林孝工 焦玉召 聶君

摘 要：實際系統(tǒng)中的噪聲具有一定的相關(guān)性，通常不滿足獨立高斯白噪聲的假設(shè)。研究了具有相關(guān)噪聲的動力定位船舶艏向估計問題，首先建立船舶艏向運動狀態(tài)方程，假設(shè)狀態(tài)噪聲和測量噪聲是一步自相關(guān)和兩步互相關(guān)的。然后基于新息分析的方法，通過使用投影定理，分別計算出濾波增益矩陣和預(yù)測增益矩陣，建立狀態(tài)預(yù)測更新方程和估計誤差協(xié)方差預(yù)測更新方程。最后，通過狀態(tài)預(yù)測值，得到對應(yīng)的狀態(tài)估計值，進而得到了一種相關(guān)噪聲下的濾波算法。通過仿真實驗，進一步驗證了所提算法的有效性。

關(guān)鍵詞：船舶艏向；互相關(guān)噪聲；新息分析；狀態(tài)估計；卡爾曼濾波

DOI：10.15938/j.emc.（編輯填寫）

中圖分類號：U 666.1 文獻標(biāo)志碼：A 文章編號：1007 -449X（2018）00-0000-00（編輯填寫）

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