不連続な時間変化を追従する非線形適応フィルタに関する考察

概要

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It has been a kind of common sense that adaptive filters can only track time-varying systems of witch the time varying rate is comparable with the convergence time of the adaptive algorithms. On the other hand, it is known that abrupt or discontinuous changes can occur in smooth systems, which proved to be results of discontinuous bifurcation of equilibrium sets. Prediction of such changes is often of vital importance in practices but also a very hard task since one needs global information about the unknown systems. Below, we show a method to predict such discontinuity by nonlinear adaptive prediction. In the first place, we locally approximate the error criterion and its equilibrium set by nonlinear ADF, then we predict their local shapes by nonlinear extrapolation of the trajectory of the parameters. By test the type of singularity of the equilibrium set, we can tell whether there will be any risk of discontinuous time variances.
1995-09-05