条件下,模糊度固定后位置误差由6.02 cm降至4.75 cm。     

相位平滑伪距GNSS PPP/INS紧耦合算法

针对在导航实践中低成本MEMS使用传统紧耦合方法计算精度受到限制的问题,提出了一种采用载波相位平滑伪距GNSS PPP/INS紧耦合的算法。实验表明,使用相位平滑伪距的GNSS PPP/INS紧耦合方法后低精度的MEMS和GPS组合位置精度为dm级,速度精度为cm/s甚至mm/s,比传统C/A码紧耦合定位精度高,有较好的收敛性;其次当增加相位平滑的历元数后精度也相应提高。当出现GPS信号中断时,该方法能够加速中断以后滤波收敛的速度,将导航精度控制在中高精度惯导作业要求范围内。该方法节约了导航作业的设备成本,具有一定实际意义。     

宽巷载波相位模糊度小数偏差时变特性分析

对使用序贯最小二乘估计非差宽巷FCB的方法进行论述,指出其不足在于事先假定了单天内的(接收机端和卫星端)宽巷FCB稳定不变,而对其时变性质缺少讨论与分析。处理了全球350个IGS测站共10d的GPS观测数据,从站星非差FCB、站间单差FCB序列两方面对接收机端宽巷FCB的时变特性进行详细的分析和讨论。数据处理结果表明:①在没有周跳的连续弧段内非差宽巷FCB的历元平滑结果具有较好的稳定性,使用不少于90个历元(45min)的数据即可收敛到0.1周以内保持精度稳定,因此,建议计算非差宽巷FCB的最短弧段不应少于45min;②接收机端宽巷FCB在每一天内随时间变化速率不一样,一天内最大变化量可以达到0.3周,并且接收机重启会使其重新赋值,破坏FCB值的连续性。关于接收机端宽巷FCB时变特性的分析表明文献[4—5]等的序贯最小二乘法所依据的假设前提并不可靠。为获得更高精度的非差卫星宽巷FCB估值,对于接收机重新启动的观测数据,需要新增一个接收机FCB参数;而对于接收机FCB的时变特性,可以在估计时将其作为随机游走过程进行估计。     

北斗/GNSS机载动态PPP性能分析

针对基于机载动态场景下的实测数据,使用开源的PRIDE PPP-AR软件,采用伪距和载波相位观测值构建双频的消电离层组合(IF)进行了动态精密单点定位(PPP)实验,并对比了单北斗卫星导航系统(BDS)以及BDS/GNSS在进行机载大动态PPP定位方面的性能.结果表明：多系统组合在卫星数、卫星几何构型以及位置精度衰减因子(PDOP)等方面均优于单系统,且对比单GPS而言,平面(东(E)、北(N)、高程(U))方向的定位精度分别提升了10%和12%;此外将开源软件PRIDE PPP-AR的解算结果与商业软件WayPoint进行了对比,结果表明前者的定位精度在E和U方向分别提升了46%和36%,N方向提升最多,提升了近2倍,因而PRIDE PPP-AR具备更高的动态解算精度与可靠性.     

非差FCB估计及其在PPP模糊度固定中的应用

模糊度固定能够显著提高精密单点定位(PPP)的精度和收敛速度,是国内外卫星导航定位领域的研究热点．本文通过最小二乘法分离接收机端和卫星端小数周偏差(FCB),恢复非差模糊度的整数特性,将得到的卫星端FCB提供给用户,能够实现非差模糊度固定的PPP．采用全球IGS跟踪站的观测数据进行非差FCB解算,实验结果表明,宽巷FCB的稳定性较好,一周内变化小于0.1周,而窄巷FCB一天内变化较大．将获得的FCB用于模糊度固定PPP实验,E、N、U三个方向的定位精度分别为0.7 cm、0.8 cm和2.1 cm,与浮点解PPP相比,分别提高68％、51％和37％,验证了本文估计的FCB用于模糊度固定PPP的定位性能      

