Optimal estimation of ship angular deformation for autonomous measurement by laser gyro unit

Based on the inertial attitude matching measurement equation calculated from angular increment output of a laser gyro unit(LGU), an optimal filter for implementing ship angular deformation measurement is formed with static deformation model and dynamic flexure model. In the optimal filter, by assuming that the ship angular deformation and sensor's error of LGU are stationary random process, the static deformation is modeled as the first order random walk process with white noise, and the dynamic flexure are modeled as second order Gaussian-Markov random process. The observability analyses of angular deformation by angular rate matching equation show that the estimation error of dynamic flexure is similar to laser gyro's error, and estimation error of static deformation is modulated by swing frequency and amplitude of ship motions. So the estimation error of static deformation is the main factor of optimal estimation in ship angular deformation measurement. The simulations are made by setting proper parameters of static deformation model, and the results show that the estimation error of angular deformation is lower than 10″.