Stochastic system identification in SO(3)

Despite the considerable literature on attitude estimation, the kinematic models used are all deterministic. The only stochastic aspect enters through observational noise. Accordingly we introduce a stochastic kinematic model, namely an Ornstein-Uhlenbeck process that evolves in SO(3) and discuss joint estimation of angular velocity as well as noise parameters in such a context for apparently the first time. In particular we develop an estimation algorithm and also discuss for the first time convergence with probability 1 of the estimators. Neither of these issues are trivial because the manifold constraint induces underlying singularities.