Platform Path Optimization Method Based on Cumulative Detection Probability of Sonar Search

doi:10.16182/j.issn1004731x.joss.23-0953

Abstract

Abstract:

To address the lack of research on the optimal path of mobile search platform to search for moving targets, this paper proposes a path optimization method of mobile search platform based on cumulative search probability theory. Based on the cumulative detection probability (CDP), one of the important criteria of sensor performance evaluation, a single-peak CDP calculation formula is constructed by using a time series correlation model, namely the ( $λ$ , $σ$ ) process model. A set of target motion scenarios are constructed, and the trajectory probability of target scenarios and their CDP at different time are corrected by Bayesian posterior probability. Considering the maximum CDP at the completion of the search and the shortest time for CDP to reach the target level as multi-objectives, a path optimization model for sonar searching moving targets is constructed to realize efficient search in continuous time and continuous space, and the optimal solution is provided by utilizing the multi-objective genetic algorithm. Through comparison with CDP results in random search mode, it can be found that the optimization method proposed in this paper can obtain a higher CDP, and the search scheme obtained has better efficiency advantages than that obtained from single-objective optimization.

Key words: sonar search, cumulative detection probability(CDP), path optimization, multi-objective optimization, genetic algorithm

CLC Number:

TP391.9

Wei Xiang, Liu Xingxuan, Fu Dianzheng, Yang Tianji, Yang Jiaxuan. Platform Path Optimization Method Based on Cumulative Detection Probability of Sonar Search[J]. Journal of System Simulation, 2024, 36(11): 2674-2683.

Figures/Tables 10

Table 1

Symbol list

序号	符号	含义
1	P	声纳瞬时搜索概率
2	r	搜索平台与目标的距离
3	r_max	理论最大搜索距离
4	v	搜索平台与目标的相对移动速度
5	x	搜索平台与目标运动轨迹的最小距离
6	Δt	声纳扫描的间隔
7	P_k	第k次扫视的瞬时搜索概率
8	F	一次航路捷径的累积探测概率
9	λ	信号跳跃的速率
10	v_t	目标运动速度
11	ps_i	第i个航路轨迹权重
12	v_s	搜索平台运动速度
13	S_j	搜索方案中的航路点
14	T_j	搜索平台运动到航路点的时间
15	θ	搜索平台与目标航向的夹角
16	ps_i^*	贝叶斯后验轨迹权重
17	$c d p t = T j$	到T_j 时刻搜索方案的累积探测概率
18	t^*	实现cdp≥0.9的最短时间
19	w	任务区域宽度
20	s	任务区域长度
21	N	搜索方案的最大折数
22	η	最大CDP未达到0.9的惩罚因子

