An Improved Gaussian Filter for Dynamic Positioning Ships With Colored Noises and Random Measurements Loss

An improved Gaussian Filter (GF) is designed for nonlinear Dynamic Positioning (DP) ships with cross-correlated colored noises and random measurements loss. For the actual nonlinear Dynamic Position System (DPS), the state noises and measurement noises do not satisfy the assumption of Gaussian white noises and the loss of measurements may occur randomly. Therefore, the following circumstances are considered: the state noises and measurement noises are cross-correlated colored noises at the same and adjacent sampling moments; the measurement loss occurs randomly for the data transmission between the sensor units and the estimator units. In order to get the estimator for nonlinear DP ships with cross-correlated colored noises and random measurements loss, a GF framework based on Bayesian theory is proposed, and then the Cubature Mix Kalman Filter based on spherical-radial method is obtained. In the end, the simulation results show that the proposed algorithm has better estimation performance than Unscented Kalman Filter with Measurements Loss and standard Cubature Kalman Filter.

[1]  A. K. Mahalanabis,et al.  A second-order method for state estimation of non-linear dynamical systems† , 1971 .

[2]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[3]  Na Li,et al.  Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises , 2016, Inf. Fusion.

[4]  G. Chang.  Marginal unscented kalman filter for cross-correlated process and observation noise at the same epoch , 2014 .

[5]  Gang Feng,et al.  Multi-rate distributed fusion estimation for sensor networks with packet losses , 2012, Autom..

[6]  Leigh McCue,et al.  Handbook of Marine Craft Hydrodynamics and Motion Control [Bookshelf] , 2016, IEEE Control Systems.

[7]  Shen-Min Song,et al.  Alternative framework of the Gaussian filter for non-linear systems with synchronously correlated noises , 2016 .

[8]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[9]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[10]  文成林,et al.  Cubature Information Filters with Correlated Noises and Their Applications in Decentralized Fusion , 2014 .

[11]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[12]  Quan Pan,et al.  Design and implementation of Gaussian filter for nonlinear system with randomly delayed measurements and correlated noises , 2014, Appl. Math. Comput..

[13]  Anton J. Haug.  Bayesian Estimation and Tracking: A Practical Guide , 2012 .

[14]  Aurora Hermoso-Carazo,et al.  Different approaches for state filtering in nonlinear systems with uncertain observations , 2007, Appl. Math. Comput..

[15]  Yuanqing Xia,et al.  UKF-based nonlinear filtering over sensor networks with wireless fading channel , 2015, Inf. Sci..

[16]  Tristan Perez,et al.  Kinematic Models for Manoeuvring and Seakeeping of Marine Vessels , 2007 .

[17]  Jing Ma,et al.  Linear estimation for networked control systems with random transmission delays and packet dropouts , 2014, Inf. Sci..

[18]  Quan Pan,et al.  A Gaussian approximation recursive filter for nonlinear systems with correlated noises , 2012, Autom..

[19]  Long Xu,et al.  Optimal filtering for systems with finite-step autocorrelated process noises, random one-step sensor delay and missing measurements , 2016, Commun. Nonlinear Sci. Numer. Simul..

[20]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[21]  Yunmin Zhu,et al.  Optimal Kalman filtering fusion with cross-correlated sensor noises , 2007, Autom..

[22]  Ming Zeng,et al.  Distributed weighted robust Kalman filter fusion for uncertain systems with autocorrelated and cross-correlated noises , 2013, Inf. Fusion.

[23]  Raquel Caballero-Águila,et al.  Information fusion algorithms for state estimation in multi-sensor systems with correlated missing measurements , 2014, Appl. Math. Comput..