| 引用本文: | 曹小群,宋君强,张卫民,等.基于MCMC方法的Lorenz混沌系统的参数估计.[J].国防科技大学学报,2010,32(2):68-72 ,145.[点击复制] |
| CAO Xiaoqun,SONG Junqiang,ZHANG Weimin,et al.Estimating Parameters of Lorenz Chaotic System with MCMC Method[J].Journal of National University of Defense Technology,2010,32(2):68-72 ,145[点击复制] |
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| 基于MCMC方法的Lorenz混沌系统的参数估计 |
| 曹小群1, 宋君强1, 张卫民1, 蔡其发2, 张理论1 |
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(1.国防科技大学 计算机学院，湖南 长沙 410073;2.中国人民解放军61741部队，北京 100071)
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| 摘要: |
| 基于贝叶斯理论，提出用马尔科夫链蒙特卡罗(MCMC)方法来估计Lorenz混沌系统的未知参数。首先导出了未知参数分布规律的后验概率密度函数；接着采用自适应Metropolis算法构造Markov链；然后截取收敛的链序列，计算混沌系统参数的估计值。数值试验表明：该方法具有很高的估计精度，同时具有较好的抗噪声性能。 |
| 关键词: Lorenz混沌系统 参数估计 马尔科夫链蒙特卡罗方法 |
| DOI： |
| 投稿日期：2009-10-13 |
| 基金项目:国家自然科学基金资助项目(40775064；40505023) |
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| Estimating Parameters of Lorenz Chaotic System with MCMC Method |
| CAO Xiaoqun1, SONG Junqiang1, ZHANG Weimin1, CAI Qifa2, ZHANG Lilun1 |
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(1.College of Computer, National Univ. of Defense Technology, Changsha 410073, China;2.61741 Troops of PLA, Beijing 100071, China)
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| Abstract: |
| Based on Bayesian theorem, a method is proposed to estimate the unknown parameters of Lorenz chaotic system using Markov Chain Monte Carlo (MCMC) method. Firstly，the posterior probability density function for unknown parameters is deduced. Secondly, taking the posterior probability as the invariant distribution, the Adaptive Metropolis algorithm is used to construct the Markov Chains. Thirdly, the converged samples are used to calculate the mathematic expectation of the unknown parameters. The results of numerical experiments show that the parameters estimated by the new method have high precision and the noise is filtered effectively from observations at the same time. |
| Keywords: Lorenz chaotic system parameter estimation Markov Chain Monte Carlo method |
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