Nonstandard methods in prediction

Recent developments in the theory and application of signal prediction are reviewed. In particular, three recently developed general methodologies for designing predictors under nonclassical operating conditions are presented. These three methodologies are robust prediction, high-speed Levinson modeling, and ACM nonlinear prediction. The first of these three methodologies deals with the design of linear predictors for situations in which the spectral model for the signal to be predicted is uncertain. In this context, a general formulation is presented through which the design of effective predictors can proceed in such situations. The second methodology involves the fitting of linear stochastic models to signals that are sampled at high rates relative to their underlying dynamics. Here, a representation of discrete-time signals based on divided-difference operators is used to develop Levinson-type algorithms that remain numerically stable in this high-speed regime. The third methodology involves the application of a family of fixed and adaptive nonlinear predictors, based on the approximate conditional mean (ACM) technique for recursive nonlinear filtering, to signals with a non-Gaussian component. This methodology is discussed in the specific context of intereference supression in wideband digital communication systems; and this is seen to be a much more effective approach to such problems than are the traditional fixed and adaptive linear prediction approaches heretofore applied in such applications.