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1.
The performance of the L-curve criterion and of the generalized cross-validation (GCV) method for the Tikhonov regularization
of the ill-conditioned normal equations associated with the determination of the gravity field from satellite gravity gradiometry
is investigated. Special attention is devoted to the computation of the corner point of the L-curve, to the numerically efficient
computation of the trace term in the GCV target function, and to the choice of the norm of the residuals, which is important
for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) in the presence of colored observation noise. The
trace term in the GCV target function is estimated using an unbiased minimum-variance stochastic estimator. The performance
analysis is based on a simulation of gravity gradients along a 60-day repeat circular orbit and a gravity field recovery complete
up to degree and order 300. Randomized GCV yields the optimal regularization parameter in all the simulations if the colored
noise is properly taken into account. Moreover, it seems to be quite robust against the choice of the norm of the residuals.
It performs much better than the L-curve criterion, which always yields over-smooth solutions. The numerical costs for randomized
GCV are limited provided that a reasonable first guess of the regularization parameter can be found.
Received: 17 May 2001 / Accepted: 17 January 2002 相似文献
2.
针对传统点质量方法在融合处理多源重力数据过程中可能出现的病态性问题,特别引入Tikhonov正则化方法,对点质量法计算模型进行正则化改造,建立了相应的正则化点质量解算模型。使用EGM2008位模型模拟产生航空重力和海面船测重力数据进行了融合处理仿真试验。实际验证结果表明,正则化处理方法能够有效抑制病态系数矩阵小奇异值放大噪声对点质量解的污染,提高解算结果的精度和稳定性。 相似文献
3.
Tikhonov正则化法是大地测量中应用最为广泛的病态问题解算方法之一。影响正则化法解算效果的重要因素是正则化参数,然而,最优正则化参数的确定一直是正则化解算的难题,如L曲线法确定的正则化参数具有稳定性好、可靠性高的优点,但存在过度平滑问题,导致正则化法对模型参数估值精度改善较小。本文从均方误差角度分析了正则化参数对模型参数估计质量的影响。基于奇异值分解技术,提出了由模型参数投影值分块计算均方误差的方法,避免了均方误差迭代计算,并基于均方误差最小准则给出了正则化参数优化方法,实现了对L曲线正则化参数的优化。数值模拟试验与PolInSAR植被高反演试验结果表明,正则化参数优化方法有效改善了正则化法解算效果,提高了模型参数估计精度。 相似文献
4.
Tikhonov正则化方法在GOCE重力场求解中的模拟研究 总被引：6，自引：4，他引：2
本文在阐述Tikhonov正则化方法基本原理的基础上,给出了四类可用于重力场解算的正则化矩阵(零次、一次、二次和Kaula),以及用于确定正则化参数的L曲线法和GCV方法的数学模型。基于SA方法利用模拟数据分析讨论了零次、一次以及Kaula正则化矩阵应用于GOCE全球重力场模型确定的有效性,并由Kaula正则化矩阵分析了L曲线法和GCV方法确定正则化参数的可行性。数值结果表明三类正则化矩阵获得的最优解(以大地水准面MSE最小为准则确定)的精度水平相近,关键在于相应正则化参数的确定,数值结果同时说明了GCV方法和L曲线法可用于确定正则化参数,且前者较后者具有更好的稳定性。 相似文献
5.
欧空局早期公布的时域法和空域法解算的GOCE模型均采用能量守恒法处理轨道数据, 但恢复的长波重力场信号精度较低, 而且GOCE卫星在两极存在数据空白, 利用其观测数据恢复重力场模型是一个不适定问题, 导致解算的模型带谐项精度较低, 需进行正则化处理。本文分析了基于轨道数据恢复重力场模型的方法用于处理GOCE数据的精度, 对最优正则化方法和参数的选择进行研究。利用GOCE卫星2009-11-01—2010-01-31共92 d的精密轨道数据, 采用不依赖先验信息的能量守恒法、短弧积分法和平均加速度法恢复GOCE重力场模型, 利用Tikhonov正则化技术处理病态问题。结果表明, 平均加速度法恢复模型的精度最高, 能量守恒法的精度最低, 短弧积分法的精度稍差于平均加速度法。未来联合处理轨道和梯度数据时, 建议采用平均加速度法或短弧积分法处理轨道数据, 并且轨道数据可有效恢复120阶次左右的模型。Kaula正则化和SOT处理GOCE病态问题的效果最好, 并且两者对应的最优正则化参数基本一致, 但利用正则化技术不能完全抑制极空白问题的影响, 需要联合GRACE等其他数据才能获得理想的结果。 相似文献
6.
