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1.
覃辉 《解放军测绘研究所学报》2000,20(1):27-30
文献^「4」采用从联系参数限制条件方程中直接解出的不独立部分联系参数,消去扩建网观测方程中不独立部分未知参数的方法推导了扩建网极大验后估计的平差计算公式,本文进一步推导其单位权方差因子的公式。 相似文献
2.
覃辉 《测绘科学技术学报》2001,18(2):79-83
联系参数函数不独立即联系参数间存在限制条件使得其协因数矩阵Q '2秩亏及权阵P '2=Q 不存在,扩建网极大验后估计的平差计算公式比较复杂.为简化计算方法,文中基于扩建网极大验后估计仅仅满足联系参数限制条件的原理推导了新的平差计算公式. 相似文献
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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
4.
联系参数函数不独立即联系参数间存在限制条件使得其协因数矩阵Q^x′2 秩亏及权阵P^x′2 =Q-1^x′2 不存在,扩建网极大验后估计的平差计算公式比较复杂。为简化计算方法,文中基于扩建网极大验后估计仅仅满足联系参数限制条件的原理推导了新的平差计算公式。 相似文献
5.
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
6.
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
7.
扩建网极大验后估计模型蕴含联系参数X2和扩建网观测量L2两个方差分量。将联系参数分解成函数不独立部分和函数独立部分,根据限制条件求出函数不独立部分代入扩建网观测方程消去不独立部分联系参数,推导了联系参数函数不独立扩建网极大验后估计的Helmert型、Welsch型和Forstner型方差分量估计。 相似文献
8.
扩建网极大验后估计模型蕴含联系参数X2'和扩建网观测量L2两个方差分量。将联系参数分解成函数不独立部分和函数独立部分,根据限制条件求出函数不独立部分代入扩建网观测方程消去不独立部分联系参数,推导了联系参数函数不独立扩建网极大验后估计的Helmert型、Welsch型和Forstner型方差分量估计。 相似文献
9.
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
10.
王仲锋 《测绘与空间地理信息》1998,(2)
本文结合参数平差和主成分估计理论,导出了误差方程中含多重共线性时未知参数的求解公式,并以定理的形式,证明了主成分估计的解是极小范数解。由此,将主成分估计推广到秩亏网平差中,同时导出了未知参数估值之协因数阵的计算公式,同时,证明了自由网平差的传统特性。 相似文献
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A universal formula of maximum likelihood estimation of variance-covariance components 总被引:2,自引:2,他引:2
Z. C. Yu 《Journal of Geodesy》1996,70(4):233-240
The derivation of a universal formula for the variance-covariance component estimation is discussed. The formula is derived adopting the universal functional model (the condition adjustment with unknown parameters and constraints among the parameters),and is based on the maximum likelihood principle. The derived formula in this paper can be applied to all adjustment models for estimating variance-covariance components, which expands the formulas given by K. Kubik (1970)and K. R. Koch (1986).Besides, it is proved that the estimator given in this paper is equivalent to that of Helmert type and best quadratic unbiased estimation (BQUE). 相似文献
13.
粗差验后方差的无偏估计与最优稳健估计 总被引:6,自引:0,他引:6
在正态粗差假设下导出了粗差验后方差的无偏估计,对误差工膨胀模型和误差均值移动模型,两者的无偏估计公式是相同的。这证明了李德仁验后方差的朱建军方差不是无偏的。由于偏方定义的彭方法是正态粗差假设下的最优稳健估计。 相似文献
14.
Khosro Moghtased-Azar Ramin Tehranchi Ali Reza Amiri-Simkooei 《Journal of Geodesy》2014,88(5):427-439
A typical problem of estimation principles of variance and covariance components is that they do not produce positive variances in general. This caveat is due, in particular, to a variety of reasons: (1) a badly chosen set of initial variance components, namely initial value problem (IVP), (2) low redundancy in functional model, (3) an improper stochastic model, and (4) data’s possibility of containing outliers. Accordingly, a lot of effort has been made in order to design non-negative estimates of variance components. However, the desires on non-negative and unbiased estimation can seldom be met simultaneously. Likewise, in order to search for a practical non-negative estimator, one has to give up the condition on unbiasedness, which implies that the estimator will be biased. On the other hand, unlike the variance components, the covariance components can be negative, so the methods for obtaining non-negative estimates of variance components are not applicable. This study presents an alternative method to non-negative estimation of variance components such that non-negativity of the variance components is automatically supported. The idea is based upon the use of the functions whose range is the set of all positive real numbers, namely positive-valued functions (PVFs), for unknown variance components in stochastic model instead of using variance components themselves. Using the PVF could eliminate the effect of IVP on the estimation process. This concept is reparameterized on the restricted maximum likelihood with no effect on the unbiasedness of the scheme. The numerical results show the successful estimation of non-negativity estimation of variance components (as positive values) as well as covariance components (as negative or positive values). 相似文献
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基于偏差矫正的一般理论提出了不适定问题的新的有偏估计。在病态条件下,Gauss-Markov模型参数的最优线性无偏估计,即LS估计是不稳健的,所得估值方差较大,严重偏离真值。因此,文中放弃了对参数估计无偏性的限制,考虑有偏估计的偏差,结合偏差矫正的正则化解法的一般理论提出了一种新的基于偏差矫正的有偏估计;结合岭估计中参数的选择方法确定了替代矩阵。最后通过GPS动态定位算例,验证了新估计的稳定性和有效性。 相似文献
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稳健最优不变二次无偏估计 总被引:1,自引:0,他引:1
导出了稳健最优不变二次无偏估计、稳健最小范数二次无偏估计、稳健Helmert估计,并说明了最优不变二次无偏估计、最小范数二次无偏估计以及Helmert估计等均是稳健最优不变二次无偏估计的特例。 相似文献
19.
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