削弱GNSS多路径效应的半天球格网点建模方法

多路径效应与测站观测环境相关,无法利用差分的方式消除或削弱,是GPS精密数据处理时的主要误差源。为此,本文提出了一种利用半天球格网点模型削弱测站多路径误差影响的新方法MHGM(multi-point hemispherical grid model)。该方法对以测站为球心的半天球进行格网点划分,通过格网点的参数化描述,实现测站处多路径误差建模,可适用于现有各类GPS数据处理的软硬件设备和观测环境。本文算例的测试结果表明,采用新方法建模后双差观测值残差的RMS均值改善率平均在73.9%左右,较传统恒星日滤波方法的改善效果平均可提升26.9%,对于静态观测数据,按实时动态相对定位处理模式可获得平面精度约1.7 mm,高程精度约3.0 mm的定位结果。此外,MHGM模型还可进一步用于对测站周边可能存在的多路径误差源进行方位评估,对从物理意义上消除多路径误差源的影响给出一定的指导性意见。     

Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning

Repeatable satellite orbits can be used for multipath mitigation in GPS-based deformation monitoring and other high-precision GPS applications that involve continuous observation with static antennas. Multipath signals at a static station repeat when the GPS constellation repeats given the same site environment. Repeat-time multipath filtering techniques need noise reduction methods to remove the white noise in carrier phase measurement residuals in order to retrieve the carrier phase multipath corrections for the next day. We propose a generic and robust three-level wavelet packets based denoising method for repeat-time-based carrier phase multipath filtering in relative positioning; the method does not need tuning to work with different data sets. The proposed denoising method is tested rigorously and compared with two other denoising methods. Three rooftop data sets collected at the University of Nottingham Ningbo China and two data sets collected at three Southern California Integrated GPS Network high-rate stations are used in the performance assessment. Test results of the wavelet packets denoising method are compared with the results of the resistor–capacitor (RC) low-pass filter and the single-level discrete wavelet transform (DWT) denoising method. Multipath mitigation efficiency in carrier phase measurement domain is shown by spectrum analysis of two selected satellites in two data sets. The positioning performance of the repeat-time-based multipath filtering techniques is assessed. The results show that the performance of the three noise reduction techniques is about 1–46 % improvement on positioning accuracy when compared with no multipath filtering. The statistical results show that the wavelet packets based denoising method is always better than the RC filter by 2–4 %, and better than the DWT method by 6–15 %. These results suggest that the proposed wavelet packets based denoising method is better than both the DWT method and the relatively simple RC low-pass filter for noise reduction in multipath filtering. However, the wavelet packets based denoising method is not significantly better than the RC filter.     

Adaptive wavelet transform based on cross-validation method and its application to GPS multipath mitigation

Global positioning system (GPS) multipath disturbance is a bottleneck problem that limits the accuracy of precise GPS positioning applications. A method based on the technique of cross-validation for automatically identifying wavelet signal layers is developed and used for separating noise from signals in data series, and applied to mitigate GPS multipath effects. Experiments with both simulated data series and real GPS observations show that the method is a powerful signal decomposer, which can successfully separate noise from signals as long as the noise level is lower than about half of the magnitude of the signals. A multipath correction model is derived based on the proposed method and the sidereal day-to-day repeating property of GPS multipath signals to remove multipath effects on GPS observations and to improve the quality of the GPS measurements.     

A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy

Multipath disturbance is one of the major error sources in high-accuracy positioning for global navigation satellite system (GNSS). Although various methods based on software and hardware strategies have been developed to mitigate this error, they are still limited by different kinds of factors and the effect is not ideal. After analyzing the existing methods, a new single-difference sidereal filtering method, based on adaptive thresholding wavelet denoising and double reference shift strategy (ATDR), is proposed to mitigate multipath effects for static short-baseline GNSS applications. The key idea of the proposed method is the use of both the adaptive thresholding wavelet denoising to extract an accurate multipath correction model from the reference Day and the double reference shift strategy to mitigate multipath for subsequent Day 2 more accurately and efficiently. By applying the introduced adaptive thresholding method, the average improvement rate of the RMS values of the single-difference residuals can reach about 15.82% compared with the constant thresholding method. Moreover, after applying the proposed ATDR method, the 3D positioning precision is improved by about 37.73% for the single epoch mode with 30 s data sampling rate and about 31.22% for the continuous mode with 1 s high sampling rate compared with the original results. Even compared with the constant thresholding single orbital reference (CTSR) method, the improvement percentage is about 33.94% in single epoch mode and about 25.40% in continuous mode for 3D positioning precision, respectively. In conclusion, the results of the two experiments indicate that the proposed ATDR method performs much better than the CTSR method in mitigating multipath for different sampling rates and different processing modes in the measurement domain for GNSS static short-baseline postprocessing applications.     

