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。     

The autocorrelation of waveforms generated from ocean-scattered GPS signals

A "waveform" is generated by cross-correlating local copies of a global positioning system (GPS) signal with an ocean-reflected GPS signal, over a range of carrier frequencies and code delays. The shape of this waveform can be inverted to obtain estimates of the ocean surface roughness. To assess the accuracy of these retrievals, a stochastic model for the waveform time series measurements was developed in a previous publication. In this letter, this model is validated by comparing the predicted autocorrelation function of the waveform against the autocorrelation computed from experimental waveforms collected from an airborne receiver. A 1-ms coherent integration time was used at first. Then, blocks of these measurements were concatenated to produce equivalent integration times of up to 5 ms to compare the dependence of model predictions on integration time. Correlation time was estimated by fitting a model Gaussian function to the magnitude or the real part of the autocorrelation function. The magnitude and phase of the complex autocorrelation function from the model were also studied to show the location of the first , and better explain cases in which the Gaussian function did not fit well. The autocorrelation is found to be weakly dependent upon the surface roughness, over a range of moderate wind speeds.     

基于高斯模型的样本缺失GPS时间序列重构方法

缺失样本的存在会造成GPS时间序列速度估计的不确定性,从而影响GPS时间序列的应用。针对该问题本文提出一种基于高斯模型的样本缺失GPS时间序列重构方法,首先利用高斯概率密度函数对GPS时间序列的先验分布进行建模,在此基础上构建全概率贝叶斯统计模型,采用期望最大(Expectation Maximization,EM)算法对模型参数(隐变量)进行迭代更新并计算其最大似然估计值,最终完成信号重构。分别对随机缺失和分段连续缺失两种情况进行实验分析,结果表明所提方法相对于传统插值方法可以获得更好的重构性能。     

震后GPS坐标时序中对数弛豫时间的估计

全球定位系统（global positioning system, GPS）坐标时序去除同震形变和震前稳态速度场后,采用加权非线性最小二乘估计震后对数弛豫时间,可更准确地提取震后对数弛豫项,从而可以分析震后弛豫项对测站位移的独立物理贡献,并为震后余滑和黏滞性松弛效应等现象的分析提供参考。以日本2009—2019年GPS坐标时序为例,估计2011年Mw 9.0地震震后对数弛豫时间,发现不同站点的对数弛豫时间与其震中距关系显著,且服从高斯分布。据此,构建高斯函数加常数模型,可由震中距概略估计震后对数弛豫时间。高斯分布曲线的峰值、峰值位置、半宽度信息、最低位置分别为3.5 a、0 km、262 km、0.5 a,由此得出震后对数弛豫项影响时间大于0.5 a的站点主要集中在震中距约524 km范围内。震后弛豫效应区域分布的差异性显著,对数弛豫时间越长的区域,弛豫项水平位移表征越大,其中存在两个平均弛豫时间2.5 a的中心区域,与震后余滑的中心区域及时间相吻合。     

Forward a spatio-temporal trend surface for long-term ground-measured albedo upscaling over heterogeneous land surface

Upscaling ground albedo is challenged by the serious discrepancy between the heterogeneity of land surfaces and the small number of ground-based measurements. Conventional ground-based measurements cannot provide sufficient information on the characteristics of surface albedo at the scale of coarse pixels over heterogeneous land surfaces. One method of overcoming this problem is to introduce high-resolution albedo imagery as ancillary information for upscaling. However, due to the low frequency of updating of high-resolution albedo maps, upscaling time series of ground-based albedo measurements is difficult. This paper proposes a method that is based on the idea of conceptual universal scaling methodology for establishing a spatiotemporal trend surface using very few high-resolution images and time series of ground-based measurements for spatial-temporal upscaling of albedo. The construction of the spatiotemporal trend surface incorporates the spatial information provided by auxiliary remote sensing images and the temporal information provided by long time series of ground observations. This approach was illustrated by upscaling ground-based fine-scale albedo measurements to a coarse scale over the core study area in HiWATER. The results indicate that this method can characterize the spatiotemporal variations in surface albedo well, and the overall correlation coefficient was 0.702 during the study period.     

