基于多因素的卡尔曼滤波模型在滑坡变形预测中的应用

分析了滑坡变形预测模型的研究现状.考虑到滑坡的变形主要受到降雨及温度等因素的影响,建立基于时效分量、降雨分量和温度分量的多因素变形预测模型,然后将基于多因素的变形预测模型的模型参数看作带有动态噪声的状态向量,建立基于多因素的卡尔曼滤波模型,以基于多因素的卡尔曼滤波模型为基础,对滑坡的变形进行预测.由于基于多因素的卡尔曼滤波模型在卡尔曼滤波过程中,模型的参数不断发生变化,从而增强了模型适应观测数据的能力,提高了模型的拟合精度和预测精度.实例计算表明用基于多因素的卡尔曼滤波模型对滑坡的变形进行预测,其预测误差较小,预测效果较为理想.     

基于AR(n)模型的卡尔曼滤波模型

考虑到对于处于不同位置的变形监测点,由于它们所处的位置不同,各种环境因素对它们的影响及影响程度也不同,作者预置数个AR(n)模型,通过计算比较,选择剩余标准差最小的AR(n)模型作为初选模型,再将初选的AR(n)模型的模型参数看作包含有动态噪声的状态向量,建立卡尔曼滤波模型.实例分析表明,采用这种方法能够提高模型的拟合精度和预测精度.     

基于泰勒级数及温度因子的卡尔曼滤波模型在链子崖危岩体变形预测中的应用

考虑到链子崖危岩体的变形受温度的影响较为明显,为此,将链子崖危岩体的变形看作时间和温度的函数,利用泰勒级数建立链子崖危岩体的变形与时间和温度的函数关系,并将泰勒级数的余项及时间变化的二次方和温度变化的二次方的系数的变化量看作数学期望为0的动态噪声,建立卡尔曼滤波模型,并用于链子崖危岩体变形的预测预报.实例计算表明,模型的拟合效果和预测效果较好.     

基于卡尔曼滤波的期货价格期限结构模型

为准确对商品期货合约进行定价和预测,本文在短期-长期模型的基础上,提出以短期偏离、中期偏离和长期均衡为状态变量的三因素模型。本文根据状态变量的假设建立相关微分方程,并推导出模型的解,再运用卡尔曼滤波和极大似然法得到模型的参数和状态变量。最后,通过比较多种误差统计量证明,本文的短期-中期-长期模型的拟合与预测能力优于短期-长期模型。     

银行间国债利率期限结构的三因子仿射模型

通过对2002年1月到2006年3月的国内银行间国债数据的主成份分析表明，利率的动态变化基本上可以被三个因子所解释。由此我们建立了一个三因子仿射模型，并给出债券的定价公式。通过卡尔曼滤波法对模型的实证分析，证实该模型基本上能在时间序列和横截面两个维度上与实际数据相符合。从预测能力来看，0．5年和1年期利率的预测结果相对误差略大，而2、3、5、10年期利率的相对误差较小，平均值相对误差在1％之内。     

基于卡尔曼滤波的MGM-多维AR(p)模型的构建及其应用

由于受到外界不确定性因素的干扰,导致实际数据偏离模拟的趋势,使得灰色多变量MGM(1,m)模型预测效果不佳,而多维平稳序列自回归模型(AR(p))能够有效反应具体数据与整体趋势之间产生的偏差,从而可以掌握外界环境对目标数据发展趋势带来的影响.由此文章首先利用卡尔曼滤波对给定的小样本数据做平滑处理,消除数据观测时产生的噪...     

基于增广的广义卡尔曼滤波模型的高精度参数估计

针对捕食模型、利用已知观测数据、在非线性最小二乘准则下,建立了基于增广的广义卡尔曼滤波模型来解决噪声背景下的高精度参数估计问题,并予以了验证.提出以相平面方程为约束的初值搜索算法,利用Matlab优化工具箱、深度搜索和剪枝加速等技术来提高搜索速度.还建立了二重规划模型以解决观测时间有误差时的高精度估计问题,并对时间误差作了正态分布检验.     

基于随机采样模糊聚类和卡尔曼滤波方法的模糊辨识

提出一种新的基于模糊聚类和卡尔曼滤波方法的模糊辨识算法 .该方法是基于快速模糊聚类 ,计算给定样本在各类中的隶属度 ,并利用卡尔曼滤波方法辨识模糊模型的结论参数 .整个辨识过程与一般的模糊聚类方法 [1 ]相比 ,需要的 CPU时间大大缩短 .最后通过仿真实例验证了该方法的有效性 .     

