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On the stability of equation-error estimates of all-pole systems

It is well known that the standard equation-error (EE) method for the identification of linear systems yields biased estimates if the data are noise corrupted. Due to this bias, the resulting estimate can be unstable in some cases, depending on the spectral characteristics of the input and the noise, the signal-to-noise ratio (SNR), and the unknown system. The set of all-pole linear systems whose equation-error estimate is stable for all wide sense stationary inputs and white measurement noise is investigated. Some results concerning the structure of this set are given.