Parametric Identification of Ship Maneuvering Motion Response Model Based on Square Root Cubature Kalman Filtering

doi:10.16182/j.issn1004731x.joss.24-0195

Abstract

Abstract:

The system identification algorithm, based on the square root cubature Kalman filter (SRCKF)is proposed to address issues such as low accuracy, poor robustness, and weak generalization ability encountered by the extended Kalman filter (EKF) algorithm in parameters identification of ship maneuvering motion models. This algorithm, within the framework of CKF, replaces the original covariance matrix with its root mean square and utilizes triangular decomposition for prediction and update to enhance identification stability. The EKF is used as a comparison algorithm to identify the parameters of the second-order nonlinear response model of a ship with rudder angles that comply with changes in the rudder servo system using the numerical simulation data solved by the fourth-order Lunger Kuta method, and the obtained identification model is subjected to a verification test of the generalisation ability. The results indicate that the SRCKF algorithm has higher identification accuracy, stability, and generalization ability than the EKF algorithm.

Key words: parameters identification, SRCKF(square root cubature Kalman filter), fourth-order Runge-Kutta method, rudder servo system, response model

CLC Number:

TP391.9

Li Qinghao, Ren Junsheng, Hua Yan. Parametric Identification of Ship Maneuvering Motion Response Model Based on Square Root Cubature Kalman Filtering[J]. Journal of System Simulation, 2024, 36(8): 1790-1799.

Figures/Tables 18

Table 1

Mariner ship model particulars

参数	数值	参数	数值
$T 1$	7.875 7	$δ r$	-0.036 993
$T 2$	0.369 4	$α$	247.117 5
$T 3$	0.378 7	$T E$	1
$K$	0.861 3	$h / d$	8.57
$L s h i p$	160.93	$L m o d e l$	3.218 6

Table 1

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 2

Solution results of maneuverability indices

参数	真实值	EKF		SRCKF
参数	真实值	辨识值	误差/%	辨识值	误差/%
$T 1$	7.875 7	5.840 3	25.844	7.870 4	0.067
$T 2$	0.369 4	0.237 6	35.680	0.344 0	6.876
$T 3$	0.378 7	0.196 3	48.165	0.370 6	2.139
$K$	0.861 3	0.690 6	19.819	0.856 4	0.569
$α$	247.117 5	180.017 6	27.153	245.391 1	0.699
$δ r$	-0.036 993	-0.032 540	12.037	-0.037 611	1.671

Table 2

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Table 3

RMSE and CC calculation results for yaw angle and position trajectory(EKF)

泛化试验	首向角/(°)		x位置轨迹/m		y位置轨迹/m
泛化试验	RMSE	CC	RMSE	CC	RMSE	CC
$10 ° / 5 °$ Z 形试验	3.952 2	0.939 4	0.273 9	1.000 0	1.243 8	0.979 9
$10 ° / 10 °$ Z 形试验	3.959 0	0.946 0	0.130 2	1.000 0	0.560 3	0.978 4
$20 ∘ / 10 °$ Z 形试验	1.609 4	0.996 6	0.201 3	1.000 0	0.472 6	0.993 7
$20 ° / 20 °$ Z 形试验	1.557 7	0.996 6	0.076 8	1.000 0	0.171 6	0.996 6
$35 °$ 旋回试验	1.290 7	1.000 0	0.133 9	0.999 8	0.214 5	0.999 7

Table 3

Table 4

RMSE and CC calculation results for yaw angle and position trajectory(SRCKF)

泛化试验	首向角/(°)		x位置轨迹/m		y位置轨迹/m
泛化试验	RMSE	CC	RMSE	CC	RMSE	CC
$10 ° / 5 °$ Z 形试验	0.310 9	0.999 7	0.009 0	1.000 0	0.098 9	0.999 9
$10 ° / 10 °$ Z形试验	0.950 3	0.997 0	0.015 5	1.000 0	0.090 1	0.998 8
$20 ° / 10 °$ Z形试验	0.323 5	0.999 9	0.027 9	1.000 0	0.049 0	0.999 8
$20 ° / 20 °$ Z形试验	0.747 3	0.999 2	0.035 8	1.000 0	0.127 0	0.998 7
$35 °$ 旋回试验	0.222 7	1.000 0	0.025 7	1.000 0	0.029 1	1.000 0

