Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling

Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8 cm for the Global Positioning System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation, but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method will have important practical applications for correcting for multipath in well-constrained environments (such as at base stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.     

Quantitative evaluation of multipath rejection capabilities of GNSS antennas

Multipath error remains the largest error source in many high precision GPS applications. To counteract this problem, solutions at both software and hardware level have been studied. Software processing by means of measurement redundancy or error predictability can be used in order to mitigate the multipath effects. In general, these techniques work properly only when the length of a reflection path exceeds that of the direct path by more than 10–20 m. Unfortunately, in most cases, reflections are generated in the area near the receiving antenna. For this reason, multipath rejection actuated at the antenna level is one of the most valid means to improve the accuracy of GPS systems. The scope of this work is twofold. First, a review of low-multipath reception requirements will be proposed for comparing different classes of high precision GNSS antennas. Based on this discussion, we introduce a quantitative evaluation of multipath rejection capabilities of a GNSS antenna. The proposed assessment technique is focused on the antenna pattern, but, in contrast to other parameters evaluating the antenna radiation characteristics, it is specifically conceived to capture the effects of multipath signals.     

Smoothing GPS carrier phase double differences using inertial measurements for high performance applications

This paper will describe an enhancement to the GPS double difference carrier phase measurements on a single airborne platform by smoothing them with inertial measurements while preserving the dynamic bandwidth. This enhancement will reduce the impact of carrier phase multipath and carrier phase noise on baseline determination between multiple antennas on an aircraft when in flight. This type of measurement system has numerous applications where platform pointing and relative body motion must be determined at the mm-level for applications such as sensor stabilization, Synthetic Aperture Radar, long range RADAR (i.e. angle-of-arrival measurements). Lower noise levels (mm-level and below) enable more performance to the stabilized system such as increased aperture for longer range, operation at higher frequencies, and more image resolution. The focus of this paper will be on a technique to provide this enhanced performance for these various applications using the available navigation systems. Additionally, this type of smoothing can effectively remove the additional noise induced by carrier phase measurement differencing. The noise level of a double or triple difference can be reduced below that of the raw measurement. A complimentary synthesized double difference quantity with ultra-low-noise characteristics will be used to smooth the GPS carrier phase double difference measurements without losing dynamic bandwidth since it follows the airborne dynamics. Flight test data will be presented to demonstrate the performance improvement in the midst of aircraft dynamics. Results will show that the noise reduction follows the theoretical prediction.     

Forward modeling of GPS multipath for near-surface reflectometry and positioning applications

Multipath is detrimental for both GPS positioning and timing applications. However, the benefits of GPS multipath for reflectometry have become increasingly clear for soil moisture, snow depth, and vegetation growth monitoring. Most multipath forward models focus on the code modulation, adopting arbitrary values for the reflection power, phase, and delay, or they calculate the reflection delay based on a given geometry and keep reflection power empirically defined. Here, a fully polarimetric forward model is presented, accounting for right- and left-handed circularly polarized components of the GPS broadcast signal and of the antenna and surface responses as well. Starting from the fundamental direct and reflected voltages, we have defined the interferometric and error voltages, which are of more interest in reflectometry and positioning applications. We examined the effect of varying coherence on signal-to-noise ratio, carrier phase, and code pseudorange observables. The main features of the forward model are subsequently illustrated as they relate to the broadcast signal, reflector height, random surface roughness, surface material, antenna pattern, and antenna orientation. We demonstrated how the antenna orientation—upright, tipped, or upside-down—involves a number of trade-offs regarding the neglect of the antenna gain pattern, the minimization of CDMA self-interference, and the maximization of the number of satellites visible. The forward model was also used to understand the multipath signature in GPS positioning applications. For example, we have shown how geodetic GPS antennas offer little impediment for the intake of near-grazing reflections off natural surfaces, in contrast to off metal, because of the lack of diversity with respect to the direct signal—small interferometric delay and Doppler, same sense of polarization, and similar direction of arrival.     

