林孝工 焦玉召 聂君

摘 要：實际系统中的噪声具有一定的相关性，通常不满足独立高斯白噪声的假设。研究了具有相关噪声的动力定位船舶艏向估计问题，首先建立船舶艏向运动状态方程，假设状态噪声和测量噪声是一步自相关和两步互相关的。然后基于新息分析的方法，通过使用投影定理，分别计算出滤波增益矩阵和预测增益矩阵，建立状态预测更新方程和估计误差协方差预测更新方程。最后，通过状态预测值，得到对应的状态估计值，进而得到了一种相关噪声下的滤波算法。通过仿真实验，进一步验证了所提算法的有效性。

关键词：船舶艏向；互相关噪声；新息分析；状态估计；卡尔曼滤波

DOI：10.15938/j.emc.（编辑填写）

中图分类号：U 666.1 文献标志码：A 文章编号：1007 -449X（2018）00-0000-00（编辑填写）

Abstract： The noise in the actual system has some relevance and does not satisfy the usual assumption of independent Gauss white noise. The problem of heading estimation for dynamic position ships with cross-correlated noises is studied. Firstly， the equation of state of ship's heading motion is established. It is assumed that the state noise and measurement noise are one step auto-correlated and two-step cross-correlated. Then， based on the method of innovation analysis， the filter gain matrix and the prediction gain matrix are calculated respectively by using projection theorem， and the state prediction update equation and the estimation error covariance update equation are established. Finally， the state estimation value of the head is obtained by the corresponding state prediction， and the filtering algorithm for system with cross-correlated noise is derived. The effectiveness of the proposed algorithm is further verified by simulation experiments.

Keywords： ship heading； cross-correlated noise； innovation analysis； state estimation； Kalman filter