Filtering GPS time-series using a Vondrak filter and cross-validation

Multipath disturbance is one of the most important error sources in high-accuracy global positioning system (GPS) positioning and navigation. A new data filtering method, based on the Vondrak filter and the technique of cross-validation, is developed for separating signals from noise in data series, and applied to mitigate GPS multipath effects in applications such as deformation monitoring. Both simulated data series and real GPS observations are used to test the proposed method. It is shown that the method can be used to successfully separate signals from noise at different noise levels, and for varying signal frequencies as long as the noise level is lower than the magnitude of the signals. A multipath model can be derived, based on the current-day GPS observations, with the proposed method and used to remove multipath errors in subsequent days of GPS observations when taking advantage of the sidereal day-to-day repeating characteristics of GPS multipath signals. Tests have shown that the reduction in the root mean square (RMS) values of the GPS errors ranges from 20% to 40% when the method is applied.     

一种基于交叉证认技术的自适应小波变换及其在削减GPS多路径误差中的应用

多路径效应影响是目前限制GPS定位精度进一步提高的瓶颈。提出用交叉证认技术自动识别小波分解的信号层,再通过小波重构实现降噪和信号提取,并将该方法应用于GPS多路径误差的削减中。对模拟数据和实际GPS观测资料的分析表明,该方法能合理分离不同噪声水平下资料序列中的信号和噪声;当噪声水平小于信号振幅的一半时,能成功分离资料序列中的高频信号。同时,运用该方法得到的多路径改正模型和GPS多路径效应的重复性,可有效地削弱多路径效应的影响,提高GPS定位精度。     

Multipath mitigation via component analysis methods for GPS dynamic deformation monitoring

Multipath is one of the main error sources in high-precision global positioning system (GPS) dynamic deformation monitoring, as it is difficult to be mitigated by differencing between observations. In addition, since a specific frequency threshold value between multipath and deformation signals may not exist, multipath is usually inseparable from the low-frequency vibration signal using conventional frequency-domain filter methods. However, the multipath repeats in two sidereal days when the surroundings of a GPS antenna remain unchanged. This characteristic can be exploited to model and thus mitigate multipath effectively in dynamic deformation monitoring. Unfortunately, a major issue is that the degree of repeatability decreases as the interval between first day and subsequent days increases. To overcome this problem, we develop a new sidereal filtering referred to as reference EMD-ICA (EMD-ICA-R), where empirical mode decomposition (EMD) and independent component analysis (ICA) are jointly used to model multipath and renew the reference multipath. For the successful implementation of the EMD-ICA-R, an a priori denoised multipath signal is needed as a reference. We further propose to use the principal component analysis (PCA) method to extract more accurate reference multipath signal and form a combined PCA-EMD-ICA-R approach. Simulation experiments with a motion simulation platform were conducted, and the testing results indicate that the proposed methods can mitigate the multipath by around 67 % when a reliable reference multipath signal is extracted from a static situation. Furthermore, simulation experiments with different deformation signals added into the coordinate time series of three consecutive days show that the two proposed methods are also effective in a dynamic situation. Since wavelet filtering is used to denoise the reference multipath signals in the new approaches, simulation experiments with several wavelet filters are tested, and the results indicate that the PCA-EMD-ICA-R approach can work well with various wavelet filters.     

Wavelet Shrinkage: High frequency multipath reduction from GPS relative positioning

The wavelet transform is used to reduce the high frequency multipath of pseudorange and carrier phase GPS double differences (DDs). This transform decomposes the DD signal, thus separating the high frequencies due to multipath effects. After the decomposition, the wavelet shrinkage is performed by thresholding to eliminate the high frequency component. Then the signal can be reconstructed without the high frequency component. We show how to choose the best threshold. Although the high frequency multipath is not the main multipath error component, its correction provides improvements of about 30% in pseudorange average residuals and 24% in carrier phases. The results also show that the ambiguity solutions become more reliable after correcting the high frequency multipath.     

Sidereal filtering based on single differences for mitigating GPS multipath effects on short baselines

Carrier-phase multipath effects are one of the most significant error sources in precise Global Positioning System (GPS) positioning applications. A new sidereal filtering algorithm based on single differences is developed to mitigate multipath effects for short-baseline high-rate GPS applications such as structural deformation monitoring. This method differs from traditional sidereal filtering in that our method operates on the single differences rather than the coordinates or double differences. A multipath model for the single differences on the reference day is established for each satellite and is used to remove multipath errors from observations of subsequent days by taking advantage of the sidereal repeatability of multipath signals. Using both simulated and real GPS observations, we demonstrate that this method is insensitive to different weighting strategies used in computing single differences from double differences. Applying the proposed method can reduce the root mean square (RMS) of positioning noises by 82% on average. Compared to sidereal filtering (in either coordinate or double differences domain) and aspect repeat time adjustment, this method can further reduce the RMS values by 13 and 7%, respectively. Wavelet spectra have shown that the proposed method is more effective in mitigating multipath errors of both long and short periods. This method is also more advantageous in that it is applicable when different GPS satellites are observed on different days.     

