  We present a simulation scheme for simulating Brownian bridges on complete
and connected Lie groups. We show how this simulation scheme leads to absolute
continuity of the Brownian bridge measure with respect to the guided process
measure. This result generalizes the Euclidean result of Delyon and Hu to Lie
groups. We present numerical results of the guided process in the Lie group
$\SO(3)$. In particular, we apply importance sampling to estimate the metric on
$\SO(3)$ using an iterative maximum likelihood method.
