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

By Gaussian mixture autoregressive model, the probability density and power spectrum density of non-Gaussian colored processes can be well fit. Its parameters can be exact estimated through the LS-EM algorithm discussed in this paper. After descriptions of the model and estimation problem, LS-EM algorithm is deduced. And a numerical instance is illustrated. In fact, LS-EM is an algorithm for coupling estimation of parameters between probability density and power spectrum density. Firstly, rough estimation of the latter is obtained using the conventional least squares technology and then prewhitening is applied to forecast white driving source, based on which estimation of the former is produced by the EM iteration. And then, a weighted function is founded on probability density parameter, with which the weighted least squares estimation is built up. In such a way, the accurate estimation of model parameters is obtained