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．     

Modeling of non-stationary ground motion using the mean reverting stochastic process

This paper presents a new method for modeling amplitude and frequency non-stationary earthquake ground motions using a scalar first order dynamic mean reverting stochastic differential equation driven by Brownian motion with parametric time varying coefficients. It determines the proper relationship between these time varying parametric coefficients and presents the statistical and probability distribution characteristics of the response solution. It demonstrates the applicability of the method by presenting some simulations of amplitude and frequency non-stationary earthquake ground motions. The verification of the amplitude and frequency non-stationary contents of the mean reverting stochastic ground motions is demonstrated using the Hilbert–Huang transform method. Also a corresponding interpretation between the coefficients of the proposed model and the coefficients of the usual oscillatory second order differential equation driven by white Gaussian noise is presented along with some comments how it can be applied to simulate ground motions consistent with acceleration target records such as boxcar, trapezoidal, other exponential functions, or compound and target records at source, near field, and far field distances.     

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.     

Pattern recognition based Kalman filter for indoor localization using TDOA algorithm

In this paper, we will present a motion pattern recognition based Kalman filter (PRKF), and apply it to the time difference of arrival (TDOA) algorithm of indoor localization. The state matrix in Kalman filter (KF) is determined by the motion pattern which the target node is supposed to act, and this will bring new system error if the assumption is not correct. Considering this, we first create three fuzzy sets using three KFs whose state matrix stand for different motion patterns, then linearly combined the memberships of a target node of the fuzzy sets. Finally, simulation results show that the PRKF can enhance the localization accuracy about more than 20%.     

Time-Varying Parameters Prediction

This paper develops a method of adaptive modeling that may be applied to forecast non-stationary time series. The starting point are time-varying coefficients models introduced in statistics, econometrics and engineering. The basic step of modeling is represented by the implementation of adaptive recursive estimators for tracking parameters. This is achieved by unifying basic algorithms—such as recursive least squares (RLS) and extended Kalman filter (EKF)—into a general scheme and next by selecting its coefficients with the minimization of the sum of squared prediction errors. This defines a non-linear estimation problem that may be analyzed in the context of the conditional least squares (CLS) theory. A numerical application on the IBM stock price series of Box-Jenkins illustrates the method and shows its good forecasting ability.     

A simple smoothing spline,III

Summary  Computational methods for spline smoothing are studied in the context of the linear smoothing spline. Comparisons are made between two efficient methods for computing the estimator using band-limited basis functions and the Kalman filter. In particular, the Kalman filter approach is shown to be an efficient method for computing under the Kimeldorf-Wahba representation for the estimator. Run time comparisons are made between band-limited B-spline and Kalman filter based algorithms.     

New approach to applying neural network in nonlinear dynamic model

In this work, radial basis function neural network (RBF-NN) is applied to emulate an extended Kalman filter (EKF) in a data assimilation scenario. The dynamical model studied here is based on the one-dimensional shallow water equation DYNAMO-1D. This code is simple when compared with an operational primitive equation models for numerical weather prediction. Although simple, the DYNAMO-1D is rich for representing some atmospheric motions, such as Rossby and gravity waves. It has been shown in the literature that the ability of the EKF to track nonlinear models depends on the frequency and accuracy of the observations and model errors. In some cases, just fourth-order moment EKF works well, but will be unwieldy when applied to high-dimensional state space. Artificial Neural Network (ANN) is an alternative solution for this computational complexity problem, once the ANN is trained offline with a high order Kalman filter, even though this Kalman filter has high computational cost (which is not a problem during ANN training phase). The results achieved in this work encourage us to apply this technique on operational model. However, it is not yet possible to assure convergence in high dimensional problems.     

The extended Kalman Filter and the unscented Kalman Filter for Material Parameter Identification with Application in Tunneling

We present in this work the use of the extended Kalman filter (EKF) and unscented Kalman filter (UKF) for identification of constitutive material parameters with application in mechanized tunneling. Although both filters are based on the principle of recursive least squares estimation, one differs from another in terms of where approximation is made. Whereas in the EKF first-order Taylor series expansion is used to approximate the nonlinear modeling equation, in the UKF approximation of the probability density of the state is made using a small number of well defined points. To validate the methods, we performed parameter identification of the Hardening Soil constitutive model used for describing the soil behavior in an tunnel excavation model. Both methods showed fast and stable convergence of the considered soil parameters - the four parameters of the Hardening Soil model. Although the EKF requires less number of forward calculations of the numerical model, the UKF is favored since it does not require calculation of the derivatives of the observables with respect to the identifying parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An intensity‐based approach for equity modeling

This paper analyzes an intensity‐based approach for equity modeling. We use the Cox–Ingersoll–Ross (CIR) process to describe the intensity of the firm's default process. The intensity is purposely linked to the assets of the firm and consequently is also used to explain the equity. We examine two different approaches to link assets and intensity and derive closed‐form expressions for the firms' equity under both models. We use the Kalman filter to estimate the parameters of the unobservable intensity process. We demonstrate our approach using historical equity time series data from Merrill Lynch. Copyright © 2011 John Wiley & Sons, Ltd.     

股票指数的时间序列模型分析

借助于SA S软件将工程中的K a lm an滤波方法与时间序列的状态空间模型结合对上海A股指数进行了拟合与预测分析,通过对拟合与预测误差的计算可以发现这种模型是可行的;然后还把与滤波结合的状态空间模型的分析结果和常见的时间序列模型如:AR IM A模型、逐步自回归模型以及指数平滑模型的分析结果进行比较,比较的结果说明结合滤波的状态空间模型分析的结果比后三种的结果更加精确.结果为时间序列数据分析提供了一个较好的分析工具.     

