Continuous wavelet based linear time-varying system identification

A systematic framework is developed to address the parametric linear time-varying system identification problem, using the continuous wavelet transform (CWT). The system is modeled by a differential equation with unknown parameters and identified via the time–frequency representation, the ratio of the CWTs of the output and the input. The efficient execution of this system identification algorithm requires selecting appropriate scales from the wavelet transform. Scale selection can be formulated as an optimization problem: find a set of scales that contains the most information about the system’s dynamics and has high signal to noise ratio. In addition, selecting scales that have a minimum amount of redundant information is desirable. Three candidate selection metrics are presented that address these criteria and are based on an analytic investigation of the wavelet transform’s probabilistic structure. Finally, a non-linear least squares algorithm, coupled with a scale selection algorithm, is presented to identify the system model. Simulations and experiments verify this algorithm’s capability of tracking different types of model variation.