Uppsala University Department of Information Technology

Technical Report 2004-035

Bias Analysis in Least Squares Estimation of Periodic Signals Using Nonlinear ODE's

Emad Abd-Elrady and Torsten Söderström

August 2004

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.

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