The current is considered in the conventional manoeuvering equation. This equation is represented as the nonlinear state and measurement equations in which external forces and the direction and the velocity of current are augmented as that variables. The external forces are modeled as the third-order Gauss-Markov processes and the direction and the velocity of current are assumed to be constant. The augmented state variables are estimated with extended Kalman-Bucy filter and the fixed-interval smoother. While Hwang estimated motion state variables, hydrodynamic coefficients and the current variables simultaneously by using extended Kalman filter, external forces of surge, sway and yaw and the direction and the velocity of current are the only parameters to be estimated in the estimation-before-modeling method. The current variables are satisfactorily estimated in simulation process where the measurement noise is present.