Optimal Estimation of EMG Standard Deviation (EMG $\sigma$ ) in Additive Measurement Noise: Model-Based Derivations and Their Implications

Typical electromyogram (EMG) processors estimate EMG signal standard deviation (EMGσ) via moving average root mean square (RMS) or mean absolute value (MAV) filters, whose outputs are used in force estimation, prosthesis/orthosis control, etc. In the inevitable presence of additive measurement noise, some processors subtract the noise standard deviation from EMG RMS (or MAV). Others compute a root difference of squares (RDS)-subtract the noise variance from the square of EMG RMS (or MAV), all followed by taking the square root. Herein, we model EMG as an amplitude-modulated random process in additive measurement noise. Assuming a Gaussian (or, separately, Laplacian) distribution, we derive analytically that the maximum likelihood estimate of EMGσ requires RDS processing. Whenever that subtraction would provide a negative-valued result, we show that EMGσ should be set to zero. Our theoretical models further show that during rest, approximately 50% of EMGσ estimates are non-zero. This result is problematic when EMGσ is used for real-time control, explaining the common use of additional thresholding. We tested our model results experimentally using biceps and triceps EMG from 64 subjects. Experimental results closely followed the Gaussian model. We conclude that EMG processors should use RDS processing and not noise standard deviation subtraction.