In this paper we give a geometrical framework for the design of observers on
finite-dimensional Lie groups for systems which possess some specific
symmetries. The design and the error (between true and estimated state)
equation are explicit and intrinsic. We consider also a particular case:
left-invariant systems on Lie groups with right equivariant output. The theory
yields a class of observers such that error equation is autonomous. The
observers converge locally around any trajectory, and the global behavior is
independent from the trajectory, which reminds of the linear stationary case.Comment: 12 pages. Submitted. Preliminary version publicated in french in the
CIFA proceedings and IFAC0