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.     

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。     

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。     

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.     

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。     

GPS snow depth meter with geometry-free linear combinations of carrier phases

Multipath in global positioning system (GPS) is the interference of the microwave signals directly from satellites and those reflected before reaching the antenna, typically by the ground. Because reflected signals cause positioning errors, GPS antennas are designed to reduce such interference. Recent studies show that multipath could be utilized to infer the properties of the ground around the antenna. Here, we report one such application, i.e. a fixed GPS station used as a snow depth meter. Because the satellite moves in the sky, the excess path length of reflected waves changes at rates dependent on the antenna height. This causes quasi-periodic variations of the amplitude and phase of the received signals. Accumulation of snow reduces effective antenna heights, and we can see it by analyzing multipath signatures. Signal-to-noise ratios (SNR) are often used to analyze multipath, but they are not always available in raw GPS data files. Here, we demonstrate that the geometry-free linear combination (L4), normally used to study the ionosphere, can also be used to analyze multipath signatures. We obtained snow depth time series at a GPS station in Hokkaido, Japan, from January to April in 2009 using L4 and SNR. Then, we compared their precisions. We also discuss mechanisms responsible for the possible underestimation of the snow depth by GPS. Finally, we investigate the possibility of inferring physical conditions of the snow surface using amplitudes of multipath signatures.     

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。     

基于交叉证认的EMD滤波及其在GPS多路径效应中的应用

利用交叉证认的方法,提出一种新的基于EMD滤波去噪方法,并将其应用于GPS多路径效应的研究中。通过模拟实验及实测数据分析表明,该方法能够自适应地选择IMF中的信号层数,削弱随机噪声,合理地分离信号和噪声。利用该滤波方法去噪并建立具有重复性的多路径误差效应改正模型,可有效地削弱多路径效应的影响,进而提高GPS动态变形监测的精度。     

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.     

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.     

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.     

GPS/Galileo long baseline computation: method and performance analyses

Modernized GPS and Galileo will provide triple-frequency signals for civil use, generating a high interest to examine the improvement of positioning performance using the triple-frequency signals from both constellations over baselines up to hundreds or thousands of kilometers. This study adopts a generalized GPS/Galileo long-range approach to process the mutually compatible GPS and Galileo triple-frequency measurements for high-precision long baseline determination. The generalized approach has the flexibility to deal with GPS and Galileo constellations separately or jointly, and also the capability to handle dual or triple-frequency measurements. We compared the generalized long-range approach with the Bernese v5.0 software on two test baselines located in East Asia and obtained highly compatible computational results. Further, in order to assess possible improvement of GPS/Galileo long baseline determination compared with the current dual-frequency (L1/L2) GPS, we simulated GPS and Galileo measurements of the test baselines. It is shown that the current level of accuracy of daily baseline solutions can be improved by using the additional Galileo constellation. Both the additional constellation and the triple-frequency measurements can improve ambiguity resolution performance, but single-constellation triple-frequency ambiguity resolution is more resistant to the influences of code noise and multipath than dual-constellation dual-frequency ambiguity resolution. Therefore, in environments where large code noise or multipath is present, the use of triple-frequency measurements is the main factor for improving ambiguity resolution performance.     

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.     

Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals

Stochastic properties of GNSS range measurements can accurately be estimated using a geometry-free short and zero baseline analysis method. This method is now applied to dual-frequency measurements from a new field campaign. Results are presented for the new GPS L5Q and GIOVE E5aQ wideband signals, in addition to the GPS L1 C/A and GIOVE E1B signals. As expected, the results clearly show the high precision of the new signals, but they also show, rather unexpectedly, significant, slowly changing variations in the pseudorange code measurements that are probably a result of strong multipath interference on the data. Carrier phase measurement noise is assessed on both frequencies, and finally successful mixed GPS-GIOVE double difference ambiguity resolution is demonstrated.     

Evolution of Multipath Error Reduction with Signal Processing

GPS Solutions - The described method of code and carrier multipath error reduction is a refinement of the strobe method of pseudo random noise (PRN) signal processing. This method utilizes as a...     

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.     

一种计算北斗三频多路径的方法及其结果分析

多路径误差分析是北斗卫星导航系统性能评估的一项重要内容。本文给出了一种新的计算3频多路径误差的方法,该方法只需对B1和B2载波相位观测值进行处理就能得到3个频率的伪距多路径误差。利用MGEX跟踪站的数据计算了BDS的多路径误差,从GPS和BDS多路径误差比较以及纬度、轨道和频率因素分析了BDS多路径误差的特性,结果表明,BDS多路径误差小于0．5 m,符合质量检查要求,其性能优于GPS卫星系统。     

Performance of the L2C civil GPS signal under various ionospheric scintillation effects

As GPS is modernizing, there are currently fourteen satellites transmitting L2C civil code and seven satellites transmitting L5 signal. While the GPS observables are subject to several sources of errors, the ionosphere is one of the largest error sources affecting GPS signals. Small irregularities in the electrons density along the GPS radio signal propagation path cause ionospheric scintillation that is characterized by rapid fluctuations in the signal amplitude and phase. The ionospheric scintillation effects are stronger in equatorial and high-latitude geomagnetic latitude regions and occur mainly due to equatorial anomaly and solar storms. Several researchers have analyzed the L2C signal quality since becoming available in December, 2005. We analyze the performance of L2C using GPS data from stations in the equatorial region of Brazil, which is subject of weak, moderate and strong ionospheric scintillation conditions. The GPS data were collected by Septentrio PolaRxS–PRO receivers as part of the CIGALA/CALIBRA network. The analysis was performed as a function of scintillations indexes S4 and Phi60, lock time (time interval in seconds that the carrier phase is tracked continuously without cycle slips), multipath RMS and position variation of precise point positioning solutions. The analysis shows that L2C code solutions are less affected by multipath effects than that of P2 when data are collected under weak ionospheric scintillation effects. In terms of analysis of positions, the kinematic PPP results using L2C instead P2 codes show accuracy improvements up to 33 % in periods of weak or strong ionospheric scintillation. When combining phase and code collected under weak scintillation effects, the results by applying L2C against P2 provide improvement in accuracy up to 59 %. However, for data under strong scintillation effects, the use of L2C for PPP with code and phase does not provide improvements in the positioning accuracy.     

星载GPS伪距多路径误差与观测噪声对自主定轨的影响分析

对搭载美国BlackJack接收机的CHAMP/GRACE-A/Jason-2卫星和搭载国产接收机的HY2A/ZY3/TH1卫星的星载GPS数据的伪距多路径误差与观测噪声进行了研究,重点分析了国产接收机伪距多路径误差的变化特性,并研究了多路径误差与观测噪声对星载GPS自主定轨的影响。结果表明:国产接收机的C/A码与P1码伪距观测精度要整体差于美国的BlackJack接收机,而P2码伪距观测精度要整体优于BlackJack接收机;国产接收机P1码伪距受多路径效应影响较大,其多路径误差随高度角减小存在单调递增的变化趋势,其中HY2A、ZY3与TH1卫星的多路径误差最大分别可达3.6 m、1.8 m与0.7 m;这种单调递增变化的多路径误差会导致星载GPS自主定轨位置结果在径向与切向产生系统性偏差。