隐马尔科夫模型的改进及其在金融预测中的应用

隐马尔科夫模型(Hidden Markov Model)在诸多领域都有广泛应用.本文从不同角度对现有的HMM进行改进并应用于金融预测.首先,我们采取固定K-means方法的初始点,使得K-means的聚类结果更加稳定,由此为Baum-Welch算法确定更好的初始迭代值.其次,为更进一步提升预测效果,与已有方法不同,我们将由BaumWelch算法所得到的模型参数值作为Vertibi算法的输入来确定隐状态的最优取值序列,由此重新划分观测向量,进而得到各个隐状态对应的观测向量的集合;基于Vertibi算法的输出结果,我们重新计算不同类观测向量的均值与方差,将新的均值向量和协方差矩阵作为Baum-Welch算法初始迭代值,最终确定HMM最优的模型参数.最后,代替现有方法仅在历史区间中简单寻求相似走势的做法,我们不仅导出了预测值发生的多步条件概率的精细表达式,而且通过极大化该条件概率的值来得到更佳的预测值.基于中国证券市场具体数据的实证结果表明了本文所提出改进HMM的优越性.     

基于二阶转换测量Kalman滤波的目标跟踪算法(英文)

为了减小传统跟踪滤波算法线性化误差,提高光电跟踪系统的跟踪速度和跟踪精度,本文在三维空间中,提出了二阶去偏转换测量卡尔曼滤波算法.该算法利用二阶泰勒展开的方法,推导出了光电跟踪系统观测方程的转换测量值误差的均值和协方差矩阵表达式,并对测量误差进行去偏差补偿处理,再经过转换测量卡尔曼滤波,可显著减小传统滤波算法的线性化误差.仿真结果表明,二阶去偏转换测量卡尔曼滤波(SCMKF)算法的跟踪精度优于非去偏转换测量卡尔曼滤波(CMKF)和扩展卡尔曼滤波(EKF),以及unscented卡尔曼滤波(UKF)算法,并且具 有更快的收敛速度,和采用统计方法的去偏转换测量卡尔曼滤波(DCMKF)的跟踪精度相当,但计算简单,提高了跟踪速度.     

GPS测量中的坐标系统及其转换

在GPS测量中通常采用两类坐标系统,一类是在空间固定的坐标系统,另一类是与地球体相固联的坐标系统,也称固定坐标系统。如:WGS-84世界大地坐标系和1980年西安大地坐标系。在实际使用中需要根据坐标系统间的转换参数进行坐标系统的变换,来求出所使用的坐标系统的坐标。这样更有利于表达地面控制点的位置和处理GPS观测成果,因此在GPS测量中得到了广泛的应用。     

三维坐标转换精度及其影响因素的研究

为了对大空间组合测量中的三维坐标转换精度进行分析,指导现场测量公共点的布置方案,通过对坐标转换参数的最小二乘不等精度估计,建立了坐标转换精度在空间中分布的数学模型.通过模型可以得到空间中任意被测点的转换精度,并且转换精度受到公共点的测量点位误差及其几何分布的影响.最后结合多个公共点三维坐标数据分析了转换精度影响因素.实验表明,通过改进公共点坐标测量精度及几何分布能够有效地提高三维坐标转换精度.     

基于距离约束的关节式坐标测量机蛙跳测量方法研究

针对关节式坐标测量机(ACMM)在大尺寸工件的检测过程中测量范围有限且误差较大的问题,提出了一种基于距离约束的ACMM的蛙跳测量方法。在ACMM进行坐标转换的过程中,利用蛙跳球作为公共基准点,用高精度的三坐标测量机对蛙跳球之间的空间位置关系进行标定。在计算坐标转换参数的过程中,将任意两蛙跳球之间的位置关系作为距离约束条件,消除测量过程中产生的粗大误差并优化坐标转换模型的参数,以提高坐标转换精度。实验结果表明:距离约束能够有效地提高坐标转换参数的精度,同时增加公共基准点的个数会较大地提高蛙跳测量精度。     

ICF靶丸表面形貌及球度误差检测

为了对ICF靶丸的表面形貌及球度误差进行高精度测量,开发了一台五轴坐标测量机,并采用锥光全息技术的激光测头实现对靶丸表面的高精度、非接触检测。首先,根据靶丸表面的结构特点,改进了基于最小二乘的球度误差评价算法;然后,介绍了作为实验平台的五轴坐标测量机的整体配置,推导了该坐标测量机的测量数学模型,该坐标测量机可实现在多个姿态下对靶丸的非接触取点测量;最后,在相同条件下,进行了5次实验测量,其结果表明:靶丸球度误差测量的均值为0.0021 mm,标准差为2.07 x10^-4 mm。该检测方法可以满足对靶丸表面形貌及球度误差高精度、高稳定性的测量要求。     

坐标系统网上转换平台设计与实现

本文介绍了我国常用的坐标系统,指出了在使用过程中存在坐标转换的不便之处,设计了网上转换平台的功能模块,并结合ASP.NET技术开发实现。     

不同坐标系下界址点坐标与宗地面积的转换计算

为确立不同坐标系统之间的转换关系,结合地籍工作中的实际应用,本文提出了一种基于赫尔默特变换模型的坐标转换和精度评价的方法,并利用数学知识,讨论不同坐标系统宗地面积转换和计算面积变形的方法.     

