Fourier Series-Based Approximation of Time-Varying Parameters Using the Ensemble Kalman Filter

In this work, we propose a Fourier series-based approximation method using ensemble Kalman filtering to estimate time-varying parameters in deterministic dynamical systems. We demonstrate the capability of this approach in estimating both sinusoidal and polynomial forcing parameters in a mass-spring system. Results emphasize the importance of the choice of frequencies in the approximation model terms on the corresponding time-varying parameter estimates.