共查询到20条相似文献，搜索用时 265 毫秒
1.
The two-temperature method (TTM) allows the separation of land-surface temperature and land-surface emissivity information from radiance measurements, and therefore, the solution can be uniquely determined by the data. However, the inverse problem is still an ill-posed problem, since the solution does not depend continuously on the data. Accordingly, we have used some mathematical tools, which are suited for analyses of ill-posed problems in order to show TTM properties, evaluate it, and optimize its estimations. Related to this last point, we have shown that it is necessary to constrain the problem, either by defining a region of physically admissible solutions and/or by using regularization methods, in order to obtain stable results. Besides, the results may be improved by using TTM with systems that possess a high temporal resolution, as well as by acquiring observations near the maximum and minimum of the diurnal temperature range. 相似文献
2.
用于GPS姿态确定的矢量化算法可等价于两级最优问题。第一级把GPS载波相位观测量转换为矢量观测量。第二级是Wahba问题,即从矢量观测量获得最佳姿态解。Wahba问题可用四元数法求解,如QUEST方法。本文采用基于小角度的迭代法求解Wahba问题。在均衡星座或均衡基线务件下,两级最优解亦是全局最优解。实验结果表明迭代解的精度与QUEST解相同。实验中也应用了改进的TRIAD算法以比较两级最优解。 相似文献
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Mudanyal O. Yldz S. Semerci O. Yapar A. Akduman I. 《Geoscience and Remote Sensing Letters, IEEE》2008,5(2):180-184
A microwave imaging method for nondestructive testing of perfectly conducting surfaces beyond a layered media is presented. The method is an adaptation of the surface reconstruction approach by Yapar et al. to the present problem. It is based on the analytical continuation of the measured data to the surface under test through a special representation of the scattered field in terms of Fourier transform and Taylor expansion. Then the problem is reduced to the solution of a nonlinear equation which is solved iteratively via the Newton method and regularization in the least squares sense. Numerical simulations show that defects as small as lambda/500 can be recovered through the presented algorithm. 相似文献
4.
基于虚拟观测的病态问题解法 总被引：2，自引：0，他引：2
在大地测量数据处理领域中,处理病态问题的主要方法有:岭估计方法、奇异值分解法(SVD)、Tik-honov正则化方法等,但是这些方法大多数是强调数学上的意义,没有充分联系大地测量的实际情况,因此不利于在测绘领域病态问题本质的理解和研究。为使病态问题的求解具有实际的物理意义,提出了基于虚拟观测的岭估计方法。该方法将先验约束条件作为一类互相独立的虚拟观测值,从而把病态问题转化为测量平差问题,然后运用Helmert方差估计法来确定岭参数。该方法还可以得到的参数之间的权矩阵,用它来代替虚拟观测值的权矩阵,重新对参数进行计算,则实现了该方法向广义岭估计的推广。实际算例分析的结果表明该方法不仅计算简单而且能保证结果精确。 相似文献
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Qingbiao Fan Caijun Xu Lei Yi Yang Liu Yangmao Wen Zhi Yin 《Journal of Geodesy》2017,91(10):1163-1177
When ill-posed problems are inverted, the regularization process is equivalent to adding constraint equations or prior information from a Bayesian perspective. The veracity of the constraints (or the regularization matrix R) significantly affects the solution, and a smoothness constraint is usually added in seismic slip inversions. In this paper, an adaptive smoothness constraint (ASC) based on the classic Laplacian smoothness constraint (LSC) is proposed. The ASC not only improves the smoothness constraint, but also helps constrain the slip direction. A series of experiments are conducted in which different magnitudes of noise are imposed and different densities of observation are assumed, and the results indicated that the ASC was superior to the LSC. Using the proposed ASC, the Helmert variance component estimation method is highlighted as the best for selecting the regularization parameter compared with other methods, such as generalized cross-validation or the mean squared error criterion method. The ASC may also benefit other ill-posed problems in which a smoothness constraint is required. 相似文献
7.
The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE. 相似文献
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用遗传算法搜索GPS单频单历元整周模糊度 总被引：10，自引：2，他引：10
介绍了短基线利用单频单历元双差载波相位定位时模糊度固定的基本理论，探讨了利用遗传算法快速搜索GPS单频单历元整周模糊度的一些理论和实现的方法．提出了用改进的正则化方法改善浮动解来提高搜索成功率的新思路。算例分析表明，在一定的条件下．应用遗传算法搜索整周模糊度成功率高、稳键性较好。 相似文献
10.
均方误差意义下正则化解优于最小二乘解的条件 总被引：3，自引：0，他引：3
利用矩阵理论导出了均方误差意义下正则化解优于最小二乘解的条件，构造了相应的检验统计量，推导出的条件式及其相应的假设检验适合于各种正则化矩阵类型的Tikhonov正则化方法。 相似文献
11.