原子钟模型和频率稳定度分析方法

首先给出典型的原子钟时差观测量模型,包括确定性部分（时差、频差、线性频漂和周期性波动项）、随机性部分（即原子钟噪声）和观测噪声;分析了各分量对应的Allan偏差的表达式。针对部分文献对Kalman滤波器估计原子钟状态原理描述不清晰的问题,描述了原子钟随机微分方程模型和各物理量的含义,从最优估计和低通滤波器两个角度阐述其原理。针对观测噪声过大、存在周期性波动等原因造成无法准确估计原子钟噪声强度的情况,提出了综合Kalman滤波器状态估计结果和Allan偏差图,估计原子钟噪声和观测噪声强度的方法;提出了3种不同的估计线性频漂幅度的方法,并通过实测数据相互验证;针对周期性波动在时差中不明显的问题,结合原子钟随机微分方程模型,提出了综合Kalman滤波器状态估计的结果和对数Allan偏差图估计周期性波动周期和幅度的方法。对两台国产氢钟的实测数据进行了验证,证明该方法物理原理清晰,操作简便易行,具有实用性。通过该方法可以外推得到所有平滑时间的Allan偏差估计值。     

改进TS-InSAR方法的白格滑坡灾前-灾后形变演化特征分析

2018年10至11月,金沙江上游白格滑坡先后两次垮塌渡江并致堰塞湖,且至今仍存在较显著的蠕滑形变。针对时序InSAR技术在高植被发育区的应用局限,本文提出了一种改进的时序InSAR解算方法(ITSI),结合Sentinel-1A卫星2017年9月-2021年3月期间获取的SAR影像数据,针对滑坡区域分别开展了灾前和灾后时序干涉处理,提取了灾害-灾后时段内的年平均蠕滑速率场(灾前极值为9.71cm/a,灾后达到25.42cm/a)和累计蠕滑形变量(灾前极值为13cm,灾后两年内达61cm),并结合灾前-灾后形变时间序列,重点分析了蠕滑形变的时序演化特征,发现白格滑坡灾后两年间渐趋稳定。此外,监测结果发现白格滑坡上游5km处的肖莫久滑坡也处于活动状态。相关结果可为该区域防灾减灾领域研究提供参考。     

Optimizing and comparing gap-filling techniques using simulated NDVI time series from remotely sensed global data

NDVI (Normalized Difference Vegetation Index) time series usually suffer from remaining cloud presence, even after data pre-processing. To address this issue, numerous gap-filling (or reconstruction) techniques have been developed in the literature, although their comparison has mainly been local to regional, with only two global studies to date, and has led to sometimes contradictory results. This study builds on these different comparisons, by testing different parameterizations for five NDVI temporal profile reconstruction techniques, namely HANTS (Harmonic Analysis of Time Series), IDR (iterative Interpolation for Data Reconstruction), Savitzky-Golay, Asymmetric Gaussian and Double Logistic, and then comparing them as generally parameterized, and then with the best of the tested parameterizations. These comparisons show that the HANTS reconstruction technique provides lower errors in cloud prone areas, while the IDR method works best with shorter cloud covers. However, the remaining errors in cloud prone areas are still high, and there is room for new reconstruction techniques. Although these results are only applicable to the range of the tested parameterizations, these latter have been chosen within widely used configurations, and should provide interested users with a better understanding of the different methods and the best parameterization for their needs, as well as an estimate of the expected error in the reconstruction of NDVI time series.     

Using the Existing Spectral Clutter Filter With the Nonuniformly Spaced Time Series Data in Weather Radar

The National Weather Service (NWS) has a network of weather surveillance Doppler radars, WSR-88D, that is routinely upgraded to reflect current technological and engineering advances. During the last decade, the staggered pulse repetition time (SPRT) was proposed to mitigate range/velocity ambiguity in WSR-88D; however, it could not be used at lowest elevation tilts due to the inability to filter ground clutter from the nonuniformly spaced time series. A complicated spectral procedure was developed to address this issue, but the procedure was derived for a specific set of data acquisition parameters and used a lookup table to provide a value for the clutter spectrum width. Attempts to use SPRT with different sets of acquisition parameters always led to the degradation of filtering. It is proposed here that the clutter spectrum width be estimated by using Gaussian model adaptive processing (GMAP) that is currently used by NWS for uniformly sampled time series. GMAP is an adaptive ground clutter filter that performs an iterative fit of a Gaussian curve to the spectral coefficients identified as being due to ground clutter. GMAP cannot be used directly with the SPRT spectrum because of multiple clutter replicas that are due to staggered nonuniform sampling. However, the elements of GMAP can be exploited and used in the SPRT procedure. This letter presents how the elements of GMAP can be used with the SPRT data to provide successful clutter filtering at lowest elevation tilts.      

