RECURSIVE PARAMETER-ESTIMATION OF AN AUTOREGRESSIVE PROCESS DISTURBED BY WHITE NOISE

The problem of estimating parameters of an autoregressive process based on the data corrupted by unknown white noise is considered. We shall mainly discuss two methods, the one based on the Yule-Walker equations and the other based on the modified least-squares estimation previously proposed by Sagara and Vada. The latter is based on the fact that a consistent estimator may be obtained by compensating an asymptotic bias on the least-squares estimator. An asymptotic expression of the error covariance matrix of tho latter estimator is derived by using the pcriodogram technique. In order to compare the accuracies of above two estimators, simulation results and theoretical error covariances are presented together with the corresponding Cramer-Rao bound. Simulation results indicate the correctness of the theoretical error covariance matrix. For comparison, simulation results by the bootstrap method due to Mayne and Rowe are also presented. It may be concluded that on the whole, the modified least-squares (l1LS) estimator is better than the Yule-Walker (Y-W) estimator and the bootstrap (BS) estimator. © 1979 Taylor and Francis Group, LLC.