Least-squares periodic signal modeling using orbits of nonlinear ODEs and fully automated spectral analysis

Periodic signals can be modeled by means of second-order nonlinear ordinary differential equations (ODEs). 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 a fully automated spectral analysis (ASA) technique is used to eliminate these noise contributions. A simulation study shows that using the ASA technique significantly improves the performance of the least-squares estimator.