基于信息扩散的极大似然估计

提出了扩散极大似然估计方法,利用实际观测值的概率密度函数的信息扩散估计,代替了对观测值分布的主观假设,从而具有很强的自适应性。最后设计了两个算例,说明了扩散极大似然估计的过程,并考察了扩散极大似然估计的特性。     

方差的边缘极大似然估计

测量平差问题中,方差估计理论是复杂的。本文基于概括模型,组成自由项f(极大似然估计MLE)的密度函数和改正数向量V的线性函数(边缘极大似然估计MMLE)的密度函数,详细推导了函数模型与随机模型中,未知参数X与σ₀²的似然估计公式,分析了基于两种密度函数所得σ₀²的似然估计存在差异的真正原因,并对两种方法所得的σ₀²和X的统计性质进行了讨论。指出边缘极大似然估计,σ₀²的具有良好的统计性质,可改善极大似然估计σ₀²的不定性(有偏);并且对任一平差模型的边缘极大似然估计,σ₀²无偏、有效的统计性质是一致的。     

图像中圆参数近似极大似然估计

把数学统计方法与数字图像处理方法有机结合,给出了图像中圆参数极大似然估计的数学模型,并导出了利用二维卷积求近似极大似然估计的圆参数。仿真实验显示,与其他方法相比该方法有计算快、能得到亚像素精度等优点。     

部分变量误差模型的整体抗差最小二乘估计

部分变量误差模型(partial EIV model)的加权整体最小二乘(weighted total least-squares,WTLS)估计不具备抵御粗差的能力。鉴于粗差可能同时出现在观测值和系数矩阵中,本文在提出部分变量误差模型WTLS估计的两步迭代解法的基础上,运用抗差M估计的等价权方法,发展了一种整体抗差最小二乘(TRLS)估计方法,并采用一致最大功效统计量确定降权因子。针对WTLS估计两步迭代解法的特点,设计了两个不同的降权方案:第1个方案是在估计系数矩阵元素时,不对观测值降权,仅对系数矩阵降权;第2个方案是在估计系数矩阵元素时,既对系数矩阵降权,同时也对观测值降权。通过对模拟2D仿射变换和线性拟合实例进行计算和分析,结果表明第1方案优于第2方案,并且优于基于残差和验后单位权方差的抗差估计和现有的变量误差模型抗差估计。     

方差—协方差分量极大似然估计的通用公式

本文由概括平差函数模型出发，按极大似然做估计原则导出了适用于所有平差函数模型的方差分量估计的通用公式，由Ｋ．Ｋｕｂｉｋ和Ｃ．Ｒ．Ｋｏｃｈ所导出的两个公式都是它的特例。     

GIS叠置图层方差分量的极大似然估计

针对GIS叠置中的同名点,以维希特分布密度为似然函数,提出了各图层方差分量的极大似然估计方法。该方法不依赖残差,不需要迭代就能估计未知参数和方差分量。     

病态变量含误差模型的分步正则化算法

针对数值逼近理论的病态变量含误差模型正则化算法无法顾及模型的随机性质,以及获得的参数估值不具有统计意义的问题。该文在对现有算法进行拓展的基础上,提出了分步的正则化算法:首先通过构造约束矩阵改善模型的病态性,获得稳定的参数初值;然后应用参数的最小二乘正则化解作为初值,建立附有不等式约束的总体最小二乘参数估计模型;最后,通过实例对已有算法与本文所建立的算法进行比较。结果表明,该算法弥补了现有的算法单一通过正则化参数实现模型正则化存在的不足,避免了总体最小二乘算法具有的降正则化性质导致的参数估计发散,具有稳定的收敛性质。     

极大可能性估计

提出了一个新的估计类——极大可能性估计。详细研究了以p次抛物线为参照函数的极大可能性估计。在以p次抛物线为参照函数的极大可能性估计中，p=1对应可能性带权绝对值和最小估计，p=2对应可能性最小二乘估计。给出了确定观测值的权的一般方法。最后结合实例说明了极大可能性估计的实用性与正确性。     

A universal formula of maximum likelihood estimation of variance-covariance components

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).     