小波和傅里叶变换在坐标时间序列分析中的应用

正确提取坐标时间序列中的特征信息是非线性变化分析的前提．根据傅里叶变换和小波变换各自的特点,提出将两种方法结合起来对时间序列在时域和频域上进行分析的算法．首先采用小波函数db4对坐标时间序列分解5层得到高频和低频部分,进而分析各次谐波的时域波形以及可能存在的突变信息和区间,再在快速傅里叶变换的基础上求得各次谐波的准确频率和幅值．研究结果表明,低频分析可以直观地得到“周年项”和“两年周期项”,而高频分析能够较准确提取“半周年项”、“一季项”等短周期．与单独采用傅里叶变换或小波变换相比,基于小波变换与傅里叶变换相结合的方法能够有效地提取坐标时间序列中的特征信息,具有较高的研究价值.      

Mass evolution of Mediterranean,Black, Red,and Caspian Seas from GRACE and altimetry: accuracy assessment and solution calibration

We present new measurements of mass evolution for the Mediterranean, Black, Red, and Caspian Seas as determined by the NASA Goddard Space Flight Center (GSFC) GRACE time-variable global gravity mascon solutions. These new solutions are compared to sea surface altimetry measurements of sea level anomalies with steric corrections applied. To assess their accuracy, the GRACE- and altimetry-derived solutions are applied to the set of forward models used by GSFC for processing the GRACE Level-1B datasets, with the resulting inter-satellite range-acceleration residuals providing a useful metric for analyzing solution quality. We also present a differential correction strategy to calibrate the time series of mass change for each of the seas by establishing the strong linear relationship between differences in the forward modeled mass and the corresponding range-acceleration residuals between the two solutions. These calibrated time series of mass change are directly determined from the range-acceleration residuals, effectively providing regionally-tuned GRACE solutions without the need to form and invert normal equations. Finally, the calibrated GRACE time series are discussed and combined with the steric-corrected sea level anomalies to provide new measurements of the unmodeled steric variability for each of the seas over the span of the GRACE observation record. We apply ensemble empirical mode decomposition (EEMD) to adaptively sort the mass and steric components of sea level anomalies into seasonal, non-seasonal, and long-term temporal scales.     

黄土台塬滑坡变形的时序InSAR监测分析

黄土台塬由于经常性的农业灌溉容易造成边缘区域滑坡发育。因此,需要利用有效手段对这些潜在的滑坡隐患进行早期识别与监测。利用时间序列合成孔径雷达干涉测量（interferometric synthetic aperture radar,InSAR）技术对2016-01至2018-08期间获取的升降轨Sentinel-1数据集进行分析,获取了甘肃永靖黑方台典型台塬地区的滑坡隐患分布情况。将InSAR结果与GPS观测资料进行对比,验证了时序InSAR处理方法的有效性。对该地区滑坡的历史变形分析表明,持续的农业灌溉引起的地下水位抬升是台塬边缘坡体失稳的主要诱因。同时,InSAR时序分析发现,研究区域内的跨黄河大桥受季节更替和温度波动的影响,存在周期性变形现象。实验结果证明了时序InSAR方法在地表变形监测中的有效性,可在黄土滑坡识别与监测防治中发挥重要作用。     

A set-membership approach for high integrity height-aided satellite positioning

A Robust Set-Inversion via Interval Analysis method in a bounded-error framework is used to compute three-dimensional location zones in real time, at a given confidence level. This approach differs significantly from the usual Gaussian error model paradigm, since the satellite positions and the pseudorange measurements are represented by intervals encompassing the true value with a particular level of confidence. The method computes a location zone recursively, using contractions and bisections of an arbitrarily large initial location box. Such an approach can also handle an arbitrary number of erroneous measurements using a q-relaxed solver and allows the integration of geographic and cartographic information such as digital elevation models or three-dimensional maps. With enough data redundancy, inconsistent measurements can be detected and even rejected. The integrity risk of the location zone comes only from the measurement bounds settings, since the solver is guaranteed. A method for setting these bounds for a particular location zone confidence level is proposed. An experimental validation using real L1 code measurements and a digital elevation model is also reported in order to illustrate the performance of the method on real data.     

Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances

Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities. The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered. Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating them for each application.     

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.     