向量灰色模型的建立及应用

针对传统多变量灰色预测模型(MGM(1,m))有时存在的建模数据失真问题,以系统中关联变量具有趋同性为基础,提出了一种新的模型——向量灰色模型(VGM(1,m))。与MGM(1,m)模型相比,VGM(1,m)结构更简单,模型参数更少,从而有利于参数的估计。将VGM(1,m)、MGM(1,m)、GM(1,1)模型应用于四个实例的分析,结果表明VGM(1,m)消除了MGM(1,m)的建模失真现象,模型的稳定性得到了增强。进一步,与GM(1,1)建模结果相比,VGM(1,m)模型的预测精度更高,即新模型有更好的泛化性。     

基于状态驻留时间下由转移弧产生输出的HMM模型中的参数估计

本讨论了用状态驻留时间来模型化传统的HMM模型。HMM的一个基本假设是它认为语音信号是准平稳的。然而由状态输出yt的HMM模型，并不能很好地表征语音信号中平稳段或平稳段之间的具体特征；由转移弧产生输出的自左向右HMM系统,则对语音特征作更为细致的描述。本主要讨论在[2]的基础上,对新建模型进行参数估计。     

地震动瞬时谱估计的UnscentedKalman滤波方法

用时变ARMA模型描述地震动时程,提出了采用Unscented Kalman滤波技术实现地震动瞬时谱估计的思路．算例分析表明,Unscented Kalman滤波方法较Kalman滤波方法适用范围广,具有较高的时间和频率分辨率,能够更好地跟踪地震动的局部特性,适合处理非线性模型或有突变特性的模型的辨识问题．不同阶数ARMA模型的估计结果还表明,以往被忽略的ARMA模型的理论频率分辨力对地震动瞬时谱估计精度有重要影响,应作为一个参考指标在ARMA模型的判阶中加以考虑．     

卡尔曼滤波在光纤监测中的应用

薛毅,杨中华．卡尔曼滤波在光纤监测中的应用．本文提出用卡尔曼滤波方法对光纤的接口位置进行确定。该方法的优点是：可以自动地、较为准确地得到光纤的接口位置,为光纤监测数据的自动分析提供了依据     

Unscented Kalman filter for time varying spectral analysis of earthquake ground motions

A novel parametric time-domain method for time varying spectral analysis of earthquake ground motions is presented. Based upon time varying autoregressive moving average (ARMA) modeling of earthquake ground motion, unscented Kalman filter (UKF) is used to estimate the time varying ARMA coefficients. Then, time varying spectrum is yielded according to the time varying ARMA coefficients. Analysis of the ground motion record El Centro (1940, N–S) shows that compared to Kalman filter (KF) based method, short-time Fourier transform (STFT) and wavelet transform (WT), UKF based method can more reasonably represent the distribution of the seismic energy in time–frequency plane, which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity. Analysis of the seismic response of a building during the 1994 Northridge earthquake shows that UKF based method can be potentially a useful tool for structural damage detection and health monitoring. Lastly, it is found that the theoretical frequency resolving power of ARMA models usually neglected in some studies has considerable effect on time varying spectrum and it is one of the key factors for ARMA modeling of earthquake ground motion.     

Credibility theory and the Kalman filter

Following Mehra (1975) we indicate how some of the well known credibility models may be formulated as Kalman filters. The formulation yields recursive premium forecasts including recursive predictions errors which are of importance to practitioners.     

基于方根分解形式的带衰减因子UKF算法应用

UKF作为一种新的非线性滤波方法已在目标跟踪问题中得到应用,在状态的时间更新阶段直接使用非线性模型,不引入线性化误差,而且不必计算Jacobians矩阵.提出了一种基于方根分解形式的带有衰减因子的UKF算法(SRDMA-UKF),算法的方根形式增加了数字稳定性和状态协方差的半正定性.通过衰减因子的引入加强对当前测量数据的利用,减小历史数据对滤波的影响.仿真实验结果表明,该算法与UKF算法相比具有更好的滤波性能.     

Restricted Kalman filter applied to dynamic style analysis of actuarial funds

We use dynamic style analysis to unveil the strategies followed by Brazilian actuarial funds from January 2004 to August 2008 and investigate whether managers’ decisions were compatible with the intention of protecting the investor against the negative effects of inflation. The main goal of this paper is to show that this methodology is suitable for allowing insurance companies to increase their capacity to monitor the behavior of portfolios and to control the amount of risk they assume. The basic steps of the method are to build and/or choose market indexes capable of characterizing the returns of the main securities available and to apply restricted linear state space models estimated with a Kalman filter with exact initialization. The main conclusions of this paper are the following: (1) the use of exact initialization of the Kalman filter promotes numerical stability; (2) there is no need to consider the entire set of market indicators because a subset containing only three indexes spans the relevant space of investment opportunities; and (3) the actuarial funds’ resources were primarily invested in inflation‐indexed bonds, but fund managers also left room to adjust their exposure to other assets not directly related to the objective of providing protection against inflation. Copyright © 2011 John Wiley & Sons, Ltd.     

A Multiresolution Tree-Structured Spatial Linear Model

Multiresolution spatial models are able to capture complex dependence correlation in spatial data and are excellent alternatives to the traditional random field models for mapping spatial processes. Because of the multiresolution structures, spatial process prediction can be obtained by direct and fast computation algorithms. However, the existing multiresolution models usually assume a simple constant mean structure, which may not be suitable in practice. In this article, we focus on a multiresolution tree-structured spatial model and extend the model to incorporate a linear regression mean. We explore the properties of the multiresolution tree-structured spatial linear model in depth and estimate the parameters in the linear regression mean and the spatial-dependence structure simultaneously. An expectation-maximization algorithm is adopted to obtain the maximum likelihood estimates of the model parameters and the corresponding information matrix. Given the estimated parameters, a one-pass change-of-resolution Kalman filter algorithm is implemented to obtain the best linear unbiased predictor of the true underlying spatial process. For illustration, the methodology is applied to optimally map crop yield in a Wisconsin field, after accounting for the field conditions by a linear regression.