BeiDou B2/Galileo E5b短基线紧组合相对定位模型及性能评估

随着GPS和GLONASS系统的现代化以及Galileo和BeiDou卫星导航系统的建设,GNSS正朝多频多系统的方向发展。本文对BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法进行了研究,详细推导了BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法,并对其定位性能进行了分析。重点分析了BeiDou B2与Galileo E5b频点的接收机间差分系统间偏差的长期稳定性,结果表明:基线两端的接收机类型(包括固件版本)相同时,差分系统间偏差接近于0;基线两端的接收机类型不同时,差分系统间偏差较大,但具有长期稳定性,因此能够事先标定并作为改正数用于后续的定位中。最后基于BeiDou B2/Galileo E5b单频单历元相对定位试验对系统间紧组合模型的定位效果进行了比较验证。结果表明,相对于传统的松组合模型,使用改正系统间偏差的紧组合模型能够显著提高模糊度固定的成功率,尤其是在遮挡比较严重、单系统可观测到的卫星数较少的情况下,模糊度固定成功率可以提高10%~25%。     

GPS/Galileo/BDS-3试验星短基线紧组合相对定位性能初步评估

北斗全球卫星导航系统(简称北斗三号系统,BDS-3)的试验星播发了与GPS L1/L5、欧洲的伽利略(Galileo)系统E1/E5a/E5b频率重叠的新体制信号B1C/B2a/B2b,这为GPS/Galileo/BDS-3试验星重叠频率的紧组合相对定位提供了条件。首先评估了GPS/Galileo/BDS-3试验星重叠频率差分系统间偏差(differential inter-system bias,DISB)的大小与时域稳定性,结果表明,相同类型接收机的DISB接近于0,在紧组合相对定位中可以忽略其影响。然后初步评估了GPS/Galileo/BDS-3试验星短基线单历元紧组合相对定位性能,结果表明,相较于传统的松组合模型,紧组合模型能够显著提高模糊度固定的成功率与可靠性。尤其是在单系统可观测卫星数较少、仅单频观测值可用的情形下,模糊度固定成功率可提高约25%～45%。     

GNSS接收机伪距偏差确定方法及其对定位的影响

全球导航卫星系统（global navigation satellite system,GNSS）接收机伪距偏差是指卫星导航信号非理想特征导致的不同接收机的伪距测量常数偏差。研究表明,接收机伪距偏差无法被钟差参数吸收,将影响GNSS精密应用。选取了多GNSS实验全球跟踪网的9条零/短基线,将基线按照接收机类型分为3组,即相同厂商相同型号、不同厂商以及相同厂商不同型号,通过双差法确定了每组基线GPS/北斗卫星导航系统(BeiDou satellite navigation system,BDS)/伽利略卫星导航系统（Galileo satellite navigation system,Galileo）的接收机伪距偏差,并分析了接收机伪距偏差的稳定性及其对整周模糊度解算和伪距相对定位的影响。结果表明,不同厂商接收机构成的基线,伪距偏差可达160 cm,即使同一厂商不同型号的接收机间也存在不可忽略的伪距偏差;对于GPS、BDS和Galileo,Galileo伪距偏差最小,BDS伪距偏差最大。此外,接收机伪距偏差具有良好的稳定性,60 d标准差不超过12 cm。接收机伪距偏差改正后,GPS、...     

BDS／GPS 组合 RTK 定位性能分析

针对单系统RTK存在可见卫星数少等问题,文中研究BDS/GPS站间单差的RTK算法模型,该模型采用二次型函数部分最小化及LAMBDA方法联合搜索模糊度。利用该模型分析BDS/GPS组合RTK的定位性能,通过短基线实测数据分析表明:站间单差RTK模型与双差模型是等价的;BDS/GPS组合系统相比于单一系统,明显提高定位的稳健性和精度,改善模糊度固定的成功率。     

GPS/BDS接收机端系统偏差稳定性对整周模糊度固定的影响

GNSS接收机端的UPD与接收到的信号频率有关,这导致GPS和BDS系统间的双差模糊度不具有整数特性,为了恢复其整数特性,两系统间的系统偏差需要进行估计或改正。在顾及GPS和BDS之间的时间系统、坐标系统和频率间偏差的基础上,推导出GPS/BDS系统偏差计算模型,并利用不同实验对系统偏差的稳定性进行验证。实验结果表明,不同品牌接收机在GPS/BDS系统偏差方面在一定条件下均具有稳定性;天线类型和天线连接线长度没有对GPS/BDS系统偏差产生显著影响。加入系统偏差改正的GPS/BDS紧组合定位在恶劣环境下表现良好,可将模糊度固定平均所需时间缩短33%,模糊度固定成功率提高31%。     

