Noise compensation for autoregressive spectral estimates

The autoregressive spectral estimator possesses excellent resolution properties for time series which satisfy the "all-pole" assumption. When noise is added to the time series under analysis, the resolution of the spectral estimator decreases rapidly as the signal-to-noise ratio decreases. The usual approach to this problem is to model the resulting time series by the more appropriate autoregressive-moving average process and to use standard time series analysis techniques to identify the autoregressive parameters. This standard technique, however, does not result in a positive-definite autocorrelation matrix. As a result, it is shown that the resulting spectral estimator may exhibit a large increase in variance. An alternative approach, termed the noise compensation technique, is proposed. It attempts to correct the estimated reflection coefficients for the effect of white noise, assuming the noise variance is known or can be estimated. Simulation results indicate that a significant decrease in the degrading effects of noise may be realized using the noise compensation technique.