Underwater High Accuracy Localization Method with Lp Norm Constraints

doi:10.12382/bgxb.2024.0940

Abstract

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

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

Figures/Tables 20

Fig.1 Array with 3 elements on the same plane

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

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

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

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

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

Fig.5 Contour map of localization error

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

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

Fig.8 Spatial structures of receiving array and transmitting source

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

Fig.9 Top view of equipment connection and array arrangement

Fig.10 Waveform of signal received by the hydrophone

Fig.11 Measurement for the sound velocity in water

Fig.12 Real position of acoustic source

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

Fig.14 Localization results of LPM and LS algorithms

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

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

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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