On the double Levinson recursion formulation of ARMA spectral estimation

This paper addresses the ARMA spectral estimation problem, using as starting point, the Double Levinson Recursion Formulation proposed by Carayannis and al. in 1980 , to compute the AR parameters of an ARMA model. A theoretical analysis of the Double Levinson Recursion Formulation led to the derivation of a theorem from which the correct AR and MA orders may be computed. The algorithm is described in terms of an inner product formulation, using the theory of orthogonal polynomials. The Double Levinson Recursion Formulation is associated with a double lattice structure in a generalized Burg method fashion. When facing a purely AR process, the solution obtained is the same as that of Burg´s MEM.