Cumulants and genetic algorithm for parameters estimation of noncausal autoregressive models

Abstract

The authors introduce a new method for estimating the coefficients of a noncausal autoregressive (AR) model. This method is based on a new formulation that relates the unknown AR parameters to both second- and third-order cumulants. The new formulation facilitates the use of linear and nonlinear least-square estimation techniques, and includes some published works as a special case. The nonlinear least-square estimation techniques presented in this work make use of a genetic algorithm (GA) to minimize a cost function that is defined in terms of the model's output cumulants. We also introduce a new method for estimating the coefficients of a noncausal AR model using the power spectrum and a one-dimensional (1-D) slice of the bispectrum. To illustrate the effectiveness of the proposed AR modelling approaches, extensive simulation examples are presented.