Multi-output parameter estimation of dynamic systems by output shapes

A multi-output method of parameter estimation is introduced for dynamic systems that relies on the shape attributes of model outputs. The shapes of outputs in this method are represented by the surfaces that are generated by continuous wavelet transforms (CWTs) of the outputs in the time-scale domain. Since the CWTs also enhance the delineation of outputs and their sensitivities to model parameters in the time-scale domain, regions in the time-scale plane can be identified wherein the sensitivity of the output with respect to one model parameter dominates all the others. This allows approximation of the prediction error in terms of individual model parameters in isolated regions of the time-scale domain, thus enabling parameter estimation based on a small set of wavelet coefficients. These isolated regions of the time-scale plane also reveal numerous transparencies to be exploited for parameter estimation. It is shown that by taking advantage of these transparencies, the robustness of parameter estimation can be improved. The results also indicate the potential for improved precision and faster convergence of the parameter estimates when shape attributes are used in place of the magnitude.