On the stability of adaptive lattice filters

A new approach to stability of adaptive filters is presented. The notion of constrained-input/constrained-output (CICO) stability is introduced as a generalization of the standard notion of bounded-input/bounded-output (BIBO) stability. This new notion involves a set of constraints on the filter data (i.e., signals and parameters) that, unlike boundedness, are specific to the filter in consideration. The set of all data that satisfy the constraints is the feasibility domain of the adaptive filter. Three particular adaptive lattice filters are analyzed: (i)Burg´s lattice, (ii)the unnormalized RLS lattice, and (iii)the normalized RLS lattice. We derive the feasibility domains of these adaptive filters and prove that they are CICO stable.