研究了反演区域陆地水储量变化的点质量模型方法,采用Tikhonov正则化方法解决了反演过程中参数估计病态问题。利用GRACE（gravity recovery and climate experiment）时变重力场模型数据,用点质量模型方法反演了中国大陆及其周边地区陆地水储量变化,将点质量模型反演结果与球谐系数法反演结果、GLDAS（global land data assimilation）水文模型数据进行了验证分析,并选取了4个特征点计算了陆地水储量变化时间序列。实验结果表明,由于点质量模型方法将研究区域内不同网格质量变化对地球重力场的影响分离开来,所得区域陆地水储量变化局部信号更明显,并且点质量模型方法反演结果与GLDAS水文模型数据相关性更强。 相似文献
7.
Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models 总被引：6，自引：1，他引：6
Jürgen Kusche 《Journal of Geodesy》2007,81(11):733-749
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. 相似文献
8.
Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACE monthly solutions using an improved mascon approach 总被引：1，自引：0，他引：1
We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35–69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24–47%. 相似文献
9.
On the postprocessing removal of correlated errors in GRACE temporal gravity field solutions 总被引：9，自引：2，他引：7
We revisit the empirical moving window filtering method of Swenson and Wahr (Geophys Res Lett 33:L08402, 2006) and its variants,
Chambers (Geophys Res Lett 33:L17603, 2006) and Chen et al. (Geophys Res Lett 34: L13302, 2007), for reducing the correlated
errors in the Stokes coefficients (SCs) of the spherical harmonic expansion of the GRACE determined monthly geopotential solutions.
Based on a comparison of the three published approaches mentioned, we propose a refined approach for choosing parameters of
the decorrelation filter. Our approach is based on the error pattern of the SCs in the monthly GRACE geopotential solutions.
We keep a portion of the lower degree-order SCs with the smallest errors unchanged, and high-pass filter the rest using a
moving window technique, with window width decreasing as the error of the SCs increases. Both the unchanged portion of SCs
and the window width conform with the error pattern, and are adjustable with a parameter. Compared to the three published
approaches mentioned, our unchanged portion of SCs and window width depend on both degree and order in a more complex way.
We have used the trend of mass change to test various parameters toward a preferred choice for a global compromise between
the removal of the correlated errors and the minimization of signal distortion. 相似文献
10.
Targeting the multicollinearity problem in dam statistical model and error perturbations resulting from the monitoring process,we built a regularized regression model using Truncated Singular Value Decomposition(TSVD).An earth-rock dam in China is presented and discussed as an example.The analysis consists of three steps:multicollinearity detection,regularization pa-rameter selection,and crack opening modeling and forecasting.Generalized Cross-Validation(GCV) function and L-curve criterion are both adopted in the regularization parameter selection.Partial Least-Squares Regression(PLSR) and stepwise regression are also included for comparison.The result indicates the TSVD can promisingly solve the multicollinearity problem of dam regression models.However,no general rules are available to make a decision when TSVD is superior to stepwise regression and PLSR due to the regularization parameter-choice problem.Both fitting accuracy and coefficients’ reasonability should be considered when evaluating the model reliability. 相似文献
11.
A special class of regularization methods for satellite gravity gradiometry based on Tikhonov spherical regularization wavelets
is considered, with particular emphasis on the case of data blurred by random noise. A convergence rate is proved for the
regularized solution, and a method is discussed for choosing the regularization level a posteriori from the gradiometer data.
Received: 23 March 2000 / Accepted: 20 September 2000 相似文献
12.
针对短基线集形变模型反演中法方程系数矩阵呈病态的问题,提出一种正则化稳健解算方法。该方法基于Tikhonov正则化理论,将形变速率求解问题转化为极小化问题,根据L-曲线法选取正则化参数,考虑最小二乘残差各个分量间的关系选取正则化矩阵,实现短基线集形变模型反演的稳健解算。分别采用LS法、岭估计法和Tikhonov正则化法对覆盖北京地区的29景ENVISAT ASAR数据进行处理,反演出研究区沉降速率图。通过对代表不同沉降情况的21个点的均方误差值和时间相干值、整个研究区的均方误差图等的对比分析,表明本文提出的短基线集形变模型反演的正则化稳健解算方法可获取更可靠的形变监测结果。 相似文献
13.
各向异性组合滤波法反演陆地水储量变化 总被引：2，自引：1，他引：1
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。 相似文献
14.
