ARMA spectral estimation of narrow-band processes via model reduction

The problem of estimating autoregressive moving average ARMA models for narrowband processes is considered. The following approach is proposed. Estimate a high-order autoregressive (AR) approximation of the process. By model reduction, based on a truncated internally balanced realization or optimal Hankel-norm model reduction, reduce the order of this high-order AR estimate to find a lower-order ARMA model. This algorithm gives ARMA spectral estimates with excellent resolution properties, without using iterative numerical minimization methods as for the maximum-likelihood method. How to take the narrowband assumption into account in the model reduction step is discussed in detail.>