## 7 Conclusions  
In this paper, an algorithm for variational modal decomposition was introduced for the processing of target signals based on the signal test requirements of the multiple five-element acoustic positioning system, establishing the solution model of multi-acoustic array positioning a target and giving