A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online....A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online. For the existing IMM filtering theory, the matrix Q is determined by means of design experience, but Q is actually changed with the state of the maneuvering target. Meanwhile it is severely influenced by the environment around the target, i.e., it is a variable of time. Therefore, the experiential covariance Q can not represent the influence of state noise in the maneuvering process exactly. Firstly, it is assumed that the evolved state and the initial conditions of the system can be modeled by using Gaussian distribution, although the dynamic system is of a nonlinear measurement equation, and furthermore the EM algorithm based on IMM filtering with the Q identification online is proposed. Secondly, the truncated error analysis is performed. Finally, the Monte Carlo simulation results are given to show that the proposed algorithm outperforms the existing algorithms and the tracking precision for the maneuvering targets is improved efficiently.展开更多
EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极...EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极大似然估计(MLE)存在的困难,设计问题链启发学生探寻参数估计的数值方法,并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程,对比MLE目标函数和EM迭代目标函数,分析EM算法的内涵思想并结合图形进行直观展示,并且挖掘其中蕴含的思政元素,在知识传授的同时实现价值塑造。Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.展开更多
基金Supported by the National Key Fundamental Research & Development Programs of P. R. China (2001CB309403)
文摘A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online. For the existing IMM filtering theory, the matrix Q is determined by means of design experience, but Q is actually changed with the state of the maneuvering target. Meanwhile it is severely influenced by the environment around the target, i.e., it is a variable of time. Therefore, the experiential covariance Q can not represent the influence of state noise in the maneuvering process exactly. Firstly, it is assumed that the evolved state and the initial conditions of the system can be modeled by using Gaussian distribution, although the dynamic system is of a nonlinear measurement equation, and furthermore the EM algorithm based on IMM filtering with the Q identification online is proposed. Secondly, the truncated error analysis is performed. Finally, the Monte Carlo simulation results are given to show that the proposed algorithm outperforms the existing algorithms and the tracking precision for the maneuvering targets is improved efficiently.
文摘EM (Expectation Maximization)算法是统计学中的核心算法,也是本校近代数理统计课程教学过程中的一个重难点。论文采用案例式、启发式、研讨式教学方法,以基于高斯混合模型(GMM)的轴承退化阶段划分问题为例,引导学生发现隐变量模型极大似然估计(MLE)存在的困难,设计问题链启发学生探寻参数估计的数值方法,并总结出EM算法的一般过程。基于matlab编程可视化EM算法下的GMM模型参数更新过程,对比MLE目标函数和EM迭代目标函数,分析EM算法的内涵思想并结合图形进行直观展示,并且挖掘其中蕴含的思政元素,在知识传授的同时实现价值塑造。Expectation maximization (EM) algorithm is a core algorithm in statistics and also a key and difficult point in the teaching process of modern mathematical statistics courses in our school. The paper adopts a case-based and heuristic teaching method, taking the Gaussian Mixture Model (GMM) based bearing degradation stage division problem as an example, guiding students to discover the difficulties of maximum likelihood estimation (MLE) in the latent variable model, designing a problem chain to inspire students to explore numerical methods for parameter estimation, and summarizing the general process of EM algorithm. Based on Matlab programming, the parameter update process of GMM based on EM algorithm is visualized. Comparing the MLE objective function and EM iteration objective function, the intrinsic thought of EM algorithm is analyzed and visually displayed with graphics. The ideological and political elements are also explored, so as to achieve value shaping while knowledge transmission.
