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.     

GPS多路径重复性试验研究

信号衍射和多路径效应是限制GPS定位精度进一步提高的瓶颈,观测中两者往往同时存在。衍射效应具有不完全重复的特性,为了研究多路径重复性并使其不受信号衍射的影响,本文提出先应用SIGMA-Δ信噪比加权模型削弱信号衍射的影响,再运用改进恒星时滤波法分析多路径重复性。实验观测资料分析表明,SIGMA-Δ模型能有效削弱衍射信号对定位结果影响,并且保留主要的多路径信号;而改进恒星时滤波法能适应测站周围多路径环境的变化,从而最大限度地削减多路径误差。两者组合比传统的恒星时滤波更能有效提高GPS的动态定位精度。     

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。     

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.     

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.     

A new method to mitigate multipath error in single-frequency GPS receiver with wavelet transform

One of the major errors in high-precision GPS positioning is multipath. Multipath effect modeling and reduction have been a challenging issue in high-accuracy GPS positioning applications due to its special properties. Different methods have been employed to mitigate this error including hardware and software approaches. We reduce C/A code multipath error by adopting an efficient software method which uses wavelet transform as a basic data processing trend. The key idea of the proposed method is using stationary wavelet transform (SWT) in GPS signal data processing. Since we have used SWT, there is complete access to high-frequency and low-frequency terms in both time and frequency domains, and we can apply appropriated procedures to mitigate this error. The multipath error mostly is a low-frequency term. In our proposed method, the double difference (DD) residuals are applied to the SWT to identify the multipath disturbance. The extracted multipath is then used to correct DD observations. Our experiments include three data sets to investigate the proposed method and compare it with existing algorithms. We used simulations for two of these data sets. The results indicate the efficiency of the proposed method over existing algorithms.     

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。     

变形监测中GPS信号衍射误差的环境建模法

信号衍射是GPS结构变形监测的重要误差源之一.GPS天线周围的建筑物是常见的信号衍射体.针对在变形监测中观测环境相对固定之特点,提出一种基于环境模型的衍射误差建模算法.若干试验表明所提方法能有效检测并削弱衍射误差对变形监测结果的影响.     

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,…     

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.     

一种利用增广参数Kalman滤波的GPS多路径效应处理方法

提出了一种基于增广参数Kalman滤波的多路径效应系统误差估计方法,将系统误差作为状态参数,并对其建立一阶AR模型,同时利用多路径重复性特性,更新多路径误差改正模型,在一定程度上解决了固定多路径误差模型随着时间推移重复性减小而有效性降低的问题,并利用16d实测数据例证了本方法具有一定的可行性和有效性。     

基于经验模态分解去噪提高GPS定位精度

在GPS精密定位中,多路径效应等无法建模的误差严重影响着定位结果的精度。这类误差不能通过传统的建模方式进行处理,也不能通过数据组合进行消除,更不能作为参数进行估计。因此本文基于经验模态分解提出一种数据驱动的噪声消除策略,将坐标时间序列分解为许多不同频率组成的时间序列,根据需要重构原始时间序列。并采用了仿真实验和实测数据验证所提出方法的有效性,结果显示所提出的方法可以有效的消除多路径效应等无法建模误差的影响。     

星间差分GRAPHIC观测量单频精密单点定位算法

提出了一种基于星间差分GRAPHIC观测量的单频精密单点定位算法,采用正反向滤波实现了静态和动态解算功能。该算法的优点是不需要外部电离层模型进行电离层延迟改正。采用4个IGS站7d的数据和一组机载GPS动态数据进行解算实验,结果表明:静态定位E,N和U方向的RMS分别为0.035,0.007和0.080m;动态定位E,N和U方向的RMS分别为0.117,0.122和0.180m。     

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。     

GPS残差信号提取的时间序列分析方法

作者使用零基线单差模型研究并讨论了GPS量测噪声的时相关特性,并得出了GPS观测噪声具有类似白噪声或一阶高斯马尔科夫噪声的特殊性质。利用观测噪声所具备的这种特殊性质,作者首先尝试了从时间域的角度分离和提取了残差序列中的多路径信号特性,成功验证了多路径信号在连续两个恒星日内会有所重复的结论。作者提出了一种使用时相关分析法检测观测序列中周期信号(如冰期反弹、固体潮、极潮等)的设想并就其可行性进行了分析研究。最后,针对观测噪声的这种特殊性质,探讨了结合使用小波分析法提取GPS沉降监测信号的可行性。     

GPS sidereal filtering: coordinate- and carrier-phase-level strategies

Multipath error is considered one of the major errors affecting GPS observations. One can benefit from the repetition of satellite geometry approximately every sidereal day, and apply filtering to help minimize this error. For GPS data at 1 s interval processed using a double-difference strategy, using the day-to-day coordinate or carrier-phase residual autocorrelation determined with a 10-h window leads to the steadiest estimates of the error-repeat lag, although a window as short as 2 h can produce an acceptable value with > 97% of the optimal lag’s correlation. We conclude that although the lag may vary with time, such variation is marginal and there is little advantage in using a satellite-specific or other time-varying lag in double-difference processing. We filter the GPS data either by stacking a number of days of processed coordinate residuals using the optimum “sidereal” lag (23 h 55 m 54 s), and removing these stacked residuals from the day in question (coordinate space), or by a similar method using double-difference carrier-phase residuals (observational space). Either method results in more consistent and homogeneous set of coordinates throughout the dataset compared with unfiltered processing. Coordinate stacking reduces geometry-related repeating errors (mainly multipath) better than carrier-phase residual stacking, although the latter takes less processing time to achieve final filtered coordinates. Thus, the optimal stacking method will depend on whether coordinate precision or computational time is the over-riding criterion.     

基于卡尔曼滤波和改进DBSCAN聚类组合的GPS定位算法

实时获取智能移动终端的地理位置信息是增强现实（AR）实景智能导航系统实现的关键,为了提高智能终端GPS定位的精度,提出了一种基于卡尔曼滤波与改进的具有噪声的基于密度的聚类方法（DBSCAN）结合的GPS组合定位优化方法. 通过对GPS系统采集到的位置坐标数据进行卡尔曼滤波,去除较大的数据波动,控制定位误差范围,采用DBSCAN聚类算法进行分类去噪和二次聚类,对类中数据求得算术均值和类间数据总数进行加权求重心,确定位置坐标. 实验结果表明,提出的算法能有效提高GPS单点定位精度,减少定位误差,同时很好地满足了AR实景智能导航系统实时性和鲁棒性的要求.      

基于小波分析提取单频GNSS伪距多路径误差及其对定位的影响

伪距多路径误差是影响GNSS导航定位精度的主要误差源之一。多路径误差与接收机周围环境有关,在实际应用中难以建立有效的多路径误差模型进行改正。对于多频GNSS接收机可以通过多频观测值组合估计伪距多路径,但该方法不适用于价格低廉的单频接收机,而导航中使用的大多数为单频接收机。因此,开展单频GNSS伪距多路径误差提取研究具有重要的工程应用价值。本文基于小波分析对单频GNSS接收机伪距多路径误差估计开展研究,首先验证了小波分析用于单频GNSS伪距多路径误差估计的可行性;其次,研究了采用不同的小波基和分解层次对多路径误差估计的影响;最后,研究了改正多路径误差对GNSS定位的影响。实验结果表明不同的小波基和分解层次对多路径误差提取效果没有明显的差别,但小波分解层次较低时定位误差分布相对更加集中,同时,经过多路径误差改正后在NEU3个方向RMS平均改善率达到20.4%、25.1%、16.4%。