Legendre polynomial modeling of time-varying delay applied to surface EMG signals—Derivation of the appropriate time-dependent CRBs

Abstract

In surface electromyography (sEMG), the assessment of the muscle fiber conduction velocity (CV) can be performed by estimating the time delay between sEMG signals recorded by means of electrodes. During the dynamic contractions that often occur in daily life, the sEMG signals are not stationary which, induces time-varying delays (TVD). In the present study, the problem of TVD estimation is considered using a new parametric method. First, we propose a polynomial modeling of the TVD. The model is expressed on an orthonormal polynomial basis. Then, the TVD model parameters are estimated by using a maximum likelihood (ML) strategy solved by a stochastic optimization technique, called simulated annealing (SA).The orthogonality property allows parameter decoupling, which helps enhance the estimation accuracy. The SA algorithm helps escape local minima, thereby keeping the optimality property benefit of the ML estimator. We also derive two appropriate Cramer–Rao lower bounds (CRB) for the estimated TVD model parameters and for the TVD waveforms. Simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the mean square error (MSE) obtained is close to the derived CRBs. A comparison with nonparametric approaches of TVD estimation is also presented and shows the superiority of the method proposed.