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
12.
A. C. Campbell 《Journal of Geodesy》1968,42(3):293-300
Recent accuracy requirements for navigational positioning at sea are such as to require the refinements of recent and past
geodetic methods. The computational adjustment method, of this paper, is the technique of variation of parameters. All computations
are performed directly on the surface of a reference ellipsoid, so as to preclude any distance restrictions.
The methods presented are primarily for use with observations from electronic positioning systems of ranging (circular), and
time or phase difference (hyperbolic) type. A new type of observation equation is presented which, when used with a hyperbolic
system, results in the first non-iterative solution to the positioning problem.
When redundant observational data is obtained, as is frequently the case, full use should be made of the data by using weighted
observation equations. Through the use of the new equations, all electronic surveying observations can be processed simultaneously,
in real time, with an electronic computer. A continuing error analysis, in the form of a variance-covariance matrix for both
the observed and adjusted values, provides system error analysis and diagnoisis. 相似文献
13.
平差不适定问题解性质与正则参数的确定方法 总被引：10，自引：6，他引：4
对于测量平差不适定问题的求解问题,大都可归结Tikhonov正则准则下的极值问题,而正则参数求解又至关重要。本文在讨论其解性质的基础上,归纳与总结了不适定问题正则参数的几种确定方法,通过两个算例对几种方法进行了综合分析与比较,指出了其方法的适用性及特点。 相似文献
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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
15.
Variance Component Estimation in Linear Inverse Ill-posed Models 总被引：2，自引：4，他引：2
Regularization has been applied by implicitly assuming that the weight matrix of measurements is known. If measurements are assumed to be heteroscedastic with different unknown variance components, all regularization techniques may not be proper to apply, unless techniques of variance component estimation are directly implemented. Although variance component estimation techniques have been proposed to simultaneously estimate the variance components and provide a means of regularization, the regularization parameter is treated as if it were also an extra variance component. In this paper, we assume no prior information on the model parameters and do not treat the regularization parameter as an extra variance component. Instead, we first analyze the biases of estimated variance components due to the regularization parameter and then propose bias-corrected variance component estimators. The results have shown that they work very well. Finally, we propose and investigate through simulations an iterative scheme to simultaneously estimate the variance components and the regularization parameter, in order to eliminate the effect of regularization parameter on variance components and the effect of incorrect prior weights or initial variance components on the regularization parameter. 相似文献
16.
Analytical optimization of a DInSAR and GPS dataset for derivation of three-dimensional surface motion 总被引：2，自引：0，他引：2
A revised method for derivation of three-dimensional surface motions maps from sparse global positioning system (GPS) measurements and two differential interferometric synthetic aperture radar (DInSAR) interferograms based on a random field theory and Gibbs-Markov random fields equivalency within Bayesian statistical framework is proposed. It is shown that the Gibbs energy function can be optimized analytically in the absence of a neighboring relationship between sites of a regular lattice. Because the problem is well posed, its solution is unique and stable, and additional regularization in the form of smoothness is not required. The proposed algorithm is simple in realization, does not require extensive computer power, and is very quick in execution. The results of inverse computer modeling are presented and show a drastic improvement of accuracy when both GPS and DInSAR data are used. 相似文献
17.
测量平差中不适定问题解的统一表达与选权拟合法 总被引：38，自引：6，他引：32
将测量平差中常见的几种数学模型分析比较,发现它们的解可以统一表达,形式上,都可以由吉洪诺夫正则化原理导出.在拟稳平差思想的启迪下,作者提出选权拟合法解不适定问题的思路.作者强调,解不适定问题应根据具体问题对参数作具体分析,找出合理的权阵或参数约束矩阵,利用统一的解式,可以得到符合客观实际的结果.最后介绍两个新解法算例. 相似文献
18.
Regularization of geopotential determination from satellite data by variance components 总被引：11，自引：18，他引：11
Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination
of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming
mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed
or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance
components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected
with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large
linear systems. The posterior density function for the variance components, weighting factors and regularization parameters
are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer
observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach.
Received: 5 June 2001 / Accepted: 28 November 2001 相似文献
19.
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
20.
病态总体最小二乘问题的广义正则化 总被引：4，自引：2，他引：2
总体最小二乘(TLS)算法可以视为一个降正则化的过程,对比最小二乘算法,病态总体最小二乘方法的解受系数阵数据误差和观测值误差的影响将更为严重。本文探讨用广义正则化的方法降低病态性对总体最小二乘数值求解的影响,以提高求解结果的稳定性。通过多组算例结果表明,本文采用的广义正则化方法在处理病态总体最小二乘问题上具有明显的优势。 相似文献