Estimation of all-pole model parameters from noise-corrupted sequences

Least-squares estimates of the parameters of all-pole signal models are biased when applied to noise-corrupted all-pole sequences. This bias has been shown to be proportional to the inverse of the signal-to-noise ratio. An autocorrelation-like procedure is shown to increase (under some circumstances) the signal-to-noise ratio while retaining the pole locations when the noise is white. The signal-to-noise ratio improvement varies for each mode in the all-pole sequence with modes corresponding to pole locations close to the unit circle showing the most improvement. A signal-to-noise ratio cutoff exists for each mode below which no improvement can be obtained. This cutoff depends on the proximity of the pole location to the unit circle, approaching zero as the pole nears the origin. This cutoff corresponds to the point at which a mode's spectral value just equals the level of the noise floor. This procedure can be applied recursively until an acceptable signal-to-noise ratio is obtained. The all-pole parameters can then be estimated from the processed sequence using least-squares estimation.<
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