共查询到20条相似文献,搜索用时 34 毫秒
1.
拟合推估两步极小解法 总被引:11,自引:1,他引:11
在回顾了最小二乘拟合推估的“综合极小”解法(正常拟合推估)后,分析了正常拟合推估存在的问题。考虑到随机场信号不一定完全表现为随机性,其中可能含有趋势性,顾而提出了拟合推估的“两步极小”解法,即将随机场分成趋势性部分和随机性部分,对趋势性部分采用函数拟合,对随机性部分采用协方差函数拟合。给出了“分两步极小”拟合推估的2种解法。计算表明,两步极小解法能部分地改善拟合推估的精度。 相似文献
2.
The least squares collocation algorithm for estimating gravity anomalies from geodetic data is shown to be an application
of the well known regression equations which provide the mean and covariance of a random vector (gravity anomalies) given
a realization of a correlated random vector (geodetic data). It is also shown that the collocation solution for gravity anomalies
is equivalent to the conventional least-squares-Stokes' function solution when the conventional solution utilizes properly
weighted zero a priori estimates. The mathematical and physical assumptions underlying the least squares collocation estimator
are described. 相似文献
3.
Lars Sjoberg 《Journal of Geodesy》1979,53(4):297-315
The least squares estimator is derived for a random stochastic process implied by one or two heterogeneous random stochastic
processes on a sphere. The solution can be regarded as least squares collocation in the continuous case. When the method is
applied in physical geodesy the statistical expectation is usually substituted by the global average and the method will then
give the minimum mean squares errors of the estimated quantities. The solutions can also be considered as generalizations
of the classical integral formulas in physical geodesy for heterogeneous data information. 相似文献
4.
王新洲 《武汉大学学报(信息科学版)》2000,25(3):257-260
提出了广义平差的概括模型———附有条件的最小二乘配置模型。该概括模型不仅包括滤波和推估模型 ,扩充了原有的最小二乘配置模型 ,而且经典平差模型都是它的特例。 相似文献
5.
在工程实践应用中,为了有效利用GPS高程数据,减少对传统水准测量的依赖,提高GPS高程异常的拟合精度便显得十分重要。为此,本文在介绍二次曲面拟合和最小二乘配置拟合基本原理分析、算法过程推导的基础上,提出了一种新的高程异常拟合方法。首先在二次曲面拟合的基础上,计算得到原始观测数据与拟合数据之间的残差序列,然后采用最小二乘配置模型对包括二次曲面拟合模型误差的综合误差进行优化减弱,最后得到新的高程异常。通过实例,将二次曲面拟合法,最小二乘配置法与文中提出的新方法进行比较分析。结果表明:新的组合方法的拟合预测精度要明显优于最小二乘配置及二次曲面拟合。 相似文献
6.
张亮 《测绘与空间地理信息》2008,31(2):145-148
抗差估计具有较好的抗拒异常观测值及粗差的能力,而最小二乘配置又能较好地处理系统误差,本文结合两者的优点,利用抗差最小二乘配置对数字化地图进行几何纠正,其中对协方差函数采用抗差拟合,得到了较好的结果。实验证明在GIS数据处理的扫描数字化地图几何纠正中,抗差最小二乘配置在抗拒异常值和处理系统误差方面优于单纯的最小二乘估计和单纯的最小二乘配置方法。 相似文献
7.
Inner constraints, generalised matrix inverses and S-transformations are described in relation to least squares estimation of spatial positions. A simple example is used to illustrate some of the theory. The various roles and properties of covariance functions and matrices are presented with a discussion of their practical determination and use in least squares interpolation and collocation. 相似文献
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10.
Arne Bjerhammar 《Journal of Geodesy》1982,56(4):312-328
The boundary value problem in physical geodesy is nowadays mostly presented with the use of an advanced stochastic model by
Krarup-Moritz. This model includes a primary Gauss-Markov model and an adjoining Wiener-Hopf model. Degenerations of the Wiener-Hopf
section are found in thesingular auto-covariance matrix of the residuals. The non-singular inverse of the auto-covariance matrix of the signal is proved to be a generalized inverse of the singular
auto-covariance matrix of the residuals. The joint model is given a non-stochastic evaluation for a case with spherical external
surface (using a non-singular inverse). These findings will not prevent a successful application of the model, which has important
merits, specially when using suitablea priori values for the stochastic parameters in the covariance functions.
A method for quadratic unbiased estimation ofa priori variances is presented in an introductory section. It is meant to be of value when using a solution of the boundary value problem with
the collocation technique based on the classical Gauss-Markov solution. (Bjerhammar (1963).) 相似文献
11.
Least squares adjustment and collocation 总被引:10,自引:1,他引:10
K. -R. Koch 《Journal of Geodesy》1977,51(2):127-135
Summary For the estimation of parameters in linear models best linear unbiased estimates are derived in case the parameters are random
variables. If their expected values are unknown, the well known formulas of least squares adjustment are obtained. If the
expected values of the parameters are known, least squares collocation, prediction and filtering are derived. Hence in case
of the determination of parameters, a least squares adjustment must precede a collocation because otherwise the collocation
gives biased estimates. Since the collocation can be shown to be equivalent to a special case of the least squares adjustment,
the variance of unit weight can be estimated for the collocation also. This estimate gives the scale factor for the covariance
matrices being used in the collocation. In addition, the methods of testing hypotheses and establishing confidence intervals
for the parameters of the least squares adjustment may be applied to the collocation. 相似文献
12.