Table 1

Fig. 1

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References 16

1	薛洪展, 宋业新. 具有多条搜索路线和有限个搜索概率的舰潜搜索对策问题研究[J]. 兵器装备工程学报, 2016, 37(2): 15-17.
	Xue Hongzhan, Song Yexin. Research on Problem of Search Game with Multiple Search Routes and Limited Search[J]. Journal of Ordnance Equipment Engineering, 2016, 37(2): 15-17.
2	Morin Michael, Abi-Zeid Irène, Quimper Claude-Guy. Ant Colony Optimization for Path Planning in Search and Rescue Operations[J]. European Journal of Operational Research, 2023, 305(1): 53-63.
3	Wagner DH, Mylander WC, Sanders TJ. 海军运筹分析[M]. 姜青山, 郑保华, 译. 3版. 北京: 国防工业出版社, 2008.WagnerDH, MylanderWC, SandersTJ. Naval Operations Analysis[M]. Translated by Jiang Qingshan, Zheng Baohua. 3rd ed. Beijing: National Defense Industry Press, 2008.
4	Raap Manon, Preuß Michael, Meyer-Nieberg Silja. Moving Target Search Optimization-A Literature Review[J]. Computers & Operations Research, 2019, 105: 132-140.
5	罗木生, 栾江华, 赵鑫业, 等. 反潜直升机吊放声纳巡逻线上搜潜概率建模[J]. 火力与指挥控制, 2022, 47(10): 99-102, 107.
	Luo Musheng, Luan Jianghua, Zhao Xinye, et al. Modeling Search Probability of Anti-submarine Helicopter Using Dipping Sonar at Patrol Line[J]. Fire Control & Command Control, 2022, 47(10): 99-102, 107.
6	张会, 王安, 程健, 等. 舰船往返拦截搜索发现概率计算公式的推导、检验和修正[J]. 陆军工程大学学报, 2022, 1(1): 54-59.
	Zhang Hui, Wang An, Cheng Jian, et al. Derivation, Examination and Revision of Calculation Formula for Detection Probability of Ship Round-trip Interception Search[J]. Journal of Army Engineering University of PLA, 2022, 1(1): 54-59.
7	罗光成, 黄建强, 张丹. 吊放声纳扇形搜索效能建模与仿真[J]. 国外电子测量技术, 2012, 31(5): 56-58.
	Luo Guangcheng, Huang Jianqiang, Zhang Dan. Modeling and Simulation the Efficiency of the Dipping Sonar Based on Sector Searching[J]. Foreign Electronic Measurement Technology, 2012, 31(5): 56-58.
8	李晔, 姜言清, 张国成, 等. 一种基于电子海图的欠驱动AUV区域搜索方案[J]. 机器人, 2014, 36(5): 609-618.
	Li Ye, Jiang Yanqing, Zhang Guocheng, et al. An Underactuated AUV-Oriented Region Search Method Based on Electronic Chart[J]. Robot, 2014, 36(5): 609-618.
9	徐梁, 潘宣宏, 吴铭. 有人/无人机协同反潜作战模式探析[J]. 中国舰船研究, 2018, 13(6): 154-159.
	Xu Liang, Pan Xuanhong, Wu Ming. Analysis on Manned/Unmanned Aerial Vehicle Cooperative Operation in Antisubmarine Warfare[J]. Chinese Journal of Ship Research, 2018, 13(6): 154-159.
10	Wu Yu, Kin Huat Low, Chen Lü. Cooperative Path Planning for Heterogeneous Unmanned Vehicles in a Search-and-track Mission Aiming at an Underwater Target[J]. IEEE Transactions on Vehicular Technology, 2020, 69(6): 6782-6787.
11	刘志浩, 刘彦伯, 黄波. UUV水下搜索问题建模与仿真[J]. 舰船科学技术, 2022, 44(22): 63-68.
	Liu Zhihao, Liu Yanbo, Huang Bo. Modeling and Analysis of Underwater Search for UUV[J]. Ship Science and Technology, 2022, 44(22): 63-68.
12	白桂强. 不确定性环境中AUV集群立体探测任务规划与动态重规划研究[D]. 长春: 吉林大学, 2023.
	Bai Guiqiang. Research on Dynamic Task Planning and Replanning for Multi-AUVs Stereo Detection in the Uncertain Environment[D]. Changchun: Jilin University, 2023.
13	Guo Hui, Mao Zhaoyong, Ding Wenjun, et al. Optimal Search Path Planning for Unmanned Surface Vehicle Based on an Improved Genetic Algorithm[J]. Computers & Electrical Engineering, 2019, 79: 106467.
14	牟衔臣, 谢东来, 闫威, 等. 基于遗传算法航路规划TSP问题的研究[J]. 系统仿真学报, 2013, 25(增1): 86-89.
	Mu Xianchen, Xie Donglai, Yan Wei, et al. Research Based on Genetic Algorithm Traveling Sealer Problem of Trajectory Optimization[J]. Journal of System Simulation, 2013, 25(S1): 86-89.
15	Wagner D H. Naval Tactical Decision Aids[M]. Monterey: Naval Postgraduate School, 1989.
16	Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.

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