Cramer-Rao lower bounds for estimating the time-varying delay of surface EMG signals

The muscle fiber conduction velocity (CV) is usually used as a muscle fatigue indicator. The CV evaluation can indirectly be performed by estimating the time delay between surface electromyography (sEMG) signals recorded on electrodes aligned with the muscle fiber direction. To take into account the variability of the CV along the fiber and between channel recordings, the recently published methods assume that the time delay between the channels is a function depending on time. In the present paper, we derive the theoretical Cramer-Rao Bound (CRB) appropriate for estimating the time-varying delay of sEMG signals. The new CRB expression is computed for a polynomial model of the time-varying delay and for two channels. We emphasize the relationship between this new CRB expression and the classical CRB calculated for a constant time delay. Monte Carlo simulations are conducted to assess the performance of the maximum likelihood estimator of the time-varying delay. The likelihood maximization is achieved by using a stochastic optimization technique called the simulated annealing. The simulation results show the CRB derived very optimistic.