Adaptive filtering of continuous GPS results

 An adaptive finite-duration impulse response filter, based on a least-mean-square algorithm, has been used to mitigate multipath effects, and to derive tectonic and fault movement signals from continuous global positioning system (CGPS) data. By applying the filter on both pseudo-range and carrier-phase multipath sequences from CGPS observations on consecutive days, multipath models have been reliably derived. The standard deviations of residual time series are reduced to about one-quarter on pseudo-range and to about one-half on carrier phase. The adaptive filter is then used to process baseline solutions from a five-station array. Tectonic and fault movements have been resolved, which are in good agreement with previous studies involving many more CGPS stations. Received: 11 February 2000 / Accepted: 28 June 2000     

广域差分参考站两种伪距平滑算法的再评估

广域差分GPS系统（WADGPS）参考站上，需要利用载波相位平滑伪距算法来减小多路径效应的影响。伪距平滑算法有Hatch滤波和加权Hatch滤波两种。文中基于我国WADGPS参考站的实际数据，对这两种平滑算法进行重新评估。实际数据显示，如果不能获得可靠的伪距观测值的方差，在抑制伪距中噪声的影响方面，Hatch滤波明显优于加权Hatch滤波。     

CVVF方法用于GPS多路径效应的研究

将交叉证认法与Vondrak数字滤波器相组合,提出一种分离测量资料中信号与噪声的新方法,即CVVF方法,并将该方法用于GPS多路径效应的研究中.对数字模拟试验和实际观测资料的分析表明,该方法能最大限度地削弱测量的随机误差,使资料序列中的信号和噪声合理分离.同时,利用GPS多路径效应周期性重复的特性,可有效地削弱多路径效应对观测结果的影响,从而提高GPS定位精度.     

On the link between GPS pseudorange noise and day-boundary discontinuities in geodetic time transfer solutions

When neglecting calibration issues, the accuracy of GPS-based time and frequency transfer using a combined analysis of code and carrier phase measurements highly depends on the noise of the GPS codes. In particular, the pseudorange noise is responsible for day-boundary discontinuities which can reach more than 1 ns in the time transfer results obtained from geodetic analysis. These discontinuities are caused by the fact that the data are analyzed in daily data batches where the absolute clock offset is determined by the mean code value during the daily data batch. This pseudorange noise is not a white noise, in particular due to multipath and variations of instrumental delays. In this paper, the pseudorange noise behavior is characterized in order to improve the understanding of the origin of the large day-boundary discontinuities in the geodetic time transfer results. In a first step, the effect of short-term noise and multipath is estimated, and shown to be responsible for only a maximum of 150 ps (picoseconds) of the day-boundary jumps, with only one exception at NRC1 where the correction provides a jump reduction of 300 ps. In a second step, a combination of time transfer results obtained with pseudoranges only and geodetic time transfer results is used to characterize the long-term evolution of pseudorange errors. It demonstrates that the day-boundary jumps, especially those of large amplitude, can be explained by an instrumental effect imposing a common behavior on all the satellite pseudoranges. Using known influences as temperature variations at ALGO or cable damages at HOB2, it is shown that the approach developed in this study can be used to look for the origin of the day-boundary discontinuities in other stations.     

载波相位平滑时间常数对GBAS精度增强的影响

陆基增强系统(GBAS)是利用载波相位平滑伪距差分修正实现对导航辅助定位的. 其中,平滑时间常数是影响载波相位平滑伪距精度的关键参数. 本文分析研究了不同平滑时间下电离层时间梯度和空间梯度对Hatch滤波的影响. 在结合电离层时空梯度和多径效应引起的滤波总误差方差的基础上,推导出自适应的最优平滑时间常数. 分别对GBAS静态和动态两种环境下的定位误差进行实验,实验结果表明,采用本文推导出的自适应平滑时间常数降低了GBAS伪距测量误差,从而使定位精度得到增强.      

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.     

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.     