基于单目视觉的SLAM算法研究

利用一种新型的人工路标系统-MR二维码,提出了基于单目视觉和里程计的SLAM方法.首先介绍了MR二维码系统,然后在对机器人运动模型和视觉传感器观测模型进行分析和验证的基础上,给出了一种实用的里程计位置估计误差模型.机器人移动过程中,利用扩展卡尔曼滤波器对视觉信息与里程计信息进行融合.在室内环境下进行了实际实验,实验结果表明该算法可提高机器人定位和构建地图的精度,验证了算法的有效性.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

Source mechanism model for ground motion simulation

A simple analytical model for computing ground motion in a layered half-space due to a buried seismic source is presented in this paper. The buried earthquake source is represented as a distribution of double couples varying in time as a ramp function on the fault plane. The analysis is simplified by first decoupling the governing equations into P-SV and SH problem by a coordinate transformation in the frequency-wave number domain. These two problems are solved separately and the final solution is obtained by the sum of solutions of these individual problems. Explicit expressions for ground motion in a layered half-space due to an impulsive double couple are derived. In the sequel, Green’s function for the displacement field in an infinite medium is also presented. The developed source mechanism model is also demonstrated by simulating ground motion for the Kucth earthquake (M_w = 7.7) of 26th January 2001.     

多传感器数据融合与航迹预测

多传感器数据融合技术是未来军事电子领域一个重要趋势.根据6个观测雷达的观测数据进行了数据融合算法的研究.在提取目标航迹对时,对每个雷达的数据依据一定的判定条件(时间变化,角度变化在一定范围内等),分别提取出不同的目标航迹对.在提取同一目标的航迹对时,先将目标航迹的一些异常点弃除,然后把时间重合的两段航迹提取出来,通过样条插值进行时间配准,共提取出多条相关的航迹组有3组.在使用雷达探测目标时,由于技术条件和方法等的限制,使雷达数据存在各种误差.利用卡尔曼滤波自适应算法估计出观测位置的噪声方差,对雷达偏差进行修正后,采用联合卡尔曼滤波算法对多条航迹进行融合,接着利用ARMA模型预测目标在未来10秒内的轨迹,最后,对目标在被锁定后的轨迹做出预测,结合导弹的爆炸范围求得导弹击中飞机的概率约为49.54%.     

Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems

An unscented filtering algorithm is derived for a class of nonlinear discrete-time stochastic systems using noisy observations which can be randomly delayed by one or two sample times. The update and the possible delays (of one and two sampling times) of any observation are modelled by using three Bernoulli random variables such that only one of them takes the value one. The algorithm performs in two-steps, prediction and update, and it uses a scaled unscented transformation to approximate the conditional mean and covariance of the state and observation at each time. The performance of the proposed filter is shown in a simulation example which uses a growth model with randomly delayed observations; in this example, the proposed filter is compared with the extended one obtained by linearizing the state and the observation equations and, also, with the unscented Kalman filter. A clear superiority of the proposed filter over the others is inferred.     

Likelihood-Based Analysis of Linear State-Space Models Using the Cholesky Decomposition

Data associated with the linear state-space model can be assembled as a matrix whose Cholesky decomposition leads directly to a likelihood evaluation. It is possible to build several matrices for which this is true. Although the chosen matrix or assemblage can be very large, rows and columns can usually be rearranged so that sparse matrix factorization is feasible and provides an alternative to the Kalman filter. Moreover, technology for calculating derivatives of the log-likelihood using backward differentiation is available, and hence it is possible to maximize the likelihood using the Newton–Raphson approach. Emphasis is given to the estimation of dispersion parameters by both maximum likelihood and restricted maximum likelihood, and an illustration is provided for an ARMA(1,1) model.     

基于多小波预测方法提高地震数据的信噪比

基于二维小波变换把一个二元的地震数据变换为有关时间,空间,频率和波数的局部信息的特点,讨论了用正交多小波变换和w-x预测方法对地震数据进行去噪处理.先用阈值的方法做初步处理,再用预测方法进一步压制噪声,达到较好地提高地震数据信噪比的目的.数值试验表明该方法是有效的,能有效地消除随机干扰,具有很好的空间和时间自适应性.     

考虑空间效应的多支撑管线随机地震响应分析

提出了一种能考虑地震动空间变化效应的多支撑管线随机地震响应分析的解析方法.证明了多点地震作用下结构的平稳随机响应分析可转化为求解支座简谐运动时的确定性响应,直接给出了含有待定系数的简谐响应的形式,并通过边界条件和连续性条件建立待定系数的求解方程.与拟静位移分解法相比,该方法不用计算结构的振型以及拟静位移分量,完全是基于解析推导,因此在计算效率方面优势明显.数值算例中,采用该方法和拟静位移分解法计算了一个6跨管线在空间多点地震作用下的随机响应,对比验证了方法的正确性和高效性.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

两种时变参数方法估算全要素生产率研究

本文详细介绍了两种时变参数方法估算全要素生产率,相对于传统方法而言,时变参数方法可能更符合实际情况.两种方法中,卡尔曼滤波方法由于对参数初值的依赖性较小,相对较为方便,尤其对于存在不可观测的参数时,具有较大的优越性。多层递阶方法较多的依赖于初值的选择,但是对于某些问题,其残差较卡尔曼滤波小,因此两种方法结合运用,效果较好.