混合高斯概率密度模型参数的期望最大化估计

EM estimation of PDF parameters for Gaussian mixture processes

混合高斯模型是对非高斯数据进行概率密度拟合典型模型,其参数估计可以通过期望最大化(EM)迭代算法获得。多维混合高斯模型参数的EM估计因结构庞杂而难以求解,而对主动检测背景的统计特性拟合来说,一维的混合高斯模型一般即已足够。描述了该情形下的混合高斯模型及其参数估计问题之后,导出了一种工程实用的、简化的EM迭代算法,并给出了可计算机编程实现的算法流程图。然后详细探讨了对EM估计精度与速度有着重要影响的参数初始化问题,给出了三种可选择的初值设置方案:高速度方案、高精度方案和二者的折衷方案,并分析了它们各自的适用场合。最后,结合一组数值仿真实例,演示了EM迭代算法的良好的混合高斯模型参数估计性能。

Expectation-Maximization （EM） iteration is one of the most efficient algorithms for parameter estimation for Gaussian mixture model, which is a characteristic probability density function model for nonGaussian processes. In general, EM iteration for multi-dimensional Gaussian mixture is too complicated to realize in practice. Fortunately, for fitting of the background＇s probability density function in active detection, the singledimensional Gaussian mixture is adequate. Therefore, EM iteration can be simplified efticiently. In view of active detection, followed with descriptions of single-dimensional Gaussian mixture model and its parameter estimation problem, a practicable simplified EM iteration is derived. And easily programmable flowchart is proposecL Initialization is important in EM iteration. Incorrect initialization may lead to wrong convergence to improper local extreme points of the likelihood function. Three schemes for initialization are proposed for high calculating speed, high estimation accuracy, and for the compromise of the two cases. Their applications are discussed and, finally, a numerical example is given.