Analytic Criteria Underlying the Full Rank Cumulant Slice Problem

Abstract

Many recent methods in system identification using higher order cumulants involve solving linear equations using Hankel matrices built from cumulant slices. Uniqueness of the solution requires a full rank Hankel matrix, which is not a generic property. Non full rank matrices result in certain poles being hidden from the cumulant data. A theoetical study of this phenomenon is presented, leading to necessary and sufficient conditions for a full rank slice. A worst-case scenario, in which a given pole cannot be identified from any cumulant slice, is successfully reduced to a parametric family of transfer functions. For cumulant orders larger than three, such constructs are restricted to first order transfer functions.