基于Lp范数约束的水下高精度定位方法

doi:10.12382/bgxb.2024.0940

摘要/Abstract

摘要：

针对水下到达时间定位技术定位易于受到测距误差影响的问题,提出一种基于L_p范数的相似度匹配定位算法。该算法首先建立了包含环境参数的距离矢量模型,构造了相似度匹配定位算法,通过求取距离矢量与拷贝矢量的L_p范数,完成相似度的分析,实现目标在观测区域的三维定位。为验证算法的性能,将该算法与最小二乘定位算法相比,使用蒙特卡洛仿真分析了水平面的定位误差以及三维空间的定位误差分布规律;最后使用水池试验对算法进行验证,定位误差的均值由0.0555m降低到0.0256m,误差标准差由0.0345m降低到0.0072m。仿真和实验结果表明,该算法具有与常规定位技术相似的误差分布规律,由于直接对距离矢量进行匹配,定位精度同样受到测距精度的影响,但测距误差间无耦合传递现象,可提高定位精度,且结果更稳健。此外,该算法考虑了环境参数对测距的影响,具有应对声速梯度随空间变化的能力。

关键词: 到达时间定位, L_p范数, 相似度匹配, 误差传递, 最小二乘算法

Abstract:

To address the susceptibility of underwater time of arrival localization techniques to ranging errors,this paper proposes a similarity matching localization algorithm based on the L_p norm constraint (LPM).First,a distance vector model including the environmental parameters is established,and a similarity matching localization algorithm is formulated.By calculating the L_p norm between the measured distance vector and its replica,the similarity analysis is performed to achieve the three-dimensional (3D) localization of target in the observation area.To verify the performance of the proposed algorithm,Monte Carlo simulations are conducted to compare LPM with the least squares method,and analyze the horizontal localization errors and the distribution law of localization errors in 3D space.Furthermore,validates the algorithm is verified through water tank experiment,demonstrating that the mean localization error decreases from 0.0555m to 0.0256m,and the error standard deviation reduces from 0.0345m to 0.0072m.The simulated and experimental results indicate that LPM has error distribution characteristics similar to that of conventional localization method.LPM achieves higher precision and robustness due to the direct matching of distance vectors without coupling error propagation.Additionally,the algorithm considers the influence of environmental parameters on ranging,so it has the ability to deal with the variation of sound velocity gradient with space.

Key words: time of arrival localization, L_p norm, similarity matching, error transmission, least squares algorithm

王奇, 王英民, 诸国磊. 基于L_p范数约束的水下高精度定位方法[J]. 兵工学报, 2025, 46(9): 240940-.

WANG Qi, WANG Yingmin, ZHU Guolei. Underwater High Accuracy Localization Method with L_p Norm Constraints[J]. Acta Armamentarii, 2025, 46(9): 240940-.

图/表 20

图1 同一平面上3个阵元阵型示意图

Fig.1 Array with 3 elements on the same plane

图2 LPM对(3.5m,3.5m)处目标的定位结果

Fig.2 Localization results of LPM for the target at (3.5m,3.5m)

图3 LPM和LS算法定位结果对比

Fig.3 Comparisons of localization results of LPM and LS algorithms

图4 目标定位误差对比

Fig.4 Comparisons of localization errors of LPM and LS algorithms

表1 目标位于(3.5m,3.5m)处LPM和LS的定位结果对比

Table 1 Comparisons of localization results of LPM and LS algorithms at (3.5m,3.5m) m

算法	参数	均值	标准差	方差
LS算法	x轴定位结果	3.5	0.0276	0.00076
	y轴定位结果	3.5	0.0395	0.0016
	定位误差	0.0415	0.0240
LPM	x轴定位结果	3.5	0.0178	0.00032
	y轴定位结果	3.5	0.0181	0.00033
	定位误差	0.0241	0.0078

表2 目标位于(3.5m,3.5m)处的运算速度对比

Table 2 Comparison of computational speeds of LPM and LS algorithms at (3.5m,3.5m)

蒙特卡洛次数	时间/s
蒙特卡洛次数	LS算法	LPM
500	0.032	6.02
1000	0.050	12.02
1500	0.070	17.92
2000	0.088	23.89

图5 定位误差等高线

Fig.5 Contour map of localization error

图6 切片高6m时定位误差等高线图

Fig.6 Contour map of localization error with the slice height of 6m

图7 不同高度的Oxy切片平均误差

Fig.7 Average error curve of Oxy slice at different heights

图8 接收阵及发射源的空间结构

Fig.8 Spatial structures of receiving array and transmitting source

表3 接收阵元坐标

Table 3 Coordinates for receiving array elements cm

接收阵元	x	y	z
A	-260.88	0	-451.3
B	261.30	0	-452.5
C	0	-260.82	-474.8
D	0	261.82	-471.1

图9 设备连接及布阵俯视图

Fig.9 Top view of equipment connection and array arrangement

图10 水听器接收到的声源信号波形

Fig.10 Waveform of signal received by the hydrophone

图11 水中声速的测量

Fig.11 Measurement for the sound velocity in water

图12 声源真实位置

Fig.12 Real position of acoustic source

图13 LPM和LS算法对声源1定位结果

Fig.13 Localization results for acoustic source 1 using LPM and LS algorithms

图14 LPM和LS算法定位结果

Fig.14 Localization results of LPM and LS algorithms

图15 Oxz平面定位结果局部放大图

Fig.15 Partially enlarged view of localization results of LPM and LS algorithms on the Oxz plane

图16 LPM和LS算法的定位误差对比

Fig.16 Comparisons of localization errors of LPM and LS algorithms

表4 LPM和LS算法定位结果量化对比

Table 4 Quantitative localization results of LPM and LS algorithms m

算法	参数	均值	标准差
LS算法	x轴定位结果	-0.0183	0.0233
	y轴定位结果	-0.0413	0.0363
	z轴定位结果	-0.0127	0.0161
	定位误差	0.0555	0.0345
LPM	x轴定位结果	0.0093	0.0161
	y轴定位结果	0.0082	0.0178
	z轴定位结果	0.0010	0.0020
	定位误差	0.0256	0.0072
两算法绝对值差	x轴定位结果	0.0090	0.0072
	y轴定位结果	0.0331	0.00185
	z轴定位结果	0.0117	0.0141
	定位误差	0.0299	0.0273

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