海洋磁力测量中,由于受到海流等因素的影响导致磁力仪传感器（拖鱼）的入水深度起伏变化,测得的海洋磁场数据并不在固定的平面上。为了满足不同用户对海洋磁场数据的应用需求,必须采取合理的“曲化平”,实现整个测区磁场数据垂直空间上的统一。针对位场曲面延拓积分方程的迭代解中高阶垂向导数对高频噪声的放大问题,尝试引入Tikhonov正则化方法对其进行改进,以抑制高频噪声的影响。仿真分析表明,在选择合适的正则化参数后,改进的延拓方法可将延拓精度提高1.6 nT。实测数据分析表明,采用改进曲面延拓迭代方法,将磁测成果数据归算到曲面最低平面时,归算后交叉点磁异常不符值精度可提高2 nT,进一步验证了海洋磁力测量数据垂直空间归算的必要性。 相似文献
15.
16.
针对铁磁性物质反演中正则化参数自适应选择的问题,提出了基于χ2准则的磁梯度张量3D聚焦反演方法。利用深度加权矩阵和最小支撑矩阵对经典Tikhonov正则化理论框架下的反演模型进行约束得到目标函数,避免了由于反演参数多于采集点数而导致反演解的多解性,并有效解决了核函数随深度增大而快速衰减的问题。通过对目标函数进行迭代奇异值分解获得最佳物性参数,并根据χ2准则自适应地确定目标函数在迭代过程中的正则化参数,提高了迭代速度和求解精度。仿真和实验结果表明:该方法能准确还原磁性异常体的轮廓形态,具有较好的模型分辨率。 相似文献
17.
一种解算病态问题的方法--两步解法 总被引：10，自引：0，他引：10
提出了一种解算病态问题的方法———两步解法。在两步计算中,均采用L曲线法来确定正则化参数α。通过算例,比较了该方法和LS估计、岭估计及截断奇异值方法的效果。结果表明,该方法要明显优于LS估计、岭估计及截断奇异值法。 相似文献
18.
Multiple Parameter Regularization: Numerical Solutions and Applications to the Determination of Geopotential from Precise Satellite Orbits 总被引：1，自引：0，他引：1
Kaula’s rule of thumb has been used in producing geopotential models from space geodetic measurements, including the most recent models from satellite gravity missions CHAMP. Although Xu and Rummel (Manuscr Geod 20 8–20, 1994b) suggested an alternative regularization method by introducing a number of regularization parameters, no numerical tests have ever been conducted. We have compared four methods of regularization for the determination of geopotential from precise orbits of COSMIC satellites through simulations, which include Kaula’s rule of thumb, one parameter regularization and its iterative version, and multiple parameter regularization. The simulation results show that the four methods can indeed produce good gravitational models from the precise orbits of centimetre level. The three regularization methods perform much better than Kaula’s rule of thumb by a factor of 6.4 on average beyond spherical harmonic degree 5 and by a factor of 10.2 for the spherical harmonic degrees from 8 to 14 in terms of degree variations of root mean squared errors. The maximum componentwise improvement in the root mean squared error can be up to a factor of 60. The simplest version of regularization by multiplying a positive scalar with a unit matrix is sufficient to better determine the geopotential model. Although multiple parameter regularization is theoretically attractive and can indeed eliminate unnecessary regularization for some of the harmonic coefficients, we found that it only improved its one parameter version marginally in this COSMIC example in terms of the mean squared error. 相似文献
19.
针对GRACE月时变重力场的离散球谐系数,提出联合经验正交函数分解和多通道奇异谱分析的方法,在有效实现空间维数压缩和条带噪声去除的同时,提取、分析其动态变化特征并构建相应的变化模型。结果表明,GRACE离散球谐系数存在显著的周年项和长期趋势项变化成分,其中,周年项模态的方差贡献达到50.6%,扣除周年项成分后长期趋势项的累积方差贡献达到77.4%。以长期趋势项和周年项成分构建的非线性模型能较好地反映离散球谐系数及其反演结果的动态变化特征,其对全球陆表等效水柱高的拟合标准差介于0.3~14.0 cm,平均标准差为1.8 cm。研究结果可为分析地球重力场各参量变化特征及地球动力学变化提供重要参考。 相似文献
20.
航空重力向下延拓病态问题的求解 总被引：1，自引：0，他引：1
提出将广义岭估计用于求解航空重力向下延拓病态问题,研究了求解逆Poisson积分问题的3种正则化方法：Tikhonov正则化、岭估计和广义岭估计。利用EGM2008地球位模型设计模拟数值实验,将飞行高度处含白噪声的2.5′×2.5′重力扰动向下延拓至大地水准面上,与参考值作外部检验,全面检验、比较了各向下延拓方法的可靠性、精度和稳定性,数值结果表明基于多个最优正则化参数的广义岭估计在延拓精度、稳定性和抗差性等方面要显著优于基于单个正则化参数的Tikhonov法和岭估计。 相似文献