C. Lageman, R. Mahony, J. Trumpf and T. Hamel

Applications in robotic autonomous systems have motivated the recently increasing interest
in observers for invariant systems on Lie groups. Here, we consider an
observer for left-invariant systems on the special orthogonal group
SO(n) with outputs invariant under the left action of SO(n) on the
output space S^{n-1}. We propose an observer construction for
these systems based on a gradient law. We give a criterion on the inputs for almost global
convergence of this observer.