Estimation of the Parameters of an Autoregressive Process in the Presence of Additive White Noise.

摘要

It is known that the addition of white noise to an Autoregressive (AR) process produces data that can be described by an autoregressive moving-average (ARMA) model. The AR coefficients of the ARMA model are identical to the AR coefficients of the original AR process. This dissertation investigates the practicality of this model for estimating the coefficients of the original AR process. The mathematical details for this model are reviewed. Those for the autocorrelation method linear prediction (LP) algorithm are also discussed. Experimental results obtained from several parameter estimation techniques are presented. These methods include the autocorrelation method for LP and a Newton-Raphson algorithm which estimates the ARMA parameters from the noisy data. These estimation methods are applied to several AR processes degraded by additive white noise. Results show that using an algorithm based on the ARMA model for the data improves the estimates for the original AR coefficients.