In this paper the causes of errors, the error bounds and the action regions of errors in the moment method are analysized in detail. Some improvements on the accuracy of moment Solution are proposed.

Upon this frame, use matrix Lie group to express the rotation space, then base on Bayesian estimation framework, calculate the minimum mean squared error bounds which use the matrix Lie groups.

The motivation for this study is that in the area of state estimation, the Performance requirements are usually described in terms of the upper bounds on the error variance of state estimation.