信号易遮挡环境下BDS/GPS系统定位性能分析

通过设置不同的截止高度角来模拟卫星信号受遮挡的情况,并以某CORS网4.8 km与5.1 km的2条基线为例,对截止高度角为10°～60°的遮挡情况下,GPS/BDS系统相比单GPS系统、单BDS系统在单历元双频基线解算时的卫星可见性、模糊度固定、定位精度等定位性能的改善情况进行了对比分析。结果表明GPS/BDS组合系统相对单系统,极大改善了卫星的可见性,提升了模糊度的固定率、正确率,在截止高度角为50°、60°的极端条件下,GPS/BDS组合系统单历元基线解算精度在E、N方向仍可达10.0 mm左右,在U方向仍可达20.0 mm左右。     

城市环境下BDS+GPS RTK+INS紧组合算法性能分析

城市环境下运动载体接收的GNSS信号会被频繁地干扰和遮挡,GNSS RTK独立工作模式难以连续且可靠地固定模糊度以满足厘米级高精度定位需求。为此,本文设计了一套基于集中式卡尔曼滤波的BDS+GPS RTK紧组合算法,给出了其动力学模型、观测模型和算法架构流程。通过城市环境下的实际车载测试,对比分析了BDS、GPS、BDS+GPS 3种模式下RTK及RTK+INS紧组合的定位性能。试验结果表明,BDS+GPS双系统大大增加了可见卫星数,提高了城市环境下GNSS动态精密定位的可用性和精度;相对于GNSS RTK,紧组合极大地提高了精密定位的可靠性和可用性。     

顾及伪距差分系统间偏差的GPS/BDS/Galileo/QZSS伪距差分定位精度分析

随着BDS、Galileo和QZSS等卫星导航系统的发展,GNSS正朝着多系统组合定位的方向发展。本文针对GPS/BDS/Galileo/QZSS,提出四系统间伪距差分模型,并对其定位性能分析。结果表明:无论是相同还是不同类型的接收机,伪距DISB在几天范围内是稳定不变的。同时通过设置截止高度角进行模拟遮挡实验。实验结果表明:相对于常规的系统内伪距差分方法,系统间伪距差分方法在截止高度角为30°、40°、50°下的定位精度分别提升19.62%、33.11%、57.77%。该方法可以有效提升定位的精度和可靠性,特别是在遮挡严重的环境下改进明显。     

BDS/GPS短基线解算的随机模型研究

针对BDS轨道高度存在差异进而影响短基线解算结果的问题,该文利用两组实测数据,研究BDS和BDS/GPS组合系统的短基线解算精度及可靠性,并探讨4种随机模型的性能。结果表明,BDS和BDS/GPS组合系统短基线解算精度能够达到厘米级,且模糊度解算的可靠性更高;4种随机模型性能相当,随着基线长度增加,MINQUE模型的优势降低;不同类型卫星轨道高度差异较大,高度角模型不适宜BDS和BDS/GPS组合系统短基线解算。     

BDS/Galileo紧组合系统间偏差估计与模糊度固定效果分析

多个卫星导航系统采用相同频率播发信号,使得不同系统之间可以通过紧组合方式进行数据处理。文中简要介绍了不同系统紧组合双差观测模型;利用零短基线观测数据估计了BDS/Galileo间小数ISB(Inter-System Bias);对其时变稳定性进行了分析并利用单历元相对定位解算进行了验证。实验结果表明,小数ISB具有较好的时间稳定性,能够进行长期预报。相对于松组合相对定位模型,采用紧组合模型能够显著提高模糊度固定的成功率。     

Variable duration fixed failure rate ambiguity resolution

In global navigation satellite system ambiguity resolution, it is common to use a configurable acceptance test, like the popular ratio test, to control the failure rate. Work in the literature proposes acceptance tests which let users directly choose an acceptable failure rate, but it focuses on instantaneous and fixed duration ambiguity resolution (where results may be success, failure, or undecided). We present a fixed failure rate acceptance test which avoids undecided results by varying the duration of the ambiguity resolution window. The proposed method uses Monte Carlo simulation with a time-correlated noise model to select acceptance test parameters that will minimize mean ambiguity resolution time while maintaining the target failure rate. Results of real-world experiments with single-frequency data from receivers with patch antennas show with 24 h of stationary data the method produces a mean ambiguity resolution time reduction of 52 % (from 525 to 250 s) compared with a ratio test. In a test with 90 min of kinematic data, the reduction was 33 % (from 620 to 410 s).     

