Decoding the Wavelet Puzzle: Finding the Champion Mother Wavelet for Joint Impedance System Identification

Abstract

To have a better understanding of difference in characteristics between various mother wavelets, this paper presents a comprehensive investigation into the performance of three commonly used non-orthogonal mother wavelets, namely Morlet, Paul and DOG, in a wavelet-based system identification approach when used for evaluating joint impedance. This method is further modified to make the estimation result much closer to the realistic result. Additionally, the optimization of smoothing parameters is explored across ten distinct situations, encompassing diverse stiffness waveforms such as step, square, sine, triangle, and sawtooth, as well as two different input perturbations. Performance metrics, including running time, random error, bias error, total error, and variance accounted for (VAF), are used to assess the performance of the system identification method in each scenario. The result shows that Paul wavelet yields a better result of stiffness estimation together with bias error for most situations after averaging. The DOG has the shortest running time and Morlet wavelet gives the highest VAF and lowest random and total error. The findings of this study contribute to a better understanding of the strengths and weaknesses of various mother wavelets in joint impedance estimation, providing valuable insights for future applications in the field of system identification and parameter estimation in neuromechanics control.