Observer of a dynamic positioning (DP) system utilizes DP’s measurement data, to predict vessel’s velocities, positions, and unknown environmental forces on the vessel, as well as to handle model uncertainties and errors. Stability and optimality of a DP observer is important for overall DP performance. Nonlinear observer (NLO) designs usually take global asymptotic or exponential stability as the primary goal, and discard the noise. On the other hand, linearized Kalman filter (KF) algorithm, e.g. the extended Kalman filter (EKF), is optimal in minimizing the covariance of observer states by taking both measurement and process noise into account. The applied exogenous Kalman filter (XKF) algorithm in this paper, is a two-stage cascade of NLO and linearized KF, which uses the first-stage NLO estimated states as exogenous inputs for the second-stage linearized KF. XKF approach is proved to have both the stability property inherited from NLO and optimality from linearized KF. Stability and optimality of XKF based observer is studied through DP station-keeping numerical simulations.