相关噪声下非线性滤波及在动力定位中的应用
Application of the nonlinear filtering algorithm with a correlation noise in the dynamic positioning

针对实际系统状态估计具有互相关噪声的情况, 研究了互相关噪声下非线性系统状态估计问题. 首先基于 贝叶斯理论推导出新的互相关噪声下的贝叶斯估计算法. 然后使用三阶球面径向基(spherical-radial)规则计算贝叶 斯估计中的非线性积分, 当噪声互相关时, 基于扩展卡尔曼滤波的思想分别计算状态矩阵和观测矩阵的Jacobi矩阵, 可得互相关噪声下的容积卡尔曼滤波(cubature Kalman filtering with one-step auto-correlated and two-step crosscorrelated noise, CKF–CCN); 当噪声不相关时, 可得容积卡尔曼滤波(cubature Kalman filtering, CKF)及其平方根形 式(SCKF). 最后通过动力定位系统仿真实验, 表明提出的CKF–CCN的估计精度要高于SCKF和仅考虑一步互相关 的平方根容积卡尔曼滤波(SCKF–CN).
In view of the situation that the state estimates have correlated noise in practice, the state estimation of nonlinear system under correlation noise is studied. Firstly, the new Bayesian estimation with correlated noise is obtained based on the Bayesian theory. Secondly, the third-degree-spherical-radial rule is used to solve the nonlinear integral, if the noise is correlated then the Jacobi matrix of the state matrix and the observation matrix are computed respectively and the cubature Kalman filtering with one-step auto-correlated and two-step cross-correlated noise (CKF–CCN) is obtained; if the noise is uncorrelated then the cubature Kalman filtering (CKF) algorithm and its square root form (SCKF) are obtained. Finally, through the simulation experiment of dynamic positioning and the results illustrate that the estimation accuracy of proposed CKF–CCN algorithm is higher than the SCKF algorithm and the squared root cubature Kalman filtering algorithm which only considering one-step cross-correlated noise (SCKF–CN).