Theory of integer equivariant estimation with application to GNSS

Carrier phase ambiguity resolution is the key to high-precision global navigation satellite system (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. The so-called fixed baseline estimator is known to be superior to its float counterpart in the sense that its probability of being close to the unknown but true baseline is larger than that of the float baseline, provided that the ambiguity success rate is sufficiently close to its maximum value of one. Although this is a strong result, the necessary condition on the success rate does not make it hold for all measurement scenarios. It is discussed whether or not it is possible to take advantage of the integer nature of the ambiguities so as to come up with a baseline estimator that is always superior to both its float and its fixed counterparts. It is shown that this is indeed possible, be it that the result comes at the price of having to use a weaker performance criterion. The main result of this work is a Gauss–Markov-like theorem which introduces a new minimum variance unbiased estimator that is always superior to the well-known best linear unbiased (BLU) estimator of the Gauss–Markov theorem. This result is made possible by introducing a new class of estimators. This class of integer equivariant estimators obeys the integer remove–restore principle and is shown to be larger than the class of integer estimators as well as larger than the class of linear unbiased estimators. The minimum variance unbiased estimator within this larger class is referred to as the best integer equivariant (BIE) estimator. The theory presented applies to any model of observation equations having both integer and real-valued parameters, as well as for any probability density function the data might have. AcknowledgementsThis contribution was finalized during the authors stay, as a Tan Chin Tuan Professor, at the Nanyang Technological Universitys GPS Centre (GPSC) in Singapore. The hospitality of the GPSCs director Prof Law Choi Look and his colleagues is greatly appreciated.     

The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations

Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modified Cholesky decomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning, Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on the Least Squares Ambiguity Search (LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131, 2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function, leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and (2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also proposed.     

PPP/PPP-RTK新进展与北斗/GNSS PPP定位性能比较

首先简要回顾了精密单点定位（PPP）技术在最近几年的发展现状,重点总结了高采样率钟差实时快速估计、多系统组合PPP模糊度固定、多频GNSS PPP模型及其模糊度固定、PPP快速初始化、PPP-RTK等若干热点方向的最新研究进展。在此基础上,利用目前四大卫星导航系统（GPS、GLONASS、Galileo、北斗）最新的实际观测数据,全面比较分析了各系统及多系统组合PPP定位性能,重点给出了北斗二号+北斗三号PPP浮点解和固定解的定位精度、收敛时间和首次固定时间。结果表明：我国北斗导航卫星系统已经可以实现与其他导航卫星系统基本相当的PPP定位性能。北斗二号+北斗三号组合PPP的收敛时间/首次固定时间20~30 min;静态解的东、北、天方向定位精度在毫米到厘米级;动态解水平方向约5 cm,高程方向约7 cm;多系统组合可显著提高PPP定位精度、收敛时间和首次固定时间：固定解定位精度比浮点解在东、北、天方向分别提升了14.8%、12.0%和12.8%;相比单GPS,多系统组合PPP浮点解的收敛时间和固定解首次固定时间分别缩短了36.5%和40.4%。     

差分GPS载波相位整周模糊度快速解算方法

本文提出了一种整周模糊度的快速求解方法,将差分GPS的测量值分配到主要测量值集合和次要测量值集合中,用主要集合中的相位测量值限定简约搜索空间,而次要集合中的相位测量值用来验证候选集合。利用已知的基线长度的约束条件,对搜索空间进行了简约,提高了求解整周模糊度的速度,同时,通过Cholesky分解提高搜索效率。     

载波相位约束整周模糊度在短基线RTK中的应用

针对单历元RTK定位中受到卫星升起、周跳频发等外界条件干扰时,整周模糊度长时间不能固定,严重影响RTK定位实时精度的问题。文中提出一种用载波相位约束整周模糊度的方法来提高模糊度固定率、Ratio值和解算精度,并且结合GPS单系统、GPS/GLONASS双系统两组实测数据进行未加入和加入载波相位约束整周模糊度的比较实验。结果表明该方法可行。     

