Selection of a Time-Varying Quadratic Volterra Model Using a Wavelet Packet Basis Expansion

We consider the identification of a time-varying nonlinear system based on a single realization of the system input–output. To enable identification, the system’s time variation is approximated by a weighted sum of known basis sequences. Using wavelet packet basis sequences increases the flexibility of the model, allowing a suitable basis to be selected. A basis selection procedure is formulated using the Best Basis algorithm to choose the minimum entropy wavelet packet basis. The statistical significance of each of the chosen basis sequences is then tested using a multiple hypothesis testing procedure. Selecting individual sequences in this way achieves a specified level of confidence that the final model contains only those sequences that are significant. As an alternative, we also propose a search procedure, based on an information theoretic criterion, to select basis sequences.