各向异性组合滤波法反演陆地水储量变化

地球时变重力场模型反演陆地水储量变化已为全球气候变化研究作出巨大贡献,考虑到时变重力场模型球谐系数中存在相关性,其高阶次项具有较大的误差,需采用最优的滤波方法进行空间平滑。本文提出一种新的各向异性组合滤波方法,其基本思想是将改进的高斯滤波法与均方根(root mean square,RMS)滤波法组合,即对球谐系数的低阶次采用改进的高斯滤波法,而高阶次采用RMS滤波法。首先分析了最新的GRACE RL05系列时变重力场模型系数误差特性,基于全球水储量变化反演结果,分析比较了高斯滤波、改进的高斯滤波、RMS滤波和DDK滤波与本文提出的组合滤波法的有效性及精度,并利用模型结果进行了验证,计算结果表明,组合滤波法的中误差最小。研究结果表明,本文提出的组合法相比于先前的滤波方法,可有效地过滤高阶次的噪声,消除南北条带误差,同时减少信号泄漏,提高信噪比,保留更多有效的地球物理信号,进而提高反演精度。     

GRACE时变重力场滤波方法

针对GRACE时变重力场模型高阶项误差较大导致的"南-北"条带噪声,该文利用模拟的GRACE数据分析了去相关滤波、Gaussian滤波、组合滤波和平滑先验信息滤波方法对噪声的滤除效果和对真实信号的衰减程度。实验表明:4种滤波算法均能有效降低条带噪声,但单独使用去相关滤波时效果较差,需与其他算法结合使用;Guass滤波和组合滤波在减小噪声条带的同时,也在一定程度上牺牲了空间分辨率;平滑先验信息滤波在移除噪声、保留有效信号方面比其他3种算法有较为明显的优势。     

利用GRACE RL05模型监测长江流域水储量变化

本文基于GRACE最新重力场模型RL05序列研究了高斯滤波、Wiener滤波、各向异性滤波三种方法在长江流域水储量变化监测中的适用性,计算了应用三种方法得到的水储量变化速率。通过与长江流域水文模型的比较,高斯滤波平滑半径为430km时所得的结果与Wiener滤波基本一致,但各向异性滤波反演的结果与水文模型更为接近,并且优于前面两种方法。研究结果表明GRACE RL05时变重力场球谐系数误差存在各向异性的分布特征,因此各向异性滤波更适用于GRACE区域水储量变化的研究。     

多通道奇异谱组合滤波反演水储量变化

针对GRACE时变重力场球谐系数的高阶次项中含有的较高噪声会造成反潢结果产生误差的问题,该文采用多通道奇异谱分析和高斯滤波相结合的方案来滤除GRACE数据中的噪声,并与普遍使用的去相关滤波和高斯滤波相结合的方案进行了对比验证。首先利用这两种方法分别计算了2007年4、10月份的全球水储量变化,结果显示,这两种方法反演的结果基本相同,而多通道奇异谱分析与高斯滤波相组合的方法提高了信噪比,减弱了信号泄露误差,验证了该组合方案的可行性。然后又分别计算了亚马逊流域2004—2010年的水储量时间变化序列,并与GLDAS水文模型进行了对比验证,结果显示,这两种方法得到的水储量时间序列变化趋势基本相同,各自之间具有强相关性,进一步说明了该文方案在GRACE数据滤波中的可行性。     

GRACERL05反演南极冰盖质量变化方法比较

利用UTCSR发布的2003-01~2013-07GRACE RL05月平均重力场模型,分析比较了高斯滤波、各向异性滤波、扇形滤波和维纳滤波,并结合去相关滤波在反演南极地区冰盖质量变化方面的差异。通过计算得到以下结论:1基于121组重力场模型阶方差分布得到维纳滤波与半径为300km的高斯滤波效果最为接近,说明300km滤波半径完全可以满足质量变化信号的提取;2在一定范围内,提高滤波半径能提高反演结果信噪比,建议南极区域的滤波半径为500km;采用相同滤波半径,不同空间滤波算法计算的质量变化率基本一致,在南极区域可以选取任一滤波方法;3与其他算法相比,去相关滤波算法能在一定程度消除球谐系数中存在的系统误差,改善反演结果。     

GRACE时变重力位系数扇形滤波算法分析

卫星重力探测技术为监测全球陆地水储量变化提供了新的技术手段。采用Level-2 Release-05版本GRACE时变重力场模型数据计算了2010年全球陆地水储量的月变化;着重研究了扇形滤波对反演结果的影响;并结合GLDAS水文模型数据对反演结果进行了验证分析。实验结果表明:GRACE反演结果 GLDAS水文模型结果在时空分布上符合较好;扇形滤波能够削弱GRACE时变重力场模型的高阶项误差影响,有效去除反演结果中的条带状噪声。     

