Title :
Adaptive lattice IIR filtering revisited: convergence issues and new algorithms with improved stability properties
Author :
López-Valcarce, Roberto ; Pérez-González, Fernando
Author_Institution :
Dept. of Electr. & Comput. Eng., Iowa Univ., Iowa City, IA, USA
fDate :
4/1/2001 12:00:00 AM
Abstract :
Several algorithms for adaptive IIR filters parameterized in lattice form can be found in the literature. The salient feature of these structures when compared with the direct form is that ensuring stability is extremely easy. On the other hand, while computing the gradient signals that drive the direct form update algorithms is straightforward, it is not so for the lattice algorithms. This has led to simplified lattice algorithms using gradient approximations. Although, in general, these simplified schemes present the same stationary points as the original algorithms, whether this is also true for convergent points has remained an open problem. This also applies to nongradient-based lattice algorithms such as hyperstability based and the Steiglitz-McBride algorithms. Here, we answer this question in the negative, by showing that for several adaptive lattice algorithms, there exist settings in which the stationary point corresponding to identification of the unknown system is not convergent. In addition, new lattice algorithms with properties are derived. They are based on the cascade lattice structure, which allows the derivation of sufficient conditions for local stability
Keywords :
IIR filters; adaptive filters; cascade networks; iterative methods; lattice filters; numerical stability; Steiglitz-McBride algorithms; adaptive lattice IIR filtering; cascade lattice structure; convergence; direct form update algorithms; gradient signals; hyperstability based algorithm; identification; lattice algorithms; nongradient-based lattice algorithms; stability properties; stationary points; Adaptive algorithm; Adaptive filters; Convergence; Filtering algorithms; Finite impulse response filter; IIR filters; Lattices; Signal processing algorithms; Stability; Sufficient conditions;
Journal_Title :
Signal Processing, IEEE Transactions on