协方差

The sufficient and necessary conditions of positive definitiveness of a covariance matrix from multivariate discrete data are obtained.

本论文通过引入p-向量配、I-线性组合及它们的性质，研究离散型样本协方差矩阵的正定性问题。

Further more, this thesis has provided a new method for optimizing sampling in theory, and established the probability model for the positive definitiveness of discrete sample by which the number of sampling was optimized.

在应用上，建立了离散型样本协方差矩阵正定的概率模型；提出了一种新的优化抽样调查设计方案，优化了抽样个数。

Studying the positive definitiveness of the covariance matrix from discrete data is important to design the sampling plan and provides the base for the data analysis.However, there have been few outcomes about the positive definitiveness of covariance matrix, most of which have been restricted to the Covariance-matrix of continuous sample.

研究离散型样本协方差矩阵的正定性有助于判断是否可以降低样本的维数，有利于优化抽样个数，为抽样调查的优化设计方案提供一定的理论基础；为基于特征根的多元统计分析提供理论指导。

This thesis discussed the positive definitiveness of the covariance matrix of sample whose variables are discrete data by using p-vector match, I-Linear combination and their properties.

对于变量取离散数据的样本协方差矩阵的正定性，很少有学者进行研究。

The hidden Markov model based on diagonal covariance matrix Gaussian distributions is at present the most popular and successful model in speech recognition.

状态输出概率密度为对角协方差矩阵高斯分布的隐马尔可夫模型在帧内特征相关建模方面存在缺陷。

Error analysis of direct georefencing is divided into two parts: for attitude angle error, formula is determined by the error of the direction cosine matrix, for other errors, formula is determined by covariance matrix.

为了分析各误差因素对定位精度的影响，分两步建立各误差因素和定位精度的表达式，对于姿态角误差的影响，为避免欧拉角之间的耦合，按照方向余弦矩阵误差定义求取，对于其余误差的影响，采用协方差矩阵求取。

This present algorithm further distinguishes itself through sufficiently utilizes the advantage that the vector sensors provide from other beam space DOA algorithms in several regards: 1 beams are formed in the vector-field domain; 2 produce at moderate signal-to-noise ratio estimation performance comparable to the traditional scale array methods;3 these vector-field beams are formed blindly using no apriori source information and coarse estimates of the direction cosine are derived to start off MUSICs iterative search so it demand less computation; 4 deploy agilely , since the fact that the output channel is various .

本文提出了矢量传感器阵列的自适应综合校准补偿方法，还提出利用单矢量传感器速度协方差矩阵分解来求解目标源方位，使得我们不要求校准源是合作性的，也无需知道校准源的先验知识，这比起常规辅助源校准方法具备较大宽容性。随着高性能阵列处理技术及数字信号处理硬件的快速发展和矢量传感器制造工艺的不断成熟，矢量传感器将在新型水雷、低频远程智能鱼雷、声纳浮标、低频拖曳线列阵和新型舰壳声纳，灵巧传感终端，战场监视系统，反隐形雷达，通讯等军民用领域取得良好的发展应用前景。

Then after the author researches the interaction problem of the partial derivative operators with respect to the two points P and Q, analytical expressions as well as series expansions of the kernel function within disturbing gravity field elements are determined, and their explicit expressions which can be applied practically are given for the first time.

深入研究了关于 P 和 Q 两点局部导数算子的相互作用问题，得到了扰动场元之间核函数和协方差函数的解析与级数展开式，首次给出了较为实用的明晰表达式。

All of these applications show that study on conic optimization is necessary. For detail, we conclude them as follows:The models, foreign and internal study situations on conic optimization and its dual problem are introduced in Chapter one, and we point out the key problem and research matter.Chapter two introduces some primary properties of a cone and its dual cone.

第二部分是应用实践：将所提出的锥规划及其对偶锥规划应用在各个领域，例如最小二乘问题、多项式求解、协方差矩阵估计，以及在其它方面的运用，这些应用无不显示出研究锥规划的必要。

Technical analysis; AR-ARCH model; covariance inequality; Strong law of large numbers; Glivenko-Cantelli Lemma ; empirical distribution function; central limit theorem; dependence coefficients

基础科学，数学，概率论、数理统计技术分析； AR-ARCH模型；协方差不等式；强大数定律； Glivenko-Cantelli引理；经验分布函数；中心极限定理；相依系数

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。