非高斯环境下船变测量最大熵卡尔曼滤波方法

doi:10.12305/j.issn.1001-506X.2021.11.28

摘要/Abstract

摘要：

在进行惯性量匹配船体变形测量时, 光纤陀螺组件(Fiber Gyroscope Unit, FGU)往往暴露在复杂海况的外扰环境中, 经典卡尔曼滤波误差较大甚至出现发散。针对于此, 引入最大熵准则(Maximum Correntropy Criterion, MCC)和基于权重矩阵的加权最小二乘(Weighted Least Squares, WLS)方法改进KF迭代过程, 推导了一种用于噪声模型未知和非高斯环境中的MCC卡尔曼滤波器(MCC Kalman filter, MCCKF)。最后, 基于角速度匹配法开展多组对比实验。实验证实相较于自适应和传统MCC滤波器, 新算法无需实时调参, 抑制外扰能力更优, 可实现更高精度的变形角估计, 满足快速收敛和抗复杂外扰的鲁棒性要求。

关键词: 船体变形测量, 卡尔曼滤波, 非高斯, 最大熵准则, 加权最小二乘

Abstract:

In the process of hull deformation measurement based on inertial matching method, the conventional Kalman filter possibly causes a greater deviation or even divergence of filtering when the fiber gyroscope unit (FGU) is being exposed to a certain external environment under complex sea conditions. To solve this problem, this paper introduces a maximum correntropy criterion Kalman filter (MCCKF) used for environment under model-unknown or non-Gaussian noises based on weighted matrix, into which both the maximum correntropy criterion (MCC) and weighted least squares (WLS) are introduced to improve its iterative process. Finally, a series of comparative experiments based on angular velocity matching method are carried out. Compared with adaptive and traditional MCC Kalman filter (MCCKF) avoids timely modifying parameters and achieves more precise estimation of deformation, meets the requirements of rapid convergence, as well as stronger robustness of resisting complex disturbance.

Key words: hull deformation measurement, Kalman filter, non-Gaussian, maximum correntropy criterion (MCC), weighted least squares (WLS)

中图分类号:

TN13
TN96

龙子旋, 周琪, 彭侠夫, 张霄力. 非高斯环境下船变测量最大熵卡尔曼滤波方法[J]. 系统工程与电子技术, 2021, 43(11): 3278-3287.

Zixuan LONG, Qi ZHOU, Xiafu PENG, Xiaoli ZHANG. Maximum correntropy Kalman filter used for hull deformation measurement in non-Gaussian environment[J]. Systems Engineering and Electronics, 2021, 43(11): 3278-3287.

图/表 14

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参考文献 30

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参数变量	设定值
离散步长	滤波时长2 h(即静态变形震荡周期的2倍), 采样频率100 Hz。
船舶激励	正弦运动: 俯仰角、横摇角和航向角幅值4°、5°、3°; 摇摆周期8 s、7 s、6 s; 初始相位均为0°。
安装误差	FGU1和FGU2之间的安装误差角为: [0.08°, 0.06°, 0.04°]。
静态变形	正弦信号模拟: 幅值均为0.1°; 频率均为2π/3 600;初始相位均为0°; 角速度均方差9×10^－6 rad/s
动态变形	二阶马尔可夫: 动态不规则系数μ_i分别为0.1、0.062 5、0.062 5, 单位1/s; 动态变形方差D_i分别为4.759 8×10^-8、2.115 3×10^-8、5.876 3×10^-8, 单位rad²; 动态变形主频率λ_i分别为0.13、0.1、0.13, 单位Hz; 标准高斯白噪声ω_i, b_i²=μ_i²+λ_i²。
陀螺漂移	常值漂移: 均为ε_jc =0.005°/h。随机漂移: 随机漂移不规则系数ζ_j=1/300, 随机漂移均方差离散程度σ_j =0.01°/h。

方向	算法
方向	MCKF	MAKF	TAKF	MCCKF
X轴	-	1.582 9	1.341 2	1.948 4
Y轴	-	9.866 0	3.399 5	3.820 7
Z轴	-	2.598 2	2.476 6	2.815 0

方向	算法
方向	MCKF	MAKF	TAKF	MCCKF
X轴	-	10.048 1	9.027 9	8.250 6
Y轴	-	11.658 0	11.071 7	10.292 2
Z轴	-	10.420 3	9.921 5	9.125 0

方向	算法
方向	MCKF	MAKF	TAKF	MCCKF
X轴	-	4.959 5	1.722 7	3.360 5
Y轴	-	7.831 9	2.917 8	3.509 7
Z轴	-	8.811 7	2.240 7	3.220 2

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