Model expansion applied to speech analysis and source location

A concept of model expansion that generalizes several methods already present in some time-varying autoregressive techniques is presented. These methods involve a representation of the predictors in terms of a set of mathematical functions of time. This has two effects: replacing a scalar problem by a vector one, (which is a negative effect since it increases the dimension of the model), and replacing a nonstationary problem by a time-invariant one (which is a positive effect, since it allows estimation through time averages). The generalization is an embedding technique that simplifies a nonstationary or nonlinear problem to a linear invariant problem by replacing the original signals by a larger set of signals. Three applications of this technique are given: analysis of nonstationary speech signals, location of broadband sources received on an array of equispaced sensors, and location of narrowband sources in the near field of a linear antenna