MODIS水汽反演用于InSAR大气校正的理论研究

大气效应尤其是大气水汽的影响是InSAR干涉测量中主要的误差源和限制因素之一,因此高精度的InSAR应用迫切需要及时掌握大气水汽含量及其时空变化。本文深入分析了利用MODIS的水汽反演结果进行InSAR干涉测量大气校正的可行性,对MODIS近红外水汽反演结果与地基GPS水汽探测结果进行了比较和分析。同时根据GPS解算结果,利用实例讨论了基于地面气象参数的水汽延迟模拟的效果。     

A multi-technique approach for characterizing the SVN49 signal anomaly, part 2: chip shape analysis

Due to a satellite internal reflection at the L5 test payload, the SVN49 (PRN1) GPS satellite exhibits a static multipath on the L1 and L2 signals, which results in elevation-dependent tracking errors for terrestrial receivers. Using a 30-m high-gain antenna, code and carrier phase measurements as well as raw in-phase and quadrature radio frequency samples have been collected during a series of zenith passes in mid-April 2010 to characterize the SVN49 multipath and its impact on common users. Following an analysis of the receiver tracking data and the IQ constellation provided in Part 1 of this study, the present Part 2 provides an in-depth investigation into chip shapes for the L1 and L2 signals. A single reflection model is found to be compatible with the observed chip shape distortions and key parameters for an elevation dependent multipath model are derived. A good agreement is found between multipath parameters derived independently from raw IQ-samples and measurements of a so-called Vision Correlator. The chip shapes and their observed variation with elevation can be used to predict the multipath response of different correlator types within a tracking receiver. The multipath model itself is suitable for implementation in a signal simulator and thus enables laboratory testing of actual receiver hardware.     

全波形激光雷达回波分解方法

全波形激光雷达的回波中携带了被测目标的距离与特征信息,为了获取这些信息,本文提出了一种回波分解方法。本方法将原始的全波形回波分解为几个独立的高斯脉冲,并得到其函数表达式,从而提取出被测目标的距离等信息。分解过程中,首先,采用可变阈值的经验模态分解滤波法(EMD-soft)对原始波形进行滤波和噪声水平评估;其次,采用一套应对多种波形组成的初始参数估计方法,获取后续拟合所需的初始参数;最后,采用LM(Levenberg-Marquardt)优化算法对回波进行拟合优化,从而获取全波形回波中包含的独立高斯脉冲及其函数表达式。仿真波形的分解实验表明,分解误差在0.1 ns量级,换算成距离误差为15 mm,通过实验室自制的全波形激光雷达实验系统获取的回波的分解实验表明,分解的距离误差小于0.1 m。对比另外两种高斯分解方法对于相同仿真与实验数据的分解结果可以看出,本方法在分解成功率与精度上都有较大的提高。回波分解后的独立高斯脉冲中,除距离外还含有被测目标的反射率、粗糙度、面型等丰富的信息,回波分解方法作为回波分析的基础,将在遥感、测绘等生产与科研领域中发挥非常重要的作用。     

On the improvements of the single point positioning accuracy with Locata technology

This work focuses on the performances of Locata technology in single point positioning using different firmware versions (v2.0 and v4.2). The main difference is that the Locata transmitters with firmware v2.0 are single frequency, whereas in the v4.2, they are dual frequency. The performance of the different firmware versions has been measured in different environments including an urban canyon-like environment and a more open environment on the roof of the Nottingham Geospatial Building. The results obtained with firmware v4.2 show that with more available signals, cycle slips can be more easily detected, together with the improvement of the detection of multipath fading on the received signal. As a result, the noise level on the carrier phase measurements recorded with firmware v4.2 is equal on average to a third of the level of noise on the measurements recorded with firmware v2.0. In addition, with either firmware, the accuracy of the position is at the sub-centimeter level on the East and North coordinates. The Up coordinate accuracy is generally less accurate and more sensitive to the geometry of the network in our experiments. We then show the importance of the geometry of the Locata network on the accuracy of Locata positioning system through the demonstration of the relationship between the dilution of precision value and the confidence ellipse. We also demonstrate that the model of the noise on the Locata coordinates is a white Gaussian noise with the help of the autocorrelation function. To some extent, this technique can help to detect whether the Wi-Fi technology is interfering with the Locata technology and degrades the positioning accuracy.     

Improvement of edge effect of the wavelet time–frequency spectrum: application to the length-of-day series

 The edge effect in the wavelet time–frequency spectrum of a time series is treated. The time series is first extended on both ends by applying a non-linear model, namely the leap-step time series analysis (LSTSA) model, prior to the wavelet transform. The results of a series of simulation experiments and an application to the observed length-of-day (LOD) series demonstrate that the edge effect is effectively reduced this way. Thus, the application of the LSTSA model improves the wavelet time–frequency spectrum, especially enhancing the ability to detect the low-frequency signals. Received: 15 September 1998 / Accepted: 4 October 1999