Stability of adaptive IIR predictors with nonstationary inputs

The authors consider adaptive prediction with an IIR (infinite impulse response) moving average (MA) part, controlled either by the recursive least-mean squares (LMS) algorithm or by an extended least squares (ELS) algorithm based on a posteriori errors. The predictor input is either the sum of bandpass components or a nonstationary speech sentence. The bounded input/bounded output (BIBO) stability is a major issue. Although both algorithms enjoy the self-stabilization property when the input is stationary, it is shown that with a nonstationary input the LMS algorithm can be unstable due to power jumps in the speech. The ELS algorithm always ensures BIBO stability