Bias Analysis in Periodic Signals Modeling using Nonlinear Odes

Authors:	Abd-Elrady Emad, Uppsala University, Sweden Soderstrom Torsten, Uppsala University, Sweden
Topic:	1.1 Modelling, Identification & Signal Processing
Session:	Nonlinear System Identification II
Keywords:	Bias, Discretization, Identification, Least squares, Nonlinear systems

Abstract

Second-order nonlinear ordinary differential equations (ODEs) can be used for modeling periodic signals. The right hand side function of the ODE model is parameterized in terms of polynomial basis functions. The least squares (LS) algorithm for estimating the coefficients of the polynomial basis gives biased estimates at low signal to noise ratios (SNRs). This is due to approximating the states of the ODE model using finite difference approximations from the noisy measurements. An analysis for this bias is given in this paper.