| Autoregressive (AR) models have been used extensively in many areas such as radar, sonar, speech processing, econometrics, remote sensing, and so on. For noiseless AR signals, estimation methodologies have been well developed since before 1980. AR parameter estimation from noisy observations has received great attention but focus is concentrated on the stationary-white-noise case rather than colored noise. Moreover, the AR model order has been typically assumed known or correctly estimated.; This thesis develops a new AR parameter estimation approach which is robust against arbitrary noise. The model order is determined simultaneously since the AR parameters are estimated with no prior knowledge of the model order. Noise statistics are also not required, thereby allowing full flexibility with respect to the noise type and the signal-to-noise ratio. The trade-offs are a longer observation period and the requirement for a pole-classification process.; We derive two types of exact Cramer-Rao bound for the AR parameter estimates, in terms of the coefficient parameters and in terms of the pole locations, and then analyze the accuracy of AR parameter estimates. The classical Yule-Walker AR estimation accuracy is improved, when the poles lie near the unit circle, by introducing an overmodeled AR process. The AR process corrupted by arbitrary noise is approximated to a higher-order AR process and then the original AR process is estimated by selecting the true poles from among the poles of the higher-order process. This overmodeled AR idea is theoretically analyzed and practically realized by a two-stage pole-classification algorithm in the pole-zero domain. Simulations suggest that both AR estimation and order estimation are not compromised even with nonstationary colored noise. |
