共查询到20条相似文献,搜索用时 390 毫秒
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本文讨论了如下一类线性errors-in-variables模型——多元线性结构关系模型β′xk+α=0,ξk=xk+εk.{k=1,2,…,n.其中,{xk:k=1,2,…,n}为一组i.i.d.的m维随机向量,{εk:k=1,2,…,n}是i.i.d.的随机误差,E(ε1)=0,Var(ε1)=σ2Im.且{xk:k=1,2,…,n}与{εk:k=1,2,…,n}相互独立.在一些条件下,我们证明了估计量β,α,σ2的强相合性、唯一性,并给出了估计量的收敛速度为o(n-1-1q),这里q∈[1,2).对于E(x1)u1和Var(x1)Vx的估计也得出了同样的结果 相似文献
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一类是完全平方数的连整数周月英,李振亮(内蒙古乌盟师范学校)将一个自然数连写两次而得到的数,我们称其为连整数.如2323,147147等.下面给出一类完全平方数的连整数.考虑自然数an=1011(2n+1)+1(n为非负整数),易证an能被11整除,... 相似文献
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曲线造型的本征离散法 总被引:1,自引:0,他引:1
金文标 《高校应用数学学报(A辑)》1998,(Z1)
本文提出了一种基于弧长和转角这两个本质几何参数的曲线离散造型方法.该方法计算简单,几何意义明显,适用于逼近(拟合)和插值(补角),还可作出一类分形图形.其特点是一切细分操作都在转角关于弧长的对应关系图上进行. 相似文献
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本文考虑模型Yi=X^γβ+g(T)+ε,这里(X^γ,T,Y)是k+2-维随机向量,g是未知光滑函数。ε均值为零方差有限的随机误差。本文明了β的最小二乘估计是Cramer渐近有效的充要条件是误差ε服从正态分布N(0,σ^2)。 相似文献
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运用最佳非线性滤波方法及优化算法,讨论了一类不完全数据与具有连续时间的非平稳随机过程的最佳控制问题,得到了这两种状态下的两个最佳控制数学模型,给出了这类非平稳随机传递系统的最佳编码与最佳译码的建立方法,为解决这类非平稳随机过程的最佳控制提供了一种有效可靠的解决方法. 相似文献
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Kalman滤波的自适应算法 总被引:4,自引:0,他引:4
1 引 言 本文,我们讨论时不变线性随机系统 这里A、Γ和C分别是已知的n×n,n×p和q×n阶常数矩阵,1≤p,q≤n,且{ξ_k}{η_k}是均 值为零的高斯白噪声序列,有 相似文献
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刘国庆 《高等学校计算数学学报》1997,19(1):48-53
1 引言 Kalman滤波是一种用于对含有随机摄动的动态系统的最优状态估值过程。更准确地讲,Kalman滤波器是一种从受噪声干扰的观测信号中,对被观测系统的状态进行统计估值的方法,这种估值是以线性、无偏、最小方差为准则的递推估值。它被广泛地应用于空间技术、雷达、导航、通信、工业自动化、气象和地震预报、生物医学工程等领域。 虽然Kalman滤波有许多成功的应用,但是从实用角度上看它仍有一些不足。众所周知,对于一个系统模型我们往往缺少对其真正特征的认识,即系统模型中常常含有未知的参数,而这一点将严重影响滤波器的工作。 相似文献
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《Applied Mathematical Modelling》2014,38(9-10):2422-2434
An exact, closed-form minimum variance filter is designed for a class of discrete time uncertain systems which allows for both multiplicative and additive noise sources. The multiplicative noise model includes a popular class of models (Cox-Ingersoll-Ross type models) in econometrics. The parameters of the system under consideration which describe the state transition are assumed to be subject to stochastic uncertainties. The problem addressed is the design of a filter that minimizes the trace of the estimation error variance. Sensitivity of the new filter to the size of parameter uncertainty, in terms of the variance of parameter perturbations, is also considered. We refer to the new filter as the ‘perturbed Kalman filter’ (PKF) since it reduces to the traditional (or unperturbed) Kalman filter as the size of stochastic perturbation approaches zero. We also consider a related approximate filtering heuristic for univariate time series and we refer to filter based on this heuristic as approximate perturbed Kalman filter (APKF). We test the performance of our new filters on three simulated numerical examples and compare the results with unperturbed Kalman filter that ignores the uncertainty in the transition equation. Through numerical examples, PKF and APKF are shown to outperform the traditional (or unperturbed) Kalman filter in terms of the size of the estimation error when stochastic uncertainties are present, even when the size of stochastic uncertainty is inaccurately identified. 相似文献
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A Kalman type system of integral equations is obtained for the linear filtering problem in which the noise generating the signal is a fractional Brownian motion with long-range dependence. The error in applying the usual Kalman filter to this problem is determined explicitly for a simple example 相似文献
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Mohamed Atia 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2019,25(1):40-62