本文所采用的基于输入-输出系统论的谱方法在计算结果的精度上与最小二乘配置方法相当,却很容易用于异性场的计算。用该谱方法对卫星测高及海洋重力资料进行组合求解重力场量(大地水准面差距和重力异常),其误差估计结果表明各向异性场的计算精度优于各向同性场的精度。 相似文献
13.
最小二乘配置法和Kriging法进行高程转换时均兼顾考虑高程异常的系统部分和随机部分,为对比分析两种方法在GPS高程转化时的优劣性,根据最小二乘配置法的协方差函数(或kriging法的变异函数)的不同,采用五种方案对实测数据进行处理。结果分析证明了以距离作为协方差函数的最小二乘配置法在算法和推估结果可靠性要优于其他方案。 相似文献
14.
Oscar L. Colombo 《Journal of Geodesy》1983,57(1-4):131-137
When area means are given on a regular grid, their covariance functions, needed in least squares collocation to estimate quantities
statistically related to the data, can be calculated as accurately as desired and very efficiently in the form of a Fourier
series truncated at a suitably high frequency. 相似文献
15.
In contrast to continuous global considerations of time dependent boundary value problems an attempt is made to define4D-linear observation equations in the framework of integrated geodesy for discrete, more or less regional and local applications
(deformation analysis) where time variations in position and in the gravity field have to be considered. The derivation is
a strict analogue and extension of the3D integrated approach. In addition the construction of time dependent covariance functions is discussed, which are necessary
to solve for unknown displacements and changes in the gravity potential in the generalized least squares collocation model. 相似文献
16.
Klaus-Peter Schwarz 《Journal of Geodesy》1974,48(2):171-186
When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data.
It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not
necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The
problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices
are often used.
If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment.
The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework.
It is shown in which way improvements can be made using a modified approach of principal component analysis.
As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions
on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can
be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable
covariance function is suggested.
Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973. 相似文献
17.
BRDF模型参数分阶段鲁棒性反演方法 总被引:2,自引:0,他引:2
遥感BRDF物理模型均建立于一定的假设或基于某些理想状况,其模拟的数据与观测数据之间多少会存在一些差异(误差)。利用BRDF模型反演地表参数时,如果不加选择地使用所有观测数据,势必会影响模型参数反演的准确度。遥感反演时一般都采用代价函数进行参数拟合。经典的最小二乘(LS)拟合代价函数对正态分布误差具有一定的抗干扰性,但是当观测数据含有异常值时却会导致反演结果的不稳定。最小中值平方(LMS)方法具有鲁棒性特点,反演时若将其作为代价函数,则可以有效地检测出观测数据中含有的异常值,从而可以使模型反演准确度提高。本文以遥感BRDF物理模型——SAIL模型为例,使用模拟数据与真实地面观测数据,构建LMS与LS两种代价函数,分阶段地进行地表参数的反演方法研究。结果显示,针对具有一定误差或模型不能完全表示的观测数据,本文采用的分阶段方法可以对模型参数鲁棒地反演。 相似文献
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19.
基于多面核函数配置型模型的参数估计 总被引:2,自引:1,他引:2
针对同时出现非随机参数、已测点和未测点信号的配置型模型精确建立协方差函数的困难,在研究和应用最小二乘配置和多面函数拟合法的基础上,将两法综合,提出了多面核函数配置法,导出了这种平差方法的解算公式。并与最小二乘配置、多面函数拟合作了比较分析。 相似文献
20.
An approach to modeling the regional ionospheric total electron content (TEC) based on spherical cap harmonic analysis is
presented. This approach not only provides a better regional TEC mapping accuracy, but also the capability for ionospheric
model prediction based on spectrum analysis and least squares collocation. Unlike conventional approaches, which predict the
immediate TEC with models using current observations, the spherical cap harmonic approach utilizes models using past observations
to predict a model which will provide future TEC values. A significant advantage in comparison with conventional approaches
is that the spherical cap harmonic approach can be used to predict the long-term TEC with reasonable accuracy. This study
processes a set of GPS data with an observation time span of 1 year from two GPS networks in China. The TEC mapping accuracy
of the spherical cap harmonic model is compared with the polynomial model and the global ionosphere model from IGS. The results
show that the spherical cap harmonic model has a better TEC mapping accuracy with smoother residual distributions in both
temporal and spatial domains. The TEC prediction with the spherical cap harmonic model has been investigated for both short-
and long-term intervals. For the short-term interval, the prediction accuracies for the latencies of 1-day, 2-days, and 3-days
are 2.5 TECU, 3.5 TECU, and 4.5 TECU, respectively. For the long-term interval, the prediction accuracy is 4.5 TECU for a
2-month latency. 相似文献