Full Mean Square Performance Bounds on Quaternion Estimators for Improper Data

Novel physical insights are provided into the mean square performance bounds of quaternion-valued widely linear (WL), semi-widely linear (SWL), and strictly linear estimators for the generality of quaternion-valued Gaussian data. This is achieved by first defining three kinds of complementary mean square errors (CMSEs) of these estimators and by further exploiting the corresponding degrees of 'Hi-improperness (second-order noncircularity). Next,...