Estimation of Models for Systems having Deterministic and Random Disturbances

Abstract The most common model employed in time series analysis and system identification is the well known ARMAX model having relatively prime A, B, C polynomials. However, this model does not account for purely deterministic disturbances such as sinewaves. The model can be generalized to handle this latter case, but in this situation, A, B, C are no longer relatively prime. Instead they have common (uncontrollable) roots on the stability boundary. This paper will present a new algorithm for parameter estimation in these non-minimal ARMAX models. Emphasis will be given to the problem of estimating multiple sinewave frequencies in noise. The effect of low signal to noise ratios and optimal sampling strategies will be considered. Simulation results are included.

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