Adaptive High Resolution Spectral Analysis with Noisy Data.
Abstract
This report summarizes the results of research during the past two years, in understanding the resolution of the autoregressive (AR) spectral estimators and developing and evaluating computationally efficient autoregressive-moving average (ARMA) spectral estimators. The loss in the resolution of the AR spectral estimator in the presence of noise is related to the appearance of zeros in the z-plane. A parallel resonator model is developed to relate the loss in resolution (bandwidth expansion) to the signal-to-noise ratio and parameters of the noiseless signal model. A new technique for the identification of the order of an AR model was derived that shows substantial stability compared to the popular Akaike Information Criterion method. Order determination was emphasized, since increase in the order of the AR spectral estimator, to account for the presence of noise, is naturally accompanied by larger variance of the estimates and appearance of spurious peaks. Several sub-optimum (non-maximum-likelihood) ARMA spectral estimators were also developed. These methods are computationally efficient, but statistically not very stable for small data records. An evaluation of the statistical properties of the different sub-optimum ARMA techniques led to the evaluation of asymptotic bounds on the variances of the estimates of the parameters or the poles and zeros of the model through the evaluation of Fisher's information matrix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1980
- Accession Number
- ADA100319
Entities
People
- M. Kaveh
Organizations
- University of Minnesota