Statistical subspace-based change detection residuals have been developed to infer a change in the eigenstructure of linear systems. Their statistical properties have been properly evaluated in the case of a known reference and constant noise properties. Previous residuals have favored the family of null space-based approaches, whereas the possibility of using other metrics such as the Mahalanobis distance has been omitted. This paper investigates the development and study of such a norm under the premise of a varying noise covariance. Its statistical properties have been studied and tested on a numerical example of a mechanical system.