Comparison of the Ensemble Kalman filter with the Unscented Kalman filter : application to the construction of a road embankment
Comparison of the Ensemble Kalman filter with the Unscented Kalman filter : application to the construction of a road embankment
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集成卡尔曼滤波器与无迹卡尔曼滤波器的比较：在路堤施工中的应用
DOI：
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发表时间：
2008
期刊：
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通讯作者：
S. Nishimura
中科院分区：
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作者：
A. Hommels;A. Murakami;S. Nishimura
扩展卡尔曼滤波器（EKF）已被用于地质力学领域的非线性状态空间估计（村上，1991年）。然而，在过去的几年中出现了几种替代方法，即包围卡尔曼滤波器（EnKF）和无迹卡尔曼滤波器（UKF）。设计EnKF是为了解决与使用EKF相关的两个主要问题。第一个问题涉及在EKF（一阶泰勒展开）中使用近似闭合方案。第二个问题涉及与误差协方差矩阵P的存储和前向积分相关联的巨大计算要求。在EnergyKalman滤波器中，使用Monte Carlo方法随机生成的可能状态向量的集合表示状态向量的统计特性。EnKF算法不需要EKF所需的切线线性模型，并且非常容易实现。UKF声称比EKF对非线性模型具有更高的精度和鲁棒性。UKF使用一组点并通过实际的非线性函数传播这组点，而不是像EKF中那样对函数进行线性化。选择这些点，使得它们的均值、协方差以及可能的高阶矩与高斯随机变量相匹配。可以从传播的点重新计算均值和协方差，与普通函数线性化相比，产生更精确的结果。与UKF相比，EnKF的性能将在一个基于路堤施工的概念性非线性案例研究中显示。
The Extended Kalman Filter (EKF) has been used in the field of geomechanics for nonlinear state space estimation (Murakami, 1991). However a couple of alternative approaches have emerged over the last few years, namely the Ensemble Kalman filter (EnKF) and the Unscented Kalman filter (UKF). The EnKF was designed to resolve two major problems related to the use of EKF. The first problem relates to the use of an approximate closure scheme in the EKF (first order Taylor expansion). The second problem relates to the huge computational requirements associated with the storage and forward integration of the error covariance matrix P. In the Ensemble Kalman filter, an ensemble of possible state vectors, which are randomly generated using a Monte Carlo approach, represents the statistical properties of the state vector. The EnKF algorithm does not require a tangent linear model, which is required for the EKF, and is very easy to implement. The UKF claims a higher accuracy and robustness for non-linear models than the EKF. Instead of linearizing the functions as is done in the EKF, the UKF uses a set of points and propagates this set through the actual non-linear function. These points are chosen such that their mean, covariance and possibly also higher order moments match the Gaussian random variable. The mean and the covariance can be recalculated from the propagated points, yielding more accurate results compared to the ordinary function linearization. The performance of the EnKF compared to the UKF will be shown in a conceptual nonlinear case study, based on the construction of a road embankment.