Pole identification of ARMA processes by extended Levinson recursion

Very simple algorithms are available in the technical literature for identifying an AR process. The most famous of them is the Levinson recursion. The simplicity of this recursion is a consequence of the peculiar nature of the Yule-Walker equations which it solves. A similar situation does not exist in the case of ARMA processes, also for their AR parts, in spite of the fact that these parts satisfy the extended Yule-Walker equations. The closeness of the Yule-Walker equations to their extended version suggests the possibility of extending the Levinson procedure for determining the AR part of an ARMA process. A further motivation to this extension is represented by the results obtained in [1]. In the present letter we will show such an extension and we will illustrate the resulting algorithm by an example regarding a radar application.