GNSS多路径和信噪比相关性分析

在全球导航卫星系统(Global Navigation Satellite System,GNSS)接收机附近的反射、衍射、干扰信号等所造成的多路径效应是影响定位的主要误差来源。信噪比(Signal-Noise Ratio,SNR)的振荡是由多路径信号叠加在直接信号上引起的,基于此原理学者们提出了很多检测和缓解多路径误差的方法。本文通过谱分析的方法对多路径时间序列进行了分析,并研究多路径与信噪比之间的相关性,对基于信噪比检测和缓解多路径误差的方法的适用性进行了说明。实验表明:多路径和信噪比振荡值的时间序列具有显著的相关性,能够利用信噪比观测值削弱多路径影响。     

双极性天线在多路径效应探测中的应用

多路径效应是影响卫星定位精度和稳定性的重要因素。针对多路径环境复杂多变难以进行分析的问题,该文提出了一种利用双极性天线探测多路径的方法。详细介绍了反射信号的极性特征;通过判断信号的极性可以有效地区分直射信号和反射信号。分析了通过信号极性实现多路径探测的理论:组成双极性天线的右螺旋圆极化天线和左螺旋圆极化天线能够分别输出卫星信号中的右螺旋圆极化分量和左螺旋圆极化分量,如果两个分量的载噪比差值大于一定的门槛值,就可以推断卫星信号在传输过程中经历了多路径效应。最后通过仿真实验验证了该方法的可行性和有效性。     

Improving vertical GPS precision with a GPS-over-fiber architecture and real-time relative delay calibration

A limitation of GPS positioning is that the vertical component is generally two to three times less precise than the horizontal components. In a previous work by R. Santerre of Laval University and G. Beutler of University of Bern, it was shown in simulations that it is possible to improve the GPS vertical positioning precision by using a multi-antenna GPS receiver and a precise calibration technique of the relative hardware delay between the antennas and the receiver. However, no actual implementation of the system was done to prove the concept until now. A new multi-antenna, GPS-over-fiber architecture with real-time delay monitoring, designed and implemented to improve the vertical precision is presented. The improvement in vertical precision arises from the elimination of the relative receiver clock error in single difference, between antennas, and the precision real-time calibration of the relative hardware delay. Experiments were conducted with a zero baseline and a short baseline configuration. The results show, as expected by the theory and the simulations, a two to three times improvement in the precision of the vertical component such that it reached the same level of performance as the horizontal components. These promising results will enable the use of this type of configuration in several applications where the same precision in all 3D components is essential and could not be achieved before with standard GPS positioning techniques.     

GNSS接收机天线相位中心变化相对检测方法

在精密定位中,GNSS接收机天线相位中心变化是必须进行改正的影响因素。目前成熟的微波暗室法和自动机器人法,对于一般用户而言,不具备相关实验条件,而野外相对法相对简单、易操作。为此,本文利用相对检测法,对GNSS接收机天线相位中心变化进行检测。实例表明,此方法可获得精度优于±3 mm的检测结果,因此可利用此方法对其他类型天线PCV值进行检测,也可借鉴此方法对北斗接收机天线相位中心变化进行检测。同时论文分析了影响检测精度,提出了有益改进建议。      

Variable length LMS adaptive filter for carrier phase multipath mitigation

Multipath on carrier phase measurements is among the major error sources for short baseline positioning. A new method is proposed to improve the accuracy of the positioning results by mitigating the multipath effects on carrier phase measurements using the variable length Least Mean Square (VLLMS) adaptive filter. The performance of the filter is analyzed as well as compared with that of the standard LMS adaptive filter using a set of carrier phase observation data of two consecutive days collected in a short baseline experiment. Because the two antennas are static, the multipath error is the only dominant component in the carrier phase double-differenced residuals and indicates a repeated pattern. The numerical results show that both filters can significantly mitigate the multipath effects in carrier phase double-differenced residuals, and hence improve the positioning results. Furthermore, the VLLMS filter that reduces up to about 47.4% of the multipath effects on 3D positioning performs better than the LMS filter that only reduces 22.0%. Both filters are suitable for real-time applications.     

