Before revision:  Considering a lot of measurement noise is contained in  power data and the correlation structure is complex for the residuals from power data , the approach prefers approaching the ESD of covariance matrices of the residuals through a multiplicative covariance model, which avoids making crude assumptions or simplifications on the complex structure of the data.
After revision:  Considering a lot of measurement noise is contained in the power data and the correlation structure is complex for the residuals from power data , the approach prefers approaching the ESD of covariance matrices of the residuals through a multiplicative covariance model, which avoids making crude assumptions or simplifications on the complex structure of the data.