Our simulation experiments show that the bit-error-ratio (BER) of these new detectors is much lower than that of decorrelation, minimum mean-squared error and multistage detectors.

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.

Extend the expressions of the minimum mean squared error bounds of the references, and give the relations of the minimum mean squared error bounds of pose Angle and noise standard deviation.