An exact forward-backward maximum likelihood autoregressive parameter estimation method

摘要

A method for obtaining an exact maximum likelihood estimate (MLE) of the autoregressive (AR) parameters is proposed. The method is called the forward-backward maximum likelihood algorithm. Based on a new form of the log likelihood function for a Gaussian AR process, an iterative maximization is used to obtain an MLE of the inverse covariance matrix. The AR parameters are then determined via the normal equations. Experimental results comparing the new method with other popular AR spectrum estimation methods indicate the new method achieves low bias and low variance AR parameter estimates comparable with the existing methods.