An advanced GNSS code multipath detection and estimation algorithm

A novel maximum likelihood-based range estimation algorithm is designed to provide robustness to multipath, which is recognized as a dominant error source in DS-CDMA-based navigation systems. The detection–estimation problem is jointly solved to sequentially estimate the parameters of each individual multipath component and predict the existence of a next possible component. A comparison between contemporary maximum likelihood-based multipath estimation techniques and this new technique is provided. A selection of realistic channel simulation models is used to assess relative performance under different operating situations. A set of real GPS L1/CA data processing results are also presented to further assess the applicability of the proposed algorithm for urban navigation.     

LGO解算南方静态数据的天线高改正研究

智慧城市建设需要城市基础点位的准确坐标,往往采用与当地的连续运行参考站系统(CORS)联测方式进行静态解算.?通常采用徕卡LGO数据处理软件进行静态解算,而LGO软件有时无法识别南方测绘公司生产的全球卫星导航系统(GNSS)接收机的天线类型,使用LGO解算该设备获得的静态观测数据时会遇到天线未定义的情况,从而导致天线高...     

北斗天线电气相位中心偏差检验试验研究

为满足北斗双星定位系统精密定位、定向的工程需要,提出一种北斗天线电气相位中心常值偏差3维检验方法,并建立了相应的数学模型.该方法通过基线旋转、单天线旋转、交换天线,利用载波相位单差、基线长度、天线高差测量信息来估计天线电气相位中心偏差,并且在单天线旋转条件下对不同方向、不同天线间单差观测方程求差,以减少未知参数个数.最后,应用此模型检验一对北斗天线,检验结果表明,在单差均方差为0.005周,基线长度、天线间高差均方差为1 mm的条件下,天线间电气相位中心偏差水平分量的检验精度达0.3 mm.论文所述方法操作简单,适合在野外对北斗天线进行电气相位中心偏差检验.     

景像匹配仿真的一种新方法

分析了影响景像相关匹配精度的各种误差因素，并给出它们的误差仿真模型，该模型可以适应飞行姿态、飞行器特性，天候等条件变化时的匹配概率估计，并可以与图像特征参数分析方法相结合。实验验证了该模型的有效性，且可以快速地给出影像图的适配性估计图，用于飞行器的航迹规划。     

Estimation and exclusion of multipath range error for robust positioning

In integrated systems for accurate positioning, which consist of GNSS, INS, and other sensors, the GNSS positioning accuracy has a decisive influence on the performance of the entire system and thus is very important. However, GNSS usually exhibits poor positioning results in urban canyon environments due to pseudorange measurement errors caused by multipath creation, which leads to performance degradation of the entire positioning system. For this reason, in order to maintain the accuracy of an integrated positioning system, it is necessary to determine when the GNSS positioning is accurate and which satellites can have their pseudorange measured accurately without multipath errors. Thus, the objective of our work is to detect the multipath errors in the satellite signals and exclude these signals to improve the positioning accuracy of GNSS, especially in an urban canyon environment. One of the previous technologies for tackling this problem is RAIM, which checks the residual of the least square and identifies the suspicious satellites. However, it presumes a Gaussian measurement error that is more common in an open-sky environment than in the urban canyon environment. On the other hand, our proposed method can estimate the size of the pseudorange error directly from the information of altitude positioning error, which is available with an altitude map. This method can estimate even the size of non-Gaussian error due to multipath in the urban canyon environment. Then, the estimated pseudorange error is utilized to weight satellite signals and improve the positioning accuracy. The proposed method was tested with a low-cost GNSS receiver mounted on a test vehicle in a test drive in Nagoya, Japan, which is a typical urban canyon environment. The experimental result shows that the estimated pseudorange error is accurate enough to exclude erroneous satellites and improve the GNSS positioning accuracy.     

航空测量场景下的中长基线动态定位方法

单基站中长基线动态相对定位受到大气残余误差影响,无法快速固定整周模糊度,定位精度和可靠性不如短基线场景。在航空测量场景下,流动站与基准站之间的基线由短到长变化,利用短基线场景下固定的整周模糊度反算得到高精度的电离层延迟量,并对其进行建模预报。随着基线变长,利用预报的电离层延迟约束中长基线定位模型,实现快速模糊度固定。本文分析了动态长基线情形下的电离层延迟的时变特性,采用滑动窗口进行电离层建模预报,讨论了该方法在航空测量实际作业中的实施条件、定位精度及模糊度固定情况。实测机载数据的解算结果表明,使用该方法,当测量载体出发阶段处于短基线场景下,单基站相对定位结果就可以达到接近100%的模糊度固定率,且定位精度保持在厘米级,显著减小了航空测量任务的作业成本。     

A new method for specular and diffuse pseudorange multipath error extraction using wavelet analysis

Multipath remains one of the major challenges in Global Navigation Satellite System (GNSS) positioning because it is considered the dominant source of ranging errors, which can be classified into specular and diffuse types. We present a new method using wavelets to extract the pseudorange multipath in the time domain and breaking it down into the two components. The main idea is an analysis-reconstruction approach based on application of both continuous wavelet transform (CWT) and discrete wavelet transform (DWT). The proposed procedure involves the use of L1 code-minus-carrier (CMC) observable where higher-frequency terms are isolated as residuals. CMC residuals are analyzed by applying the CWT, and we propose the scalogram as a technique for discerning time–frequency variations of the multipath signal. Unlike Fourier transform, the potential of the CWT scalogram for examining the non-stationary and multifrequency nature of the multipath is confirmed as it simultaneously allows fine detection and time localization of the most representative frequencies of the signal. This interpretation of the CWT scalogram is relevant when choosing the levels of reconstruction with DWT, allowing accurate time domain extraction of both the specular and diffuse multipath. The performance and robustness of the method and its boundary applicability are assessed. The experiment was carried out using a receiver of Campania GNSS Network. The results are given in which specular multipath error is achieved using DWT level 7 approximation component and diffuse multipath error is achieved using DWT level 6 denoised detail component.     

基于GNSS多径信号的反射面参数估计算法

全球卫星导航系统(GNSS)多径信号广泛存在于城市峡谷等复杂导航定位场景中.多径信号在干扰GNSS接收机并造成系统定位精度下降的同时,也为接收机提供了周边反射面环境信息.在码相位延迟幅度联合跟踪算法(CADLL)实现GNSS多径信号感知和特征参数提取的基础上,设计实现了基于粒子滤波的反射面参数估计算法.该算法可以在GN...     

一种提高单历元解算大高差短基线精度的方法

单历元基线解算可以避开传统基线解算中周跳探测等复杂的数据预处理过程。但是当两站高差较大时,即使是短基线,通过双差技术也不能充分消除对流层延迟,且残余对流层误差对单历元基线解算的影响较大,定位精度无法达到毫米级水平。针对以上问题,该文提出了采用半参数广义补偿最小二乘对大高差短基线进行单历元解算,削弱残余对流层误差影响的方法。实际算例表明,与常规的最小二乘法相比,该方法能很好地分离GPS残余对流层误差,各方向定位精度能达到毫米级水平。     

A comparison of P code and high performance C/A code GPS receivers for on the fly ambiguity resolution

Carrier phase ambiguity resolution on the fly is investigated using two receiver technologies, namely dual-frequency P code and high performance, single frequency, C/A code receivers. Both receiver types were used simultaneously in a series of land kinematic trials. A least-squares search technique is used to find the correct double difference carrier phase ambiguities. Both C/A and single frequency P code technologies are found to be equivalent and capable of resolving the integer ambiguities on the fly using some 30 to 200 seconds of data under benign multipath conditions. Successful ambiguity resolution on the fly results in cm-level accuracy kinematic positioning. The ambiguity resolution time required and success rate are however found to be strongly dependent on the level of carrier phase multipath and, as a consequence, on the error variance assigned to the carrier phase measurements. The use of widelaning with the dual frequency P code results in ambiguity resolution in seconds. The performance of widelaning is also superior in a comparatively high carrier phase multipath environment.     

Multipath detection based on single orthogonal dual linear polarized GNSS antenna

GPS Solutions - Based on the polarization difference between the multipath and the line-of-sight (LOS) signal, a method for multipath detection using a single antenna is proposed. The antenna has...