Comparison of single and multiple time delay estimators: application to muscle fiber conduction velocity estimation
Résumé
The problem of estimating the average conduction velocity (CV) in muscle fibers is considered. The velocity is estimated from an array of noisy deterministic and unknown motor unit action potentials (MUAP) acquired by an array of K co-linear electrodes. In this array a vector of (K−1) independent time delays (TD) are to be estimated. Three velocity estimates are deduced from TD estimates: a maximum likelihood estimation (MLE) to estimate a constant velocity and two suboptimal estimates for a spatially varying velocity. The suboptimal methods consist of a postcorrelation processing in which independent linear relations between TDs in the array are exploited. From the correlation step K(K−1)/2 possible TDs are estimated (coarse estimate) followed by a refinement of these estimates subject to the linear constraints to obtain the fine estimates. By the manner of introducing the constraints we distinguish the two suboptimal methods. The CV harmonic mean is finally calculated from the fine TD estimates. The Cramér-Rao lower bound (CRLB) for the TDs and CV are derived. It is shown that the CRLB of the TD estimates is at least two times higher than the case where the signal is known. The CRLB of the velocity estimate is shown to be lower for large interelectrode distances. Numerical results show that velocity estimates are always positively biased and the smaller the estimated TD, the higher the velocity bias. The effect of an increased number of signals in the array is shown to decrease the velocity variance. Finally, the proposed methods are applied to arrays of real SEMG signals and give velocities in the range of 4.4-5.9 m/s.