Gaussian-inverse gamma mixture distribution–based extended Kalman observer for dynamic positioning control system of offshore platform

Under different working conditions and control objectives, fuzzy model predictive control is used to optimize the control effect by adjusting the weight to achieve stable and accurate control for the dynamic positioning control of offshore platforms. Also, aiming at the situation where the measurement noise of dynamic positioning control may be time-varying and non-Gaussian and the statistics of the noise are not exact, this paper proposes a variational Bayesian extended Kalman filter observer. In order to model non-Gaussian noise more reasonably, the joint posterior distribution of non-Gaussian noise with state and time-varying covariance is described as the product of Gaussian and independent inverse gamma distributions. Then, the variational Bayesian (VB) method was used to simultaneously estimate the system state, the intermediate variable values of the new distribution, and the noise parameters through fixed-point iteration. The fuzzy algorithm is applied to the model predictive control, and the weight parameters of the model predictive control are adaptively changed to better adapt to the changing working conditions in the control process. The simulation results show that the variational Bayesian extended Kalman filter observer has better performance than the existing algorithms when dealing with the time-varying non-Gaussian observation noise, whose statistics are not exact. The variational Bayesian extended Kalman filter observer can significantly improve the accuracy of the control when it is used in fuzzy model predictive control.