@TechReport{ it:2004-001,
author = {Torsten S{\"o}derstr{\"o}m and Torbj{\"o}rn Wigren and
Emad Abd-Elrady},
title = {Maximum Likelihood Modeling of Orbits of Nonlinear
{ODE}s},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Systems and Control},
year = {2004},
number = {2004-001},
month = jan,
abstract = {This report treats a new approach to the problem of
periodic signal estimation. The idea is to model the
periodic signal as a function of the state of a second
order nonlinear ordinary differential equation (ODE). This
is motivated by Poincare theory which is useful for proving
the existence of periodic orbits for second order ODEs. The
functions of the right hand side of the nonlinear ODE are
then parameterized, and a maximum likelihood algorithm is
developed for estimation of the parameters of these unknown
functions from the measured periodic signal. The approach
is analyzed by derivation and solution of a system of ODEs
that describes the evolution of the Cramer-Rao bound over
time. The proposed methodology reduces the number of
estimated unknowns at least in cases where the actual
signal generation resembles that of the imposed model. This
in turn is expected to result in an improved accuracy of
the estimated parameters.}
}