Bayesian estimation of dynamic systems function expansions

Orthonormal function expansions have been used extensively in the context of linear and nonlinear systems identification, since they result in a significant reduction in the number of required free parameters. In particular, Laguerre basis expansions have been used in the context of biological/physiological systems identification, due to the exponential decaying characteristics of the Laguerre orthonormal basis, the rate of which is determined by the Laguerre parameter ¿. A critical aspect of the Laguerre expansion technique is the selection of the model structural parameters, i.e., polynomial model order for nonlinear systems, number of Laguerre functions and value of the Laguerre parameter ¿. This selection is typically made by trial-and-error procedures on the basis of the model prediction error. In the present paper, we formulate the Laguerre expansion technique in a Bayesian framework. Based on this formulation, we derive analytically the posterior distribution of the ¿ parameter and the model evidence, in order to perform model order selection. We also demonstrate the performance of the proposed method by simulated examples and compare it to alternative statistical criteria for model order selection.