南极IGS基准站时间序列极大似然法分析

针对南极大陆IGS的周期特性、噪声特性、趋势特性等问题,该文采用极大似然法和功率谱分析法分析南极地区8个IGS永久观测站坐标的时间序列。研究结果表明,该地区水平和垂直方向上均有较明显的年周期项,垂直方向上还普遍存在半年周期项。闪烁噪声与白噪声组合能更好描述南极基准站3个分量上噪声特性,各方向上的速率不确定度比只考虑白噪声时要大10~15倍。通过估算基准站水平方向的运动速率,发现该方向上具有较规律的运动趋势:南极洲正缓慢向南美洲移动。     

A fuzzy topology-based maximum likelihood classification

Classification is one of the most widely used remote sensing analysis techniques, with the maximum likelihood classification (MLC) method being a major tool for classifying pixels from an image. Fuzzy topology, in which the set concept is generalized from two values, {0, 1}, to the values of a continuous interval, [0, 1], is a generalization of ordinary topology and is used to solve many GIS problems, such as spatial information management and analysis. Fuzzy topology is induced by traditional thresholding and as such gives a decomposition of MLC classes.Presented in this paper is an image classification modification, by which induced threshold fuzzy topology is integrated into the MLC method (FTMLC). Hence, by using the induced threshold fuzzy topology, each image class in spectral space can be decomposed into three parts: an interior, a boundary and an exterior. The connection theory in induced fuzzy topology enables the boundary to be combined with the interior. That is, a new classification method is derived by integrating the induced fuzzy topology and the MLC method. As a result, fuzzy boundary pixels, which contain many misclassified and over-classified pixels, are able to be re-classified, providing improved classification accuracy. This classification is a significantly improved pixel classification method, and hence provides improved classification accuracy.     

PEIV模型WTLS估计的Fisher-Score算法

考虑系数矩阵含非随机元素和不同位置含相同随机元素的结构化特征,PEIV（partial errors-in-variables）模型较一般的EIV模型更为严格。现有PEIV模型加权整体最小二乘（weighted total least squares,WTLS）估计算法需多次迭代,影响计算效率。通过利用观测值误差和系数矩阵误差的统计性质构造非线性目标函数,并以此推导了新的PEIV模型WTLS估计的计算公式,同时设计了相应的Fisher-Score算法。算例分析结果表明,相比较而言,Fisher-Score算法迭代次数较少,计算效率得到大大提升。     

PEIV模型参数估计新算法

PEIV(Partial Errors-In-Variables)模型是EIV模型的扩展,它能解决系数矩阵含有非随机元素或存在结构特性的问题。针对常规PEIV模型算法的复杂性,提出了一种PEIV模型参数估计的新算法。该算法将系数矩阵含误差的元素看成是一类观测值,与平差模型原观测值构成两类观测值,将PEIV平差模型表示为类似于传统的最小二乘间接平差模型,再通过非线性最小二乘平差理论,推导出了算法的迭代公式和精度评定公式。算法迭代格式与间接平差类似,通过算例验证了算法的可行性和正确性。     

基于模糊推理的最大似然分类算法研究

本文将模糊集理论与最大似然分类原理相结合,用模糊均值和模糊协方差代替传统最大似然分类的均值和协方差矩阵,依据极大隶属度原则,对最大似然分类算法进行改进。并尝试采用一种基于相异像素空间分布算法的分类精度评定方法,得到相异像素空间分布图,依据该空间分布图对不同的分类方法进行精度评定。实验结果表明,改进后的最大似然分类法的正确率、Kappa系数均优于传统的最大似然分类方法,所采用的精度评定方法也较传统方法在有效性、效率等方面有所改善。     

Empirical likelihood estimation of the spatial quantile regression

The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect.     

Parallelizing maximum likelihood classification on computer cluster and graphics processing unit for supervised image classification

ABSTRACT

Supervised image classification has been widely utilized in a variety of remote sensing applications. When large volume of satellite imagery data and aerial photos are increasingly available, high-performance image processing solutions are required to handle large scale of data. This paper introduces how maximum likelihood classification approach is parallelized for implementation on a computer cluster and a graphics processing unit to achieve high performance when processing big imagery data. The solution is scalable and satisfies the need of change detection, object identification, and exploratory analysis on large-scale high-resolution imagery data in remote sensing applications.     

Spectrum estimation using maximum entropy and multiresolution considerations

Summary Given a sample autocovariance sequence of finite length for some observed random process, the spectrum estimation problem involves the extension of this sequence for the required Fourier transformation. The maximum entropy approach which is based on the optimal use of information contents, leads to a dual sequence of reflection coefficients with reciprocal spectrum of the process. The estimation of the maximum entropy spectrum implies results identical to those using autoregressive modeling in one dimension under appropriate white noise assumptions. In cases of a non-white noise component, the approach is generalized to an autoregressive-moving-average model. Recent developments in multiresolution analysis with spectral domain decompositions also offer possibilities of subband spectrum estimation for specific applications. Using a simulated data sequence with two close frequencies, the estimated spectrum from a two-level decomposition with autoregressive modeling shows better resolution than with conventional processing. Geodetic and geophysical applications are briefly indicated.