A nonlinear output feedback trajectory tracking control of dynamic positioning ships with only position and
orientation measurements is considered in this paper. In the earth-fixed frame, both of Coriolis and centripetal forces and
nonlinear damping are taken into account in ship maneuvering modeling, a nonlinear backstepping observer-controller with
semi-global uniform exponential stability is proposed, and the stability is proved by using Lyapunov method. Both of the
theoretical analysis and the simulation results show that the system errors converge to zero by tuning controller gains.