Structured maximum likelihood autoregressive parameter estimation

A novel method for the maximum likelihood estimation of autoregressive process parameters is presented. The approach is suited to applications in which the available data vector length is of the same order of magnitude as the autoregressive process model order, and it provides more accurate results than approximate methods that yield the maximum likelihood estimates only in the limit of long data records. The difficult nonlinear optimization problem is approached by first recursively solving for the maximum likelihood estimates of the data covariances subject to certain structural constraints, and then using these estimates in the Yule-Walker equations to obtain the autoregressive process parameter estimates. Experimental results demonstrate the potential of the method for autoregressive process power spectral density estimation using short data records