Maximum Likelihood Estimation of Motor Unit Firing Pattern Statistics

Estimation of motor unit firing pattern statistics is a valuable method in physiological studies and a key procedure in electromyographic (EMG) decomposition algorithms. However, if any firings within the pattern are undetected or missed during the decomposition process, the estimation procedure can be disrupted. In order to provide an optimal solution, we present a maximum likelihood estimator of EMG firing pattern statistics, taking into account that some firings may be undetected. A model of the inter-discharge interval (IDI) probability density function with missing firings has been employed to derive the maximum likelihood estimator of the mean and standard deviation of the IDIs. Actual calculation of the maximum likelihood solution has been obtained by means of numerical optimization. The proposed estimator has been evaluated and compared to other previously developed algorithms by means of simulation experiments and has been tested on real signals. The new estimator was found to be robust and reliable in diverse conditions: IDI distributions with a high coefficient of variance or considerable skewness. Moreover, the proposed estimator outperforms previous algorithms both in simulated and real conditions.