GRACE Level-2数据的RTS状态平滑EI北大核心CSCD

GRACE Level-2球谐系数反演得到的全球地表质量变化存在明显的南北条带噪声，严重影响区域地表质量异常估计的精度。DDK滤波引入信号协方差矩阵和正则化因子，能较好地削弱条带误差，同时保留更多的真实信号。采用状态空间模型表示球谐系数在相邻月份之间的联系，进而通过卡尔曼滤波实现去条带，即为状态空间DDK滤波方法(SS-DDK)。本文提出的SS-DDK方法状态向量只包含球谐系数，反映条带误差统计信息的协方差矩阵被用作状态空间模型中观测噪声协方差矩阵，采用幂律模型设计过程噪声协方差矩阵，通过迭代法求解方差分量因子，最后输出RTS平滑解代替卡尔曼滤波解作为最终数据处理结果。结果表明，在全球范围内，SS-DDK结果不存在明显的条带误差；计算各约束解与mascon解质量异常差异的均方根(RMSD),SS-DDK的RMSD为10.36 cm,小于任意一种DDK滤波。对比五大区域135个月所有约束解的等效水柱高、年振幅及RMSD发现，在格陵兰岛，SS-DDK所导致的信号失真更少，仅为49.8 cm;在其他区域，SS-DDK的去条带和保留信号的能力与DDK3—5滤波有不同程度的相似，在某些时段优于所有DDK滤波。对估计结果进行不确定性分析，SS-DDK解全球的不确定性大小为2.20 cm,其在所选区域的不确定性大小介于DDK2和DDK3之间。对比大地水准面阶误差的结果说明，SS-DDK解的噪声水平低于DDK4—8,保留信号能力与DDK2—3相当。增添仿真试验进一步说明SS-DDK在去条带和保留信号方面具有较好的性能。     

GRACE时变重力位系数误差的改进去相关算法

GRACE卫星时变重力场模型的高阶位系数存在较大误差,用它反演的重力场结果中表现为严重的条带噪声。Swenson提出的滑动窗多项式拟合去相关误差方法在赤道两侧区域取得了显著效果,但其在文献中并没有说明实现的具体步骤,因而许多学者在利用其思想进行滤波时并没有达到其文献中的滤波效果。针对滑动窗的特点,使用反向边界延拓技术,对滑动窗去相关误差数据处理方法作了改进。改进的滑动窗去相关误差方法应用于GRACE时变重力场模型时,在赤道两侧区域取得了显著的去条带误差效果,并利用全球地面资料同化系统GLDAS土壤湿度资料验证该方法的正确性。     

GRACE时变重力场的滤波理论及质量变化分析

正由于GRACE(gravity recovery and climate experiment)时变重力场模型直接解算质量变化时存在较大的误差,需要对其进行相应的滤波处理,提高质量变化的反演精度。本文总结了GRACE监测全球与区域质量变化的研究进展,分析了最新时变重力场模型的精度及其滤波方法;提出了基于重力位系数协方差阵的时变重力场滤波方法;分析了南极冰盖的质量变化、亚马孙流域陆地水质量和海平面变化。本文的研究成果及创新点主要包括以下几个方面:     

一种新的去除遥感影像混合噪声组合滤波方法

提出了一种三层组合滤波的去噪方法,在小波BayesShrink阈值与自适应中值滤波的基础上增加第三层Wiener滤波,利用Wiener滤波对信噪比高的信号去噪效果好的特点可有效去除残留的混合噪声,为了在去噪过程中保留影像的边缘,在滤波过程中加入了边缘提取算法,对影像的细节进行保留使去噪后的影像更加清晰。试验表明,本文提出的三层滤波方法在去除遥感影像常见的高斯与脉冲混合噪声时,效果要明显优于传统的两层组合滤波算法。     

Localized spectral analysis of global satellite gravity fields for recovering time-variable mass redistributions

A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water storage variation by GOCE gradiometer is equivocal even after localization.     

Space-wise approach to satellite gravity field determination in the presence of coloured noise

For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed.     

Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models

We discuss a new method for approximately decorrelating and non-isotropically filtering the monthly gravity fields provided by the gravity recovery and climate experiment (GRACE) twin-satellite mission. The procedure is more efficient than conventional Gaussian-type isotropic filters in reducing stripes and spurious patterns, while retaining the signal magnitudes. One of the problems that users of GRACE level 2 monthly gravity field solutions fight is the effect of increasing noise in higher frequencies. Simply truncating the spherical harmonic solution at low degrees causes the loss of a significant portion of signal, which is not an option if one is interested in geophysical phenomena on a scale of few hundred to few thousand km. The common approach is to filter the published solutions, that is to convolve them with an isotropic kernel that allows an interpretation as smoothed averaging. The downside of this approach is an amplitude bias and the fact that it neither accounts for the variable data density that increases towards the poles where the orbits converge nor for the anisotropic error correlation structure that the solutions exhibit. Here a relatively simple regularization procedure will be outlined, which allows one to take the latter two effects into account, on the basis of published level 2 products. This leads to a series of approximate decorrelation transformations applied to the monthly solutions, which enable a successive smoothing to reduce the noise in the higher frequencies. This smoothing effect may be used to generate solutions that behave, on average over all possible directions, very close to Gaussian-type filtered ones. The localizing and smoothing properties of our non-isotropic kernels are compared with Gaussian kernels in terms of the kernel variance and the resulting amplitude bias for a standard signal. Examples involving real GRACE level 2 fields as well as geophysical models are used to demonstrate the techniques. With the new method, we find that the characteristic striping pattern in the GRACE solutions are much more reduced than Gaussian-filtered solutions of comparable signal amplitude and root mean square.     

欧洲地区共模误差提取及分析

针对跨度较长时间序列共模误差噪声特征研究较少,选择空间滤波的方法对较长时间序列进行分析以满足参考框架建立的需要。选取欧洲地区58个IGS基准站2001—2011年的坐标时间序列,采用区域叠加滤波法、分区区域叠加滤波法和相关系数加权叠加滤波法求取共模误差,并以滤波后时间序列相关系数和残差时间序列标准差为标准对其进行对比分析;进而,利用极大似然估计的方法对每个区域共模误差及滤波前后坐标时间序列进行噪声分析。结果表明:分区区域叠加滤波法最适合欧洲地区共模误差的提取;共模误差主要成分是闪烁噪声,也包含白噪声、随机漫步噪声等;当时间序列长度较长时,N、E方向受共模误差影响较小,可忽略,U方向受共模误差影响较大,需要考虑。     

Spherical harmonic analysis,aliasing, and filtering

The currently practiced methods of harmonic analysis on the sphere are studied with respect to aliasing and filtering. It is assumed that a function is sampled on a regular grid of latitudes and longitudes. Then, transformations to and from the Cartesian plane yield formulations of the aliasing error in terms of spherical harmonic coefficients. The following results are obtained: 1) The simple quadratures method and related methods are biased even with band-limited functions. 2) A new method that eliminates this bias is superior to Colombo's method of least squares in terms of reducing aliasing. 3) But, a simple modification of the least-squares model makes it identical to the new method as one is the dual of the other. 4) The essential elimination of aliasing can only be effected with spherical cap averages, not with the often used constant angular block averages.     

卫星激光测距技术滤波方法的研究与实现

本文从激光测距回波方程及噪声方程出发阐明了降低背景噪声(滤波)是提高激光测距回波信噪比的关键;并通过对望远镜轴系进行指向修正并采用可变光阑减小望远镜视场来实现"空间滤波",采用窄带滤光片实现"光谱滤波",采用高精度距离门选通技术实现"时间滤波",北京房山人卫观测站的激光测距系统具备了白天观测人造地球卫星的能力。本文还引入了C-SPAD"敏感度"的概念并且提出了一种依靠C-SPAD来调整可变光阑位置及滤光片角度的方法。     

Outlier detection algorithms and their performance in GOCE gravity field processing

The satellite missions CHAMP, GRACE, and GOCE mark the beginning of a new era in gravity field determination and modeling. They provide unique models of the global stationary gravity field and its variation in time. Due to inevitable measurement errors, sophisticated pre-processing steps have to be applied before further use of the satellite measurements. In the framework of the GOCE mission, this includes outlier detection, absolute calibration and validation of the SGG (satellite gravity gradiometry) measurements, and removal of temporal effects. In general, outliers are defined as observations that appear to be inconsistent with the remainder of the data set. One goal is to evaluate the effect of additive, innovative and bulk outliers on the estimates of the spherical harmonic coefficients. It can be shown that even a small number of undetected outliers (<0.2 of all data points) can have an adverse effect on the coefficient estimates. Consequently, concepts for the identification and removal of outliers have to be developed. Novel outlier detection algorithms are derived and statistical methods are presented that may be used for this purpose. The methods aim at high outlier identification rates as well as small failure rates. A combined algorithm, based on wavelets and a statistical method, shows best performance with an identification rate of about 99%. To further reduce the influence of undetected outliers, an outlier detection algorithm is implemented inside the gravity field solver (the Quick-Look Gravity Field Analysis tool was used). This results in spherical harmonic coefficient estimates that are of similar quality to those obtained without outliers in the input data.