ARMA Lattice Identification: A New Hereditary Algorithm

International audienceThis paper derives an identification solution of the optimal linear predictor of ARMA type, as a time varying lattice of arbitrarily fixed dimension, for a process whose output signal only is known. The projection technique introduced here leads to an hereditary algorithm which is the adaptive extension to raw data of previous results of the authors on lattice realization from given autocorrelation functions ([1]). It produces a minimum phase linear model of the signal whose n-th order "whiteness" of the associated innovation has the following restricted meaning: orthogonality to an n-dimensional subspace memory of the past in a suitable Hil-bert sequence space. The metric of that sequence space leads to a least-squares Identification algorithm which possesses a "certainty equivalence principle" with respect to the corresponding Realization algorithm (i.e., sample correlation products replace true correlation terms). Due to the detailed state-space time-varying computations, this is possible here while avoiding the well known "side errors" from missing correlation products which usually occur in a blunt replacement of the output autocorrelation by averaged sample products. Application examples show the superiority of the hereditary algorithm over classical recursive and non-re-cursive algorithms, in terms of accuracy, adaptativity and order reduction capabilities