Fast Orthogonal Algorithms for Nonlinear System Identification and Time-Series Analysis

Abstract

In this paper we consider methods of obtaining parsimonious models of physiological systems and of biological time-series data. For the application to system identification, our model takes the form of a nonlinear difference equation, whose significant terms are to be deter mined and whose coefficients estimated. The system may also be modelled by a functional expansion whose kernels (a constant, and one- and multidimensional weighting functions) are to be measured. For the application to time-series analysis, our model generally takes the form of a sinusoidal series, whose component frequencies need not be commensurate. However, we also consider series approximations using other functions, such as exponentials. For both system identification and time-series applications, we use orthogonal approaches (Korenberg, 1987, 1988) which include rapid searches for significant terms to incorporate into the model.