Global stability of adaptive IIR filters for nonstationary signals

This paper presents global stability of the adaptive IIR filter in a nonstationary environment. For the estimation of time-varying parameters, the normalized least-mean-square (LMS) algorithm based on the output error method is used. We assume the presence of a possibly colored and nonstationary measurement noise. The global stability analysis is carried out in a deterministic context, and it is shown that the filter output is uniformly bounded for all initial conditions. We then consider the special case when the noise is a martingale difference sequence, and establish the almost sure mean-square performance in a stochastic framework.