球坐标系下坐标测量的重复性

几何量计量中使用直角坐标系统、球坐标系统、关节臂系统等多种不同原理的坐标测量系统。以激光跟踪仪为例,分析球坐标系统的基本测量原理,根据球坐标与直角坐标的相互转换关系,推导计算两坐标系下重复性的传播规律,说明坐标测量重复性表达方式的不同。分别在球坐标系和直角坐标系下,利用Monte Carlo法模拟坐标测量点的空间分布。从理论分析、模拟试验、实际试验3个角度说明球坐标测量系统空间坐标的测量重复性采用角度和距离分别给出更能体现测量点的空间分布,为球坐标测量系统的生产者和使用者提供理论指导。     

面向任务的坐标测量机测量不确定度评价方法

针对坐标测量机多不确定度源的分析和合成难题,利用基于球列的坐标测量机21项几何运动误差分离方法和蒙特卡洛模拟算法实现坐标测量机面向任务测量不确定度评价,并建立了基于"互联网+"的坐标测量机的溯源服务体系.省市计量院作为溯源网络节点,协助进行数据采集,包括误差参数、环境参数和仪器参数等.当用户需要进行特定任务测量时,将测量策略发送到中国计量科学研究院并通过网络将结果反馈给客户.该溯源网络在一定程度上减小了溯源链的长度,实现了计量的扁平化.     

光电跟踪系统非线性新息自适应卡尔曼滤波算法

为解决非线性部分状态卡尔曼滤波算法中由于线性化误差所导致的滤波精度下降问题,提出采用UT变换方法计算系统状态误差方差,及基于新息自适应调整系统噪声方差,进而构成一种新的非线性自适应部分状态卡尔曼滤波算法,并总结出详细算法结构.同时,将此方法应用到非线性测量光电跟踪系统中,并与U卡尔曼滤波和非线性部分状态卡尔曼滤波进行性...     

Knowledge-aided covariance matrix estimation: a MAXDET approach

The authors consider the problem of knowledge-aided covariance matrix estimation and its application to adaptive radar detection. The authors assume that an a priori (knowledge-based) estimate of the disturbance covariance M, derived from a physical scattering model of the terrain and/or of the environment, is available. Hence, starting from a set of secondary data, the authors evaluate the maximum likelihood (ML) estimate of M assuming that it lies in a suitable neighbourhood of the a priori estimate and formulate this ML estimation in terms of a convex optimisation problem which falls within the class of MAXDET problems. Both the cases of unstructured and structured disturbance covariance are considered. At the analysis stage, the authors assess the performance of the new knowledge-aided covariance estimators both in terms of estimation error and detection probability achievable by a class of adaptive detectors. The results highlight that, if the a priori knowledge is reliable, satisfactory levels of performance can be achieved with considerably less training data than those exploited by conventional algorithms.     

随机动力学响应的高斯相关过程模拟

动力学响应是描述系统振动状态、评估其性能、用于控制等的重要变量,复杂系统的不确定性、随机激励样本的不可测量性等导致传统随机响应时程与统计分析的计算困难,因此需要发展基于系统响应观测的、直接的随机过程概率模型与评估新方法。近年来,人工智能与数据处理技术等领域发展的无确定性系统模型的、直接随机过程概率模型,及其概率评估、系统状态预测等方法为动力学响应的概率分析提供了新思路,特别是具有很好普适性与可分析性的高斯相关过程已具有较完整的理论方法。鉴于此,本文提出针对动力学系统响应的、直接的随机过程概率模型与评估方法,并作探索性研究。先基于高斯白噪声激励动力学系统响应的统计特性分析,说明系统响应的高斯随机过程特性、响应在时间维度上的相关性、及其协方差随时间差的指数衰减特性等;再给出该系统响应的高斯相关过程概率建模与评估方法,包括由响应协方差计算,高斯过程协方差或核函数的拟合,到高斯相关过程概率模型的确定,响应样本过程的直接生成,及其统计评估等,并给出高斯相关过程的贝叶斯更新与系统状态预测有关基本公式。数值结果表明该高斯相关过程的概率建模与响应评估方法的可行性与有效性。     

Maximum likelihood principal component analysis with correlated measurement errors: theoretical and practical considerations

