Jump-diffusion processes on matrix Lie groups for Bayesian inference

A variety of engineering problems can be studied as inferences on constrained sets, Lie groups in particular. Additionally, the number of parameters to be estimated, namely the model-order, may also be unknown a-priori. We present a Bayesian approach by building a posterior probability distribution on a countable unions of Lie groups and utilizing the jump-diffusion processes to generate optimal estimators empirically, under this posterior. This approach is presented in the context of two well-known problems: pose estimation in object recognition and subspace estimation in signal processing.