Time-varying system identification and model validation using wavelets

Parametric identification of time-varying (TV) systems is possible if each TV coefficient can be expanded onto a finite set of basis sequences. The problem then becomes time invariant with respect to the parameters of the expansion. The authors address the question of selecting this set of basis sequences. They advocate the use of a wavelet basis because of its flexibility in capturing the signal´s characteristics at different scales, and discuss how to choose the optimal wavelet basis for a given system trajectory. They also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system´s time-variation. By formulating the problem as a regressor selection problem, they apply an P-test and an AIC based approach for multiresolution analysis of TV systems. The resulting algorithm can estimate TV AR or ARMAX models and determine their orders. They apply this algorithm to both synthetic and real speech data and compare it with the Kalman filtering TV parameter estimator