融合小波变换和自适应Kalman滤波在GPS监测中的应用研究

针对自适应卡尔曼滤波只适用于滤除高斯分布的白噪声,本文提出了融合小波变换和自适应卡尔曼滤波的算法。该算法利用小波变换的多尺度分解,将GPS高频的监测时间序列进行多层分解,重构出新的GPS监测时间序列,将其作为新的自适应卡尔曼滤波初始值,进行滤波处理。将融合算法的滤波结果与单一的自适应卡尔曼滤波结果进行对比分析,结果表明融合算法的滤波效果较为显著。同时,对融合算法滤除的噪声信息进行统计分析,结果表明融合算法滤除的噪声符合正态分布,进一步说明了该融合算法的有效性,为GPS的高频率、高精度的监测提供了技术支持。     

BDS-3新频点B1C/B2a动态数据特性及PPP精度分析

通过载噪比(CNR)、数据完整率、伪距与载波相位观测值噪声和伪距多路径效应四个指标对北斗三号卫星导航系统(BDS-3)新频点B1C/B2a车载动态数据的特性进行了分析,测试了BDS-3新频点动态精密单点定位(PPP)的性能,并与其它全球卫星导航系统(GNSS)进行了对比. 试验结果表明,BDS-3新频点B2a平均CNR优于北斗卫星导航系统(BDS)其它频率,但略差于GPS L5;相较于其它GNSS,BDS数据完整率相对较高,其中BDS-3 B2a新频点数据完整率最高;BDS-3 B2b伪距观测值噪声最小,B1C和B2a伪距观测值噪声约为B2b信号的3倍,但不同频率相位观测值噪声处于同一量级;对于伪距多路径而言,BDS-3 B1C/B2a 信号略小于B2b 信号. 总体而言,GPS L5信号抑制多路径效应的能力最强. 在动态PPP性能方面,BDS-3 B1C/B2a双频组合动态PPP定位精度最优,其三维(3D)均方根(RMS)误差为0.439 m,相比BDS B1I/B3I、GPS L1/L2、GLONASS G1/G2和Galileo E1/E5a双频组合PPP,其精度改善率分别为49%、56%、81%和42%.      

基于自适应噪声抵消与小波滤波的GPS监测误差分析

对GPS载波相位测量误差进行了理论分析和试验研究。根据噪声特征以及它们对载波相位测量结果的影响，提出了基于自适应噪声抵消与小波滤波相结合的GPS噪声抑止方法。对具有强相关特性的多路径误差采用自适应噪声抵消方法，而对于不相关的高频噪声则通过合理选择小波分解层数对信号进行分解，对作用闽值后的小波系数进行重构，得到最后的变形信号。实测数据分析表明，该方法能有效地削弱多路径效应及测量随机噪声，较用单一方法对GPS数据进行消噪处理有较大的优越性。     

GPS码跟踪环自适应多径消除算法

根据多径信号的产生机理,在对GPS接收机中的码跟踪环多径信号模型研究的基础上,提出了采用自适应滤波的来消除GPS多径效应的算法。自适应滤波的方法不需要估计模型的系统参数,而直接通过自适应滤波将多径信号滤除。在有噪声的情况下,自适应滤波的RLS算法是最小二乘意义下的最优估计,仿真的结果表明采用自适应滤波算法可以快速的消除多径的影响,修正鉴相函数的过零点偏差,提高码跟踪环的跟踪精度。由于自适应滤波算法是递推算法,易于软、硬件实现。     

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.     

一种改进的星载GPS周跳探测与修复方法

周跳探测与修复是星载GPS数据预处理的重要内容。首先使用SWARM卫星实测数据对TurboEdit算法的有效性进行了分析,针对算法在观测噪声较大情况下无法有效探测小周跳的问题,提出了一种改进算法。该算法利用载波相位观测值对伪距组合观测值进行平滑,降低了观测噪声对宽巷模糊度的影响,提高了周跳探测能力。实验结果表明,改进算法能够有效提高小周跳的探测能力。      

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.     