Procedures to compensate for correlated measurement errors in multivariate data analysis are described. These procedures are based on the method of maximum likelihood principal component analysis (MLPCA), previously described in the literature. MLPCA is a decomposition method similar to conventional PCA, but it takes into account measurement uncertainty in the decomposition process, placing less emphasis on measurements with large variance. Although the original MLPCA algorithm can accommodate correlated measurement errors, two drawbacks have limited its practical utility in these cases: (1) an inability to handle rank deficient error covariance matrices, and (2) demanding memory and computational requirements. This paper describes two simplifications to the original algorithm that apply when errors are correlated only within the rows of a data matrix and when all of these row covariance matrices are equal. Simulated and experimental data for three-component mixtures are used to test the new methods. It was found that inclusion of error covariance information via MLPCA always gave results which were at least as good and normally better than PCA when the true error covariance matrix was available. However, when the error covariance matrix is estimated from replicates, the relative performance depends on the quality of the estimate and the degree of correlation. For experimental data consisting of mixtures of cobalt, chromium and nickel ions, maximum likelihood principal components regression showed an improvement of up to 50% in the cross-validation error when error covariance information was included.     

基于自适应因子化 H∞滤波的单站无源跟踪

针对单站无源跟踪系统非线性较强、传统跟踪滤波方法收敛速度慢且容易发散的问题,提出了一种基于自适应因子化 H∞滤波的单站无源跟踪算法.该算法利用 sigma 点转换和鲁棒 H∞滤波能够减小观测方程的线性化误差和降低观测误差不确定性的特点,通过新息控制减小野值对滤波的干扰,利用比例因子和渐消因子自适应调整采样点到中心点的距离和状态预报误差的协方差,从而克服基于 UT 变换的 H∞滤波采样时的非局部效应问题,增强了单站无源跟踪系统对噪声的鲁棒性.仿真实验结果表明,本文方法通过对 UT 变换进行简化,在自适应因子化的同时,算法的计算量与基于 UT 变换的 H∞滤波基本持平,且跟踪精度优于基于 UT 变换的 H∞滤波算法.该算法在保持高精度估计能力的同时,具有较强的鲁棒性,是解决非线性系统状态估计问题的一种有效方法.     

大气相位屏的协方差冲激函数产生法

提出正交基为冲激函数的协方差法,在Matlab中仿真实现符合大气湍流统计分布(vonKarman谱和Kolmogorov谱)的大气相位屏。协方差冲激函数产生法对连续波前相位进行冲激函数正交分解,根据正交分解系数的协方差模拟平行光通过大气后的瞬时波前相位。计算多帧相位屏的波前结构函数,与理论值比对,验证产生大气相位屏的正确性。根据比对结果得,该方法产生的相位屏精度高,对于Kolmogorov谱,该方法产生的大气相位屏的波前结构函数误差约为理论波前结构函数均值的1%。     

Retrieval of atmospheric profiles from satellite sounder measurements by use of the discrepancy principle

It is known that an infrared or a microwave remote-sensing equation is an integral equation of the first kind. As a result, it is ill-posed, the solution is unstable, and difficulties arise in its retrieval. To make the solution stable, either an a priori error covariance matrix or a smoothing factor gamma is necessary as a constraint. However, if the error covariance matrix is not known or if it is estimated incorrectly, the solution will be suboptimal. The smoothing factor gamma depends greatly on the observations, the observation error, the spectral coverage of channels, and the initial state or the first guess of the atmospheric profile. It is difficult to determine this factor properly during the retrieval procedure, so the factor is usually chosen empirically. We have developed a discrepancy principle (DP) to determine the gamma in an objective way. An approach is formulated for achieving an optimal solution for the atmospheric profile together with the gamma from satellite sounder observations. The DP method was applied to actual Geostationary Operational Environment Satellite (GOES-8) sounder data at the Southern Great Plains Cloud and Radiation Testbed site. Results show that the DP method yields a 21.7% improvement for low-level temperature and a 23.9% improvement for total precipitable water (TPW) retrievals compared with the traditional minimum-information method. The DP method is also compared with the Marquardt-Levenberg algorithm used in current operational GOES data processing. Results of the comparison show significant improvement, 6.5% for TPW and 11% for low-level water-vapor retrievals, in results obtained with the DP method compared with the Marquardt-Levenberg approach.     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

基于多分辨率分析的结构物理参数识别贝叶斯估计方法:方法推导与验证

在观测噪声和模型误差等不确定性因素的影响下,结构物理参数识别问题是一个不确定性问题.针对此问题,该文从结构运动微分方程出发,利用小波多分辨率分析原理,建立结构多尺度动力方程,由该方程以结构激励和响应信息在多尺度上的细节信号和最大尺度上的概貌信号为观测量推得物理参数线性回归模型,对该模型应用贝叶斯估计理论得到物理参数后验...