Gaussian mixture density modeling of non-Gaussian source for autoregressive process

A new approach is taken to model non-Gaussian sources of AR processes using Gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions. A maximum likelihood estimation algorithm is derived for estimating the AR parameters by solving a generalized normal equation, and a clustering algorithm is used for estimating the parameters of Gaussian mixture density of the source signals. The correlation matrix of the generalized normal equation is not Toeplitz but is symmetric and in general positive definite. Higher order statistics of skewness and kurtosis are used for identifying the source distribution as being Gaussian or non-Gaussian and, consequently, determining the parameter estimation technique between the conventional method and the proposed method. Experiments on non-Gaussian source AR processes demonstrate that under high SNR conditions (SNR⩾20 dB), the proposed algorithm outperforms the conventional AR estimation algorithm and the cumulant-based algorithm by an order-of-magnitude reduction of average estimation errors. The proposed algorithm also has very low estimation errors with short data records. Finally, a maximum likelihood prediction method is formulated for non-Gaussian source AR processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding