Accuracy of the estimator of Gaussian autoregressive process

The accuracy of the estimator of the Gaussian AR process is studied depending on pole locations. Three types of AR processes, i.e., broadband AR, narrowband AR, and mixed-band AR, are defined and their theoretical limits of estimation accuracy are assessed in terms of the exact Cramer-Rao bound (CRB). The accuracy decreases as the pole closest to the origin gets closer to the origin and each coefficient parameter can show fairly different accuracy especially in the narrow-band case. The AR parameters are also estimated by applying two well-known estimation methods - the autocorrelation method and Burg´s method. A typical way of reducing the estimation variance is the averaging of multiple test-runs. But it turns out that a long data record is more important than the number of test-runs to obtain a highly accurate estimation in the narrowband case, and vice versa in the broadband case.