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Topological properties of least-squares error surfaces for adaptive IIR filters

In this paper, a new framework for understanding the performance of adaptive IIR filters is proposed and shown to enhance the understanding of filter stability during adaptation in time- varying data environments. This new understanding arises from considering the error surface as defined by the data, rather than the statistics of the data, in a manner analogous to that used to develop recursive least squares (RLS) FIR adaptive filters. The stability of the filter is shown to be dependent on the problem formulation. Defining the time-varying error surface using frequency domain, rather than time domain, methods is shown to result in substantially better stability structure in the performance surface.