Time-Varying Delay Estimation Applied to the Surface Electromyography Signals Using the Parametric Approach

Muscle Fiber Conduction Velocity (MFCV) can be calculated from the time delay between the surface electromyographic (sEMG) signals recorded by electrodes aligned with the fiber direction. In order to take into account the non-stationarity during the dynamic contraction (the most daily life situation) of the data, the developed methods have to consider that the MFCV changes over time, which induces time-varying delays and the data is non-stationary (change of Power Spectral Density (PSD)). In this paper, the problem of TVD estimation is considered using a parametric method. First, the polynomial model of TVD has been proposed. Then, the TVD model parameters are estimated by using a maximum likelihood estimation (MLE) strategy solved by a deterministic optimization technique (Newton) and stochastic optimization technique, called simulated annealing (SA). The performance of the two techniques is also compared. We also derive two appropriate Cramer–Rao Lower Bounds (CRLB) for the estimated TVD model parameters and for the TVD waveforms. Monte-Carlo simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the variance obtained is close to the derived CRBs. A comparison with non-parametric approaches of the TVD estimation is also presented and shows the superiority of the method proposed.