2.5.2 Composition of uncertain rotations

Given two Gaussian distributions on rotation, we can compose the two uncertain transformations using the adjoint. Let one mean-covariance pair be $\left(\mathbf{R}_{0},\boldsymbol{\Sigma}_{0}\right)$ and the other be $\left(\mathbf{R}_{1},\boldsymbol{\Sigma}_{1}\right)$. Then the distribution of rotations by first transforming by $\mathbf{R}_{0}$ and then by $\mathbf{R}_{1}$ is given by:

$$\left(\mathbf{R}_{1},\boldsymbol{\Sigma}_{1}\right)\circ\left(\ma... ...a}_{1}+\mathbf{R}_{1}\cdot\boldsymbol{\Sigma}_{0}\cdot\mathbf{R}_{1}^{T}\right)$$ (40)