伪卫星多路径效应分形特征及其削弱方法研究

多路径效应是伪卫星应用在精密定位领域的一项主要误差源,本文从验证多路径效应分形特征入手,利用小波分析在研究分形及信号去噪方面的优势,研究了分形信号与高斯白噪声的模极大值在小波变换下表征的不同特点,针对静态环境下伪卫星的应用,提出一种基于分形理论的多路径误差的消除方法。通过设计试验进行精度分析,验证了本文方法的有效性,且该算法从信号自身的分形特征入手,不需要额外的先验信息,对环境等条件要求较低,比较适合在形变监测等静态环境下应用。     

Carrier phase multipath error characterization and reduction in single aircraft relative positioning

This paper describes GPS carrier phase (CP) multipath characterization and error reduction techniques and their application in single aircraft relative positioning. In particular, the single aircraft relative positioning scenario has applications for high-accuracy multi-sensor stabilization where CP multipath is a major error source that limits system performance. We will briefly review the requisite multipath theory and discuss models for quantifying the error characteristics. Field-test data will be used to validate the multipath models considering the underlying assumptions. A basic geometric reflection point theory will be presented to demonstrate the physical environmental sensitivity of CP multipath to parameters such as surface flatness and antenna height. Several different quantities will be described as multipath indicators for time-domain detection and will be compared with a frequency-domain technique. A new multipath detection approach will be introduced that is suitable to track multipath from time-varying reflection/diffraction points. Finally, the narrow-lane antenna baseline processing technique will be presented as a real-time approach to mitigate CP noise and multipath errors that is well suited for a very short baseline single aircraft high accuracy relative positioning system. Field-test results and analysis will be used to illustrate the key concepts in this paper and to help characterize the total navigation system performance.     

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.     

GPS动态监测中多路径效应的规律性研究

在分析GPS多路径效应特性的基础上,结合GPS动态变形监测的特点,对连续多天的观测数据解算结果采用滤波与周日位置求差相结合的方法进行数据处理。研究结果表明,多路径误差具有较强的周日重复性,在有效地削弱多路径效应的影响后,GPS动态监测的三维位置精度可以达到mm级,尤其是垂直方向的精度改善明显。     

Characteristics of multipath effects in GPS dynamic deformation monitoring

IntroductionThere are many factors that affect the precisionand reliability of GPS measuring. Generally, theerror sources can be grouped into the followingthree classes: errors correlated with the satellites(such as ephemeris error, satellite clock error,…     

Denoising effect of multiscale multiway analysis on high-rate GPS observations

GPS Solutions - In general, high-rate GPS data sets are subject to common mode error (CME), multipath error, and high-frequency random noise, which adversely affect the GPS positioning accuracy. In...     

主成分分析模型及在变形监测中的应用

随机误差和多径效应作为GPS变形监测中的主要误差源,严重影响着GPS测量精度。针对这一问题,本文将主成分分析(Principal Component Analysis,PCA)模型引入GPS变形监测领域,首先利用传统PCA方法将测量数据转换至特征空间,通过剔除小特征值对应的特征向量实现对高斯分布随机噪声的抑制,然后将多径噪声作为色噪声进行分析,提出一种广义PCA方法利用多径噪声的时间相关性对其进行滤除,基于实际工程测试数据的实验结果表明,相对于传统的小波噪声抑制方法,所提方法可以获得更好的噪声抑制性能。     

减小伪卫星多路径效应误差的试验研究

伪卫星定位技术可以补偿GPS系统本身一些先天不足，然而GPS和伪卫星组合进行定位又带来了新的误差源，伪卫星多路径效应就是误差源之一。针对多路径的产生原理及特点，在经典最小二乘理论的基础上，推求稳健最小二乘估计的权函数，并结合实际观测数据验证了稳健最小二乘法消除多路径误差的有效性。     

小波阈值降噪在GPS伪距单点定位中的应用

单点定位中多路径效应和接收机噪声等偶然误差对定位的精度影响较大,并且很难选取固定的模型对其减弱,针对上述问题,从全球定位系统（GPS）的信号结构、误差来源出发,剖析了小波分析的原理,采用离散正交小波db3对GPS伪距观测值C1进行了降噪处理．实验表明:使用上述方法对观测值进行处理后,在观测值质量较差的时段,定位精度可提高31.93％,在观测值质量较好的时段,定位精度可提高16.02％.      

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。     

Performance analysis of integrated GPS/GLONASS carrier phase-based positioning

Due to the different signal frequencies for the GLONASS satellites, the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form, as in the case of GPS. In this paper a novel data processing strategy, involving a three-step procedure, for integrated GPS/GLONASS positioning is proposed. The first is pseudo-range-based positioning, that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias. The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities, by using the receiver clock bias estimated in the above step. The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite). A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing. Other associated issues, such as cycle slip detection, validation criteria and adaptive procedure(s) for ambiguity resolution, is also discussed. The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning. From four experiments carried out to date, the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate. The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).