Sensor fusion is the art of estimating accurate information from noisy multi-sensor data. Due to the complexity of stochastic sensor errors, design and testing of sensor fusion algorithms have been always challenging. Existing design approaches are mainly mission specific with fixed system models that do not verify if the filter can estimate hidden errors. To address these challenges, this paper presents a flexible design and simulation environment for sensor fusion. The environment utilizes symbolic engine as a flexible representation of system models to enable flexible and accurate generation of linearized error models. Inverse kinematic is used to generate pseudo-error-free inertial data to test the ability of the filte to estimate sensor errors. The developed environment is demonstrated on an Attitude and Heading Reference System using Extended Kalman Filter. The demonstration includes both simulation and experimental tests. The designed filter supports both loosely and tightly coupled filtering approaches. 相似文献
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This paper considers a robust filtering problem for a linear discrete time invariant system with measured and estimated outputs. The system is exposed to random disturbances with imprecisely known distributions generated by an unknown stable shaping filter from the Gaussian white noise. The stochastic uncertainty of the input disturbance is measured by the mean anisotropy functional. The estimation error is quantified by the anisotropic norm which is a stochastic analogue of the H ∞ norm. A sufficient condition for an estimator to exist and ensure that the error is less than a given threshold value is derived in form of a convex inequality on the determinant of a positive definite matrix and two linear matrix inequalities. The suboptimal problem setting results to a set of the estimators ensuring the anisotropic norm of the error to be strictly bounded thereby providing some additional degree of freedom to impose some additional constraints on the estimator performance specification. 相似文献
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This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity, we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using "Green's method" and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results. 相似文献
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《European Journal of Operational Research》1999,115(3):555-563
Critics of the deterministic approach to efficiency measurement argue that no allowance is made for measurement error and other statistical noise. Without controlling for measurement error, the resulting measure of efficiency will be distorted due to the contamination of noise. The stochastic frontier models purportedly allow both inefficiency and measurement error. Some proponents argue that the stochastic frontier models should be used despite the limitations because of the superior conceptual treatment of noise. However, the ultimate value of the stochastic frontier depends on its ability to properly decompose noise and inefficiency. This paper tests the validity of the stochastic frontier cross-sectional models using a Monte Carlo analysis. The results suggest that the technique does not accurately decompose the total error into inefficiency and noise components. Further, the results suggest that at best, the stochastic frontier is only as good as the deterministic model. 相似文献
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卡尔曼滤波在光纤监测中的应用 总被引:1,自引:0,他引:1
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 相似文献
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The problem of nonlinear filtering of multiparameter random fields, observed in the presence of a long-range dependent spatial noise, is considered. When the observation noise is modelled by a persistent fractional Wiener sheet, several pathwise representations of the optimal filter are derived. The representations involve series of multiple stochastic integrals of different types and are particularly important since the evolution equations, satisfied by the best mean-square estimate of the signal random field, have a complicated analytical structure and fail to be proper (measure-valued) stochastic partial differential equations. Several of the above optimal filter representations involve a new family of strong martingale transforms associated to the multiparameter fractional Brownian sheet; the latter martingale family is of independent interest in fractional stochastic calculus of multiparameter random fields. 相似文献