Passive nonlinear observer design for ships using Lyapunov methods: full-scale experiments with a supply vessel

Dynamic positioning (DP) and tracking systems for ships are usually designed under the assumption that the kinematic equations can be linearized about a set of predeened constant yaw angles, typically 36 operating points in steps of 10 degrees, to cover the whole heading envelope. This is necessary when applying linear (Kalman lter) theory and gain scheduling techniques. However, global exponential stability (GES) cannot be guaranteed if linear theory is used. In this paper a nonlinear observer is derived. The observer is proven to be passive and GES. The number of tuning parameters is reduced to a minimum by using passivity theory. This results in a simple and intuitive tuning procedure. The proposed observer includes features like estimation of both the low-frequency position and velocity of the ship from noisy position measurements, bias state estimation (environmental disturbances) and wave ltering. The nonlinear passive observer has been simulated on a computer model of a supply vessel and implemented on full-scale ships with excellent results.