A Variance Distribution Model of Surface EMG Signals Based on Inverse Gamma Distribution

Abstract

This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force. This paper describes the formulation of a surface electromyogram (EMG) model capable of representing the variance distribution of EMG signals. In the model, EMG signals are handled based on a Gaussian white noise process with a mean of zero for each variance value. EMG signal variance is taken as a random variable that follows inverse gamma distribution, allowing the representation of noise superimposed onto this variance. Variance distribution estimation based on marginal likelihood maximization is also outlined in this paper. The procedure can be approximated using rectified and smoothed EMG signals, thereby allowing the determination of distribution parameters in real time at low computational cost. A simulation experiment was performed to evaluate the accuracy of distribution estimation using artificially generated EMG signals, with results demonstrating that the proposed model's accuracy is higher than that of maximum-likelihood-based estimation. Analysis of variance distribution using real EMG data also suggested a relationship between variance distribution and signal-dependent noise. The study reported here was conducted to examine the performance of a proposed surface EMG model capable of representing variance distribution and a related distribution parameter estimation method. Experiments using artificial and real EMG data demonstrated the validity of the model. Variance distribution estimated using the proposed model exhibits potential in the estimation of muscle force.

An artificial EMG generation model based on signal-dependent noise and related application to motion classification

“…Then, σ 2 is represented by the sum of and ε : Assuming that ε is a random noise with a zero mean, the mean E [ σ 2 ] and variance Var [ σ 2 ] of σ 2 are calculated as follows: Considering that σ 2 > 0, the inverse gamma distribution IG( α , β ) is chosen as the distribution of σ 2 [13]: where α and β are parameters that determine the inverse gamma distribution and are referred to as the shape parameter and the scale parameter, respectively [20]. The relationships between [ α , β ] and the mean and variance of σ 2 are expressed as follows: The artificial EMG signal z t can be defined as the product of and random number series σ t , which is generated from the inverse gamma distribution determined by the mean and the variance Var [ ε ]: where is the Gaussian noise process, which has the same power spectrum as stationary EMG signals, and is generated from the following shaping filter based on an M th-order autoregressive (AR) model: where w t is white Gaussian noise with mean = 0 and variance = 1, v is the estimated variance of error, and a j ( j = 1, ⋯, M ) is the coefficient of the AR model.…”

“…Consequently, they proposed an approximate estimation method for the mean and variance of variance that utilizes the property of rectified-smoothed EMG signals [13]. Unlike [13], we propose a new method to determine and Var [ ε ] by proportional modulation with an introduced gain η : where a 0 , a 1 , ⋯, a N −1 and b 0 , b 1 , ⋯, b N are the coefficients of an N th-order low-pass filter, η is the gain for proportional variance modulation, y t is a rectified-smoothed EMG signal at t , E [ y t ] is the expectation of y t , and is the shape parameter of variance distribution. From Eqs (3) and (4), the estimated values of and Var [ ε ] correspond to the mean E [ σ 2 ] and variance Var [ σ 2 ] of σ 2 , respectively.…”

“…Hayashi et al . [13] assumed that the shape parameter is a constant within an individual regardless of muscle activation levels. However, this assumption has not been verified experimentally.…”

“…The EMG signals can be assumed to be stochastic processes with amplitudes that vary with muscle activity [6, 7]. Hence, attempts to extract the EMG signal features have been conducted by modeling their stochastic characteristics [6–13]. For example, De Luca [8] derived EMG signal features such as the mean rectified value, the root mean square value, and the variance of the rectified signals from the stochastic properties of the inter-pulse interval and the motor unit action potential train (MUAPT).…”

“…Inspired by this underlying concept, Hayashi et al . [13] expanded Hogan and Mann’s model by assuming that signal-dependent noise [14, 15] is superimposed according to muscle activation levels onto the EMG signal variance, resulting in an expression of the variance as a random variable following an inverse gamma distribution.…”