On the probability distribution of GNSS carrier phase observations

When processing observational data from global navigation satellite systems (GNSS), the carrier phase measurements are generally assumed to follow a normal distribution. Although full knowledge of the probability distribution of the observables is not required for parameter estimation, for example when using the least-squares method, the distributional properties of GNSS observations play a key role in quality control procedures, such as outlier and cycle-slip detection, in ambiguity resolution, as well as in the reliability assessment of estimation results. In addition, when applying GNSS positioning under critical observation conditions with respect to multipath and atmospheric effects, the validity of the normal distribution assumption of GNSS observables certainly comes into doubt. This paper illustrates the discrepancies between the normal distribution assumption and reality, based on a large and representative data set of GPS phase measurements covering a range of factors, including multipath impact, baseline length, and atmospheric conditions. The statistical inferences are made using the first through fourth sample moments, hypothesis tests, and graphical tools such as histograms and quantile–quantile plots. The results show clearly that multipath effects, in particular the near-field component, produce the dominant influence on the distributional characteristics of GNSS observables. Additionally, using surface meteorological data, considerable correlations between distributional deviations from normality on the one hand and atmospheric relative humidity on the other are detected.     

Positioning precision analysis of GNSS multi-frequency carrier phase combinations

GPS positioning precision is affected by various error sources, and traditional combinations of GPS carrier phase observations have their own limitations such as the wide-lane, the narrow-lane and the ionospheric-free combinations. To obtain the optimal positioning precision, a new linear combination method is addressed through the variance-covariance (VCV) of the GPS multi-frequency carrier phase combination equations, and the impact of the positioning precision is analyzed with the changing of the observation errors deduced by the law of error propagation. For the high precision positioning with only one carrier phase combination, the optimal combination method is deduced and further validated by an example of a baseline resolution with 60 km length. The result indicates that this method is the simplest, and the positioning precision is the best. Therefore, it is useful for long baseline quick positioning for different precision requirements in various distances.     

Positioning Precision Analysis of GNSS Multi-frequency Carrier Phase Combinations

GPS positioning precision is affected by various error sources, and traditional combinations of GPS carrier phase observations have their own limitations such as the wide-lane, the narrow-lane and the ...     

GNSS模糊度整数估计方法图形可视化软件设计与应用分析

模糊度快速准确估计是全球卫星导航系统(GNSS)高精度定位的关键,整数取整、序贯取整和整数最小二乘估计是模糊度常用的三类整数估计方法.尽管从程序上较易实现三类估计方法,但是如何根据模糊度浮点解和精度构建整数估值的几何图形却缺乏较多的研究,不利于我们对整数估计过程的直观认知.因此,本文从理论上分别给出三类估计方法的一般形式,然后基于MATLAB GUI设计了一套三类估计方法二维几何图形构建的可视化分析软件,其功能包括三类估计方法的归整域构建、映射图构建和蒙特卡洛模拟及成功率计算.实验测试结果表明,本文设计的软件能够从几何图形角度较直观地表达出三类整数估计过程及其解算性能.      

Zero-correlation transformation and threshold for efficient GNSS carrier phase ambiguity resolution

The key point of accurate and precise applications of Global Navigation Satellite Systems lies in knowing how to efficiently obtain correct integer ambiguity. One of the methods in solving the ambiguity resolution problem is applying the ambiguity searching technique coupled with an ambiguity decorrelation technique. Traditionally, an integer-valued limitation of the transformation matrix ensures that the integer characteristic of candidates exists after the inverse transformation, but this also makes the decorrelation imperfect. In this research, the float transformation matrix will be considered. To ensure both the integer characteristic and perfect decorrelation can be reached, the float transformation is used indirectly. To solve the ambiguity resolution problem, the problem is transformed by integer and float transformation matrices. The objective of integer transformation is reducing the number of candidates. The target of float transformation is validating these reduced candidates. A zero correlation domain or a near complete diagonalization covariance matrix can be obtained via the float transformation. A space in this domain will be used as the threshold; hence the zero correlation domain is called the threshold domain. The number of ambiguity candidates based on integer transformation can be reduced once again through the proposed method. The experiments in this paper prove that the method can make the ambiguity resolution become more efficient without any drop in the accuracy.