Table 4

References 15

1	张秀凤, 王晓雪, 孟耀, 等. 船舶运动建模与仿真研究进展及未来发展趋势[J]. 大连海事大学学报, 2021, 47(1): 1-8.
	Zhang Xiufeng, Wang Xiaoxue, Meng Yao, et al. Research Progress and Future Development Trend of Ship Motion Modeling and Simulation[J]. Journal of Dalian Maritime University, 2021, 47(1): 1-8.
2	Fossen T I. Guidance and Control of Ocean Vehicles[M]. New York: Wiley, 1994.
3	褚式新. 基于RLS方法的无人艇操纵性参数辨识研究[D]. 武汉: 武汉理工大学, 2020.
	Chu Shixin. Research on Parameter Identification of Unmanned Surface Vehicle Maneuverability Based on RLS Method[D]. Wuhan: Wuhan University of Technology, 2020.
4	方磊, 陈勇, 赵理, 等. 基于模糊控制的扩展卡尔曼滤波SOC估计研究[J]. 系统仿真学报, 2018, 30(1): 325-331.
	Fang Lei, Chen Yong, Zhao Li, et al. SOC Estimation with Extended Kalman Filter Based on Fuzzy Control[J]. Journal of System Simulation, 2018, 30(1): 325-331.
5	赵大明, 施朝健, 彭静. 应用扩展卡尔曼滤波算法的船舶运动模型参数辨识[J]. 上海海事大学学报, 2008, 29(3): 5-9.
	Zhao Daming, Shi Chaojian, Peng Jing. Parameter Identification to Motion Model of Ship by Extended Kalman Filter[J]. Journal of Shanghai Maritime University, 2008, 29(3): 5-9.
6	Perera Lokukaluge P, Oliveira P, Guedes Soares C. System Identification of Nonlinear Vessel Steering[J]. Journal of Offshore Mechanics and Arctic Engineering, 2015, 137(3): 031302.
7	Guan Wei, Peng Haowen, Zhang Xianku, et al. Ship Steering Adaptive CGS Control Based on EKF Identification Method[J]. Journal of Marine Science and Engineering, 2022, 10(2): 294.
8	Dong Zaopeng, Yang Xin, Zheng Mao, et al. Parameter Identification of Unmanned Marine Vehicle Manoeuvring Model Based on Extended Kalman Filter and Support Vector Machine[J]. International Journal of Advanced Robotic Systems, 2019, 16(1): 1729881418825095.
9	Zheng Jian, Yan Ming, Li Yun, et al. An Online Identification Approach for a Nonlinear Ship Motion Model Based on a Receding Horizon[J]. Transactions of the Institute of Measurement and Control, 2021, 43(13): 3000-3012.
10	Zeng Daohui, Xia Guihua, Cai Chengtao. Parameter Identification of Hydrodynamic Model of Ship Using EKF[C]//2021 China Automation Congress (CAC). Piscataway: IEEE, 2021: 1427-1432.
11	Wang Tongtong, Li Guoyuan, Wu Baiheng, et al. Parameter Identification of Ship Manoeuvring Model Under Disturbance Using Support Vector Machine Method[J]. Ships and Offshore Structures, 2021, 16(S1): 13-21.
12	Luo Weilin, Guedes Soares C, Zou Zaojian. Parameter Identification of Ship Maneuvering Model Based on Support Vector Machines and Particle Swarm Optimization[J]. Journal of Offshore Mechanics and Arctic Engineering, 2016, 138(3): 031101.
13	Wang Ning, Meng Joo Er, Han Min. Large Tanker Motion Model Identification Using Generalized Ellipsoidal Basis Function-based Fuzzy Neural Networks[J]. IEEE Transactions on Cybernetics, 2015, 45(12): 2732-2743.
14	任俊生. 船舶运动与控制[M]. 大连: 大连海事大学出版社, 2021.
15	Wang Sisi, Wang Lijun, Im Namkyun, et al. Real-time Parameter Identification of Ship Maneuvering Response Model Based on Nonlinear Gaussian Filter[J]. Ocean Engineering, 2022, 247: 110471.

[1]	Li Lin, Lin Yanlong, Zou Yanbiao. Simulation and Experiment of Friction Modeling and Compensation of Scara [J]. Journal of System Simulation, 2019, 31(8): 1572-1581.
[2]	Ning Fangxin, Xiong Yong, Mou Junmin, Huang Xingdong. Ship Maneuverability Index Identification Based AIS Data [J]. Journal of System Simulation, 2017, 29(2): 402-408.
[3]	Xu Xiaoyang, Wang Yan, Ji Zhicheng. Parameter Identification of Induction Motor Based on Tabu-chaotic Firefly Algorithm [J]. Journal of System Simulation, 2016, 28(6): 1296-1305.