Numerical solution of the linearized fixed gravimetric boundary-value problem

The fixed gravimetric boundary-value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. Terrestrial gravimetric measurements located by precise satellite positioning yield oblique derivative boundary conditions in the form of surface gravity disturbances. In this paper, we discuss the boundary element method (BEM) applied to the linearized FGBVP. In spite of previous BEM approaches in geodesy, we use the so-called direct BEM formulation, where a weak formulation is derived through the method of weighted residuals. The collocation technique with linear basis functions is applied for deriving the linear system of equations from the arising boundary integral equations. The nonstationary iterative biconjugate gradient stabilized method is used to solve the large-scale linear system of equations. The standard MPI (message passing interface) subroutines are implemented in order to perform parallel computations. The proposed approach gives a numerical solution at collocation points directly on the Earth’s surface (on a fixed boundary). Numerical experiments deal with (i) global gravity field modelling using synthetic data (surface gravity disturbances generated from a global geopotential model (GGM)) (ii) local gravity field modelling in Slovakia using observed gravity data. In order to extend computations, the memory requirements are reduced using elimination of the far-zone effects by incorporating GGM or a coarse global numerical solution obtained by BEM. Statistical characteristics of residuals between numerical solutions and GGM confirm the reliability of the approach and indicate accuracy of numerical solutions for the global models. A local refinement in Slovakia results in a local (national) quasigeoid model, which when compared with GPS-levelling data, does not make a large improvement on existing remove-restore-based models.     

On a scalar fixed altimetry—gravimetry boundary value problem

For some years existence and uniqueness of the solution of a mixed altimetry — gravimetry boundary value problem is under investigation. Usually the size and the shape of the continental part of the Earth's surface is considered as unknown. This leads to a partly free and partly fixed mixed boundary value problem. A solution exists if the area of the continental part is sufficiently small. Obviously, this condition is not fulfilled in reality. Because the GPS is now fully operational, nowadays the size and the shape of the continental part of the Earth's surface can be considered as known, too. The aim of this article is to study the resulting fixed mixed boundary value problem and to prove the existence and uniqueness of its solution for an arbitrary distribution of land and sea at the Earth's surface.     

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      

On the non-linear geodetic boundary value problem for a fixed boundary surface

Summary The fixed gravimetric boundary value problem of Physical Geodesy is a nonlinear, oblique derivative problem. Expanding the non-linear boundary condition into a Taylor series—based upon some reference potential field approximating the geopotential—it is shown that the numerical convergence of this series is very rapid; only the quadratic term may have some practical impact on the solution. The secondorder solution term can be described by a spherical integral formula involving the deflections of the vertical with respect to the reference field. The influence of nonlinear terms on the figure of the level surfaces (e.g. the geoid) is roughly estimated to have an order of magnitude of some few centimetres, based upon a Somigliana-Pizzetti reference field; if on the other hand some high-degree geopotential model is used as reference then the effects by non-linearity are negligible from a practical point of view.     

Integrity monitoring of fixed ambiguity Precise Point Positioning (PPP) solutions

Traditional positioning methods, such as conventional Real Time Kinematic (cRTK) rely upon local reference networks to enable users to achieve high-accuracy positioning. The need for such relatively dense networks has significant cost implications. Precise Point Positioning (PPP) on the other hand is a positioning method capable of centimeter-level positioning without the need for such local networks, hence providing significant cost benefits especially in remote areas. This paper presents the state-of-the-art PPP method using both GPS and GLONASS measurements to estimate the float position solution before attempting to resolve GPS integer ambiguities. Integrity monitoring is carried out using the Imperial College Carrier-phase Receiver Autonomous Integrity Monitoring method. A new method to detect and exclude GPS base-satellite failures is developed. A base-satellite is a satellite whose measurements are differenced from other satellite’s measurements when using between-satellite-differenced measurements to estimate position. The failure detection and exclusion methods are tested using static GNSS data recorded by International GNSS Service stations both in static and dynamic processing modes. The results show that failure detection can be achieved in all cases tested and failure exclusion can be achieved for static cases. In the kinematic processing cases, failure exclusion is more difficult because the higher noise in the measurement residuals increases the difficulty to distinguish between failures associated with the base-satellite and other satellites.     

变权组合模型两种定权方法精度探讨

以指数曲线模型和泊松曲线模型为基础,对基于绝对误差平方和最小与绝对误差绝对值之和最小的两种定权方法进行比较分析,分别对两种模型进行变权组合。文中就确定最佳变权系数的方法进行分析研究,并以某大楼的等时距沉降观测数据为例进行验证,最后得出两种定权方法拟合精度大致相等。     

The free versus fixed geodetic boundary value problem for different combinations of geodetic observables

Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential or gravity or the vertical gradient of gravity is assumed to be given on the boundary. The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical harmonics with Wigner 3j-coefficients.