Intrinsic filtering on SO(3) with discrete-time observations

This paper proposes a stochastic approach to the problem of intrinsic filtering on the special orthogonal group SO(3). The continuous-time dynamics with discrete measurements problem is cast into a rigorous stochastic and geometric framework. It is shown that under some specific conditions on the noises´ distributions, the problem admits an exact time discretization. A discrete-time filter is proposed. It is a mere transposition of a linear discrete-time Kalman filter where the addition in ℝⁿ has been replaced with the group multiplication law on SO(3). The state error is proved to be a Markov chain, and not to depend on the problem inputs, as in the theory of continous-time symmetry-preserving deterministic observers on Lie groups. The gain tuning exploits the Perrin formula on rotational Brownian motion. Monte-Carlo simulations illustrate the interest of the approach.