@TechReport{ it:2004-035,
author = {Emad Abd-Elrady and Torsten S{\"o}derstr{\"o}m},
title = {Bias Analysis in Least Squares Estimation of Periodic
Signals Using Nonlinear {ODE}'s},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2004},
number = {2004-035},
month = aug,
abstract = {Periodic signals can be modeled by means of second-order
nonlinear ordinary differential equations (ODE's). The
right hand side function of the ODE is parameterized in
terms of known basis functions. The least squares algorithm
developed for estimating the coefficients of these basis
functions gives biased estimates, especially at low signal
to noise ratios. This is due to noise contributions to the
periodic signal and its derivatives evaluated using finite
difference approximations. In this paper an analysis for
this bias is given.}
}