混合高斯自回归模型参数估计方法之LS-EM

LS-EM Algorithm of Parameter Estimation for Gaussian Mixture Autoregressive Model

混合高斯自回归模型对有色非高斯数据的概率密度和功率谱密度进行有效的拟合,而LS-EM算法则可解决这一模型的参数估计问题.描述了混合高斯自回归模型及其参数估计问题之后,导出了具体的LS-EM算法,并给出了一组仿真实例.这是一种参数耦合估计算法,首先基于传统的最小二乘技术得到功率谱密度参数粗估计,进行预白,然后应用EM迭代得到白激励的概率密度估计,并基于此构建一加权函数,以此权函数改进最小二乘算法,进而得到模型参数的精估计.

With Gaussian mixture autoregressive model, the probability density and power spectrum density of non-Gaussian colored processes can be fit. Its parameters can be estimated through the LS-EM algorithm. Based on descriptions of the model and the estimation problem, the LS-EM algorithm is deduced. And an instance of simulation is illustrated. In fact, this is an algorithm for coupled estimation of parameters. Firstly, the rough estimation of power spectrum density parameters is obtained through the conventional least squares technology and then prewhitenning is carried out. Secondly, estimation of probability density parameters for the white driving processes is obtained through the EM iterative algorithm. Based on this, a weighted function is constructed, with which the weighted least squares estimation is built up. The accurate estimation of model parameters is obtained in succession.