Stochastic stability of an attitude estimation algorithm on SO(3)

We consider the impact of noise on a modification of a recently developed attitude estimation algorithm which is formulated directly as a rotation matrix tracking problem on SO(3). By means of a stochastic Lyapunov analysis we derive several results. Firstly in the presence of noise the estimation algorithm no longer converges. Rather it fluctuates in the vicinity of the true rotation matrix and angular velocity bias vector. We compute the magnitude of these fluctuations as a function of noise variance and show how they influence the choice of algorithm gains.