共查询到18条相似文献，搜索用时 156 毫秒
1.
非线性模型平差中单位权方差的估计 总被引：2，自引：0，他引：2
王新洲 《武汉测绘科技大学学报》2000,25(4):358-361
导出了非线性模型平差中单位的严密估计公式,证明了线性模型平差位权方差的估计公式是其特例,给出了在实际工作中用近似公式代替严密公式的理论根据。 相似文献
2.
基于最小二乘估计理论,建立了更加合理的GIS多层叠置同名点元的不确定性估计模型,改善了叠置点的精度。得出的单位权方差估计公式,理论上符合在一个平差系统中,其母体单位权方差应具有唯一性的要求。从理论和实例两方面验证了当同层内观测数据精度相同时,经多层叠置后各点精度均相同的结论。 相似文献
3.
GIS叠置后同名点元不确定性的严密估计 总被引：1，自引：0，他引：1
基于最小二乘估计理论,建立了更加合理的GIS多层叠置同名点元的不确定性估计模型,改善了叠置点的精度.得出的单位权方差估计公式,理论上符合在一个平差系统中,其母体单位权方差应具有唯一性的要求.从理论和实例两方面验证了当同层内观测数据精度相同时,经多层叠置后各点精度均相同的结论. 相似文献
4.
三角洲量单位权方差的先验估值一般用经典菲列罗公式计算。实践中，经常出现三角测量单位权方差的先验估值不等于后验估值的情形．本文根据条件平差的原理，证明了单位权方基的先验估值是有偏估计，经典菲列罗公式是后验估计公式的特殊形式，并推导出了广义菲列罗公式。 相似文献
5.
本文从极大验后估计的一般模型出发,分两种情形推导了方差分量的Helmert型、Welsch型、F(?)rstner型极大验后估计公式。这些公式可以用于极大验后平差的迭代定权,以消除平差中模型随机扰动误差的影响,提高平差计算精度。 相似文献
6.
方差分量估计的通用公式 总被引：1，自引：0，他引：1
应用最小二乘原理将方差分量估计公式从参数平差模型推广到概括函数平差模型。通过选取恰当的权阵,基于概括函数模型的最小范数二次无偏估计及赫尔默特法得到的公式均是本文的特例。视协方差矩阵为权逆阵,得到了最小方差估计,并证明了该公式与最优二次无偏估计的通用公式等价,从而表明最优二次无偏估计和极大似然估计的通用公式也是本文的特例。除此之外,本文还给出了最小二乘方差分量估计的简化公式,并对其进行了扩展。最小二乘方差分量估计的假设检验理论同样得到了推广。 相似文献
7.
本文首先分析了L_p平差的统计意义,证明了当观测误差服从p-范分布时,参数的极大似然估计即为L_p解。同时讨论了L_p的迭代解法及收敛性,给出了用改进的线性规划求L_1、L_∞解的方法。证明了L_p迭代解及L_1、L_∞严密解都是参数的无偏估计,同时构造了与L_p平差P值无关的单位权方差的无偏估计公式,并对L_p平差的效率作了讨论。最后分析了L_p平差与抗差估计的关系,给出了一种基于L_1解的抗差估计方法。 相似文献
8.
著名的Helmert方差分量估计公式是基于间接观测平差模型导出的。基于条件观测平差模型导出了方差分量估计公式并给出了实际应用范例,且对两种模型的方差分量估计公式的等价性进行了理论证明。算例表明,文中的估计公式能正确地估计出各类观测值的方差因子。 相似文献
9.
本文从二次型的期望公式出发，推导了经典最小二乘平差、最小二乘滤波、最小二乘推估和最小二乘配置的验后单位权方差的估计公式。 相似文献
10.
11.
12.
王新洲 《武汉大学学报(信息科学版)》1997,(2)
由于不同的非线性模型具有不同的非线性强度，使得一些非线性模型可以线性近似，而另一些则不能。本文介绍度量非线性强度的方法，提出判断非线性模型能否线性近似的数值标准——容许曲率 相似文献
13.
针对现有的非线性平差精度评定理论中，蒙特卡罗法模拟次数的选择不具有客观性，无法对结果进行直接控制，以及没有同时考虑到平差参数估值、随机量改正数和单位权方差估值的有偏性等问题，把自适应蒙特卡罗法融入到非线性平差精度评定理论中。通过基于自适应蒙特卡罗法的估值偏差计算和参数估值协方差阵计算，设计了非线性平差精度评定一套理论完整的算法流程。基于对偶变量的思想，提出了参数估值偏差计算的对偶自适应蒙特卡罗法。直线拟合模型和椭圆拟合模型两个算例结果表明，非线性平差精度评定的自适应蒙特卡罗法能获得稳定且合理的精度评定结果，具有更强的适用性；对偶自适应蒙特卡罗法计算估值偏差的收敛速度更快，效率更高。 相似文献
14.
15.
Least-squares variance component estimation 总被引：19，自引：15，他引：4
Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown
variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible
because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing
body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its
various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix
from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We
also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE.
We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of
VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of
nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected
by the results of LS-VCE. Various examples are given to illustrate the theory. 相似文献
16.
Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem
then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation
is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate
the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency
between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency.
Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters
involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate
integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle
used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer
estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated
exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples. 相似文献
17.
Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis 总被引：10，自引：4，他引：6
The weighted total least squares (TLS) method has been developed to deal with observation equations, which are functions of both unknown parameters of interest and other measured data contaminated with random errors. Such an observation model is well known as an errors-in-variables (EIV) model and almost always solved as a nonlinear equality-constrained adjustment problem. We reformulate it as a nonlinear adjustment model without constraints and further extend it to a partial EIV model, in which not all the elements of the design matrix are random. As a result, the total number of unknowns in the normal equations has been significantly reduced. We derive a set of formulae for algorithmic implementation to numerically estimate the unknown model parameters. Since little statistical results about the TLS estimator in the case of finite samples are available, we investigate the statistical consequences of nonlinearity on the nonlinear TLS estimate, including the first order approximation of accuracy, nonlinear confidence region and bias of the nonlinear TLS estimate, and use the bias-corrected residuals to estimate the variance of unit weight. 相似文献