Nonlinear Observer Design For Ships Based On Cubature Kalman Filter

Dynamic Positioning Systems (DP Systems) are an important class of shipcontrol systems. It uses the ship’s own propulsion system allows the ship to maintain thedesired position and heading, or follow the sated trajectory. Observer is an important part ofthe DP system, with the following functions: filtering the ship’s position and attitudemeasurement noise, separating vessel high frequency and low frequency motion, estimatingship’s speed, the estimating the slowly changing environment disturbance force. This paperaims to design the nonlinear observer for DP vessels, using Cubature Kalman Filter (CKF)method.Firstly, one mathematical model of the ship dynamic positioning isestablished. Under the influence of marine environment and propeller systems force, the DPvessels, will produce complex six degrees freedom motion in the three-dimensional space. ForDP vessels, the movement can be seen as low-frequency and high-frequency motionmovement superimposed. According to its movement characteristics, ignoring heave, pitch,and roll motion of vessels, the low frequency and high frequency motion models areestablished in the horizontal plane, while a dynamic positioning measurement model isdeveloped. And a DP model in state-space form is also built. In general, using digital deviceto measure the position and heading of DP ships, the output signal is discrete ship’s positionand heading. So the DP system is a continue-discrete system, the model is continue-discretestate space model.Secondly, the marine environment force models are established, The marineenvironment force is the main factors which leading the DP ships to deviate from the desiredlocation or trajectory. In this paper, in order to better design observer, as well as computersimulation, the mathematical models of marine environmental force are developed, includingthe wind model, wave model and current model.Thirdly, according to the basic principles and methods of CKF, theSquare-Root Continue-discrete Cubature Kalman Filter (SCD-CKF) algorithm isgiven. In order to solve these problem, the model has errors and time-varying parameters, theprocess noise and measurement noise statistics characteristics are time-varying unknown, theidear of Two-Stage Bootstrap Filter is introduced into CKF algorithm, the Two-StageBootstrap Cubature Kalman Filter (TSB-CKF) algorithm is designed. In order to improve thestability of the proposed method, one square-root form of TSB-CKF algorithm is given.Meanwhile put this method into continue-discrete system filtering problem, the Square-Root Continue-Discrete Two-Stage Bootstrap Cubature Kalman Filter (SCDTSB-CKF) algorithm isderived.Next, two ship nonlinear observers are designed using the SCD-CKF andSCDTSB-CKF methods. The former applies to this situation, Ship DynamicPositioning model is accurate, sea state is constant or has minimal variation, andthe process noise and measurement noise statistical characteristics are known.The latter is designed for Ship Dynamic Positioning model has errors and time-varyingparameters, sea state changes greatly, and the process noise and measurement noise statisticalcharacteristics are time-varying unknown situation.Finally, the simulations of the two designed dynamic positioning vesselsnonlinear observers are taken. Experiment include the SCD-CKF nonlinear observersimulation, SCD-CKF nonlinear observer combined with the PID controller simulation, thesetwo simulations are include passive nonlinear observer simulation as comparison. It alsoincludes the simulation of SCDTSB-CKF nonlinear observer. Simulation results confirm thevalidity of two s designed nonlinear observers for ships...