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。     

Single-Epoch Ambiguity Resolution for Real-Time GPS Attitude Determination with the Aid of One-Dimensional Optical Fiber Gyro

High-accuracy real-time GPS-based attitude determination requires that integer ambiguities be resolved very quickly so that the attitude angles can be output with minimum delay. This article describes an attitude determination algorithm that can resolve integer ambiguities instantaneously, relative to one antenna of a multi-antenna array configuration. The carrier phase and pseudorange observations are used with fixed baseline length constraints and fiberoptic gyro data. Real-time stochastic model improvement using empirical elevation-dependent standard deviation function and an estimated scale factor are a feature of this algorithm. Integer ambiguity search using the LAMBDA method, sophisticated validation criteria, and an adaptive procedure has also been implemented within the software. An experiment was carried out using four Leica dual-frequency GPS receivers (but only the L1 carrier phase and pseudorange data were used) and a low-cost fiberoptic on a car. The results indicate that integer ambiguities can be resolved on a single-epoch basis with a 98.9% success rate. ? 1999 John Wiley & Sons, Inc.     

Evaluating pseudorange multipath effects at stations in the National CORS Network

A preliminary study was conducted to evaluate the amount of pseudorange multipath at 390+ sites in the National Continuously Operating Reference Station (CORS) Network. The National CORS Network is a cooperative effort involving over 110 different agencies, universities, and private companies who seek to make GPS data from dual-frequency receivers located throughout the United States and its territories available to the general public. For CORS users, pseudorange multipath can seriously degrade the accuracy of any application that relies on precise measurements of the pseudorange observable over a short period of time, including differential pseudorange navigation, kinematic and rapid-static surveying, and ionospheric monitoring. The main objectives of this study were to identify the most affected and least affected sites in the network, to closely investigate problematic sites, and to compare various receiver/antenna combinations. Dual-frequency carrier phase and pseudorange measurements were used to estimate the amount of L1 and L2 pseudorange multipath at each site over a one-year period. Some of the most severely affected sites were maritime Differential GPS and Nationwide Differential GPS (DGPS/NDGPS) sites. Photographs obtained for these sites verified the presence of transmission towers and other reflectors in close proximity to the GPS antennas. Plotting the variations of the L1 and L2 pseudorange multipath with respect to azimuth and elevation further verified that even above a 60° elevation angle there was still as much as five meters of pseudorange multipath at some sites. The least affected sites were the state networks installed in Ohio and Michigan; these sites used excellent antenna mounts, choke ring antennas, and new receiver technology. A comparison of the 12 most commonly used receiver/antenna combinations in the CORS Network indicated that newer receivers such as the Ashtech UZ-12, Leica RS-500, and Trimble 5700 help to significantly mitigate pseudorange multipath, while the receivers/antennas at some DGPS/NDGPS sites, and the antennas formerly used at the Wide Area Augmentation System (WAAS) sites, are among those most affected by pseudorange multipath. The receiver/antenna comparison did not take into account the potential presence of reflectors at the sites (i.e., it is possible that a well-performing receiver/antenna combination could have been consistently placed at very poor site locations, and vice-versa).Product Disclaimer: Mention of a commercial company or product does not constitute an endorsement by the National Oceanic and Atmospheric Administration. Use for publicity or advertisement purposes of information from this paper concerning proprietary products or the comparison of such products is not authorized.     

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.     

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.     

Analysis of early late phase in single-and dual-frequency GPS receivers for multipath detection

Much of the research into multipath detection and mitigation has not considered the carrier phase delay between the line of sight (LOS) and reflected signals. A new variable referred to as early late phase (ELP) has recently been proposed to exploit this phase difference. It has been found that in a receiver tracking the L1 GPS signal, the probability of detecting multipath is lower when the carrier phase difference between the LOS and a reflected signal is an integer multiple of π. Since the pseudorange error caused by the multipath’s presence is the highest in this case, we propose to exploit the coexistence of another GPS civilian signal, the L2C. We present an analysis of ELP for the L1 and L2C signals, and a combination of both, for detecting multipath. The multipath detection performance has been compared using probabilities of false alarm and detection. An ideal algorithm should have lower probability of false alarm and higher probability of detection. However, it has been found that using dual-frequency ELP increases both probabilities. Thus, receiver operator characteristics (ROC) curves, and the area under the ROC curves, have been used for effective comparison. It has been found that the L2C signal individually gives worse performance than L1 because of its weaker signal strength. However, the combination of L1 and L2C gives the best overall performance, and thus it can be claimed that ELP using dual-frequency receivers is a more effective approach for detecting multipath.