Application of Benveniste's convergence results in the study of adaptive IIR filtering algorithms

Abstract

It is shown that the weak convergence results of A. Benveniste et al. (IEEE Trans. Automat. Contr., vol.AC-25, p.1042-58, Dec. 1980) can be used to prove convergence of some adaptive infinite impulse response (IIR) filtering algorithms. The association of the algorithms with some ordinary differential equations for constant gains, which parallels the theory of L. Ljung et al. (1983), is suitable for constant-gain adaptive filtering applications. Convergence proofs for a prefiltering algorithm, for a simple constant-gain version of the recursive maximum-likelihood algorithm, and for the well-known simple hyperstable adaptive recursive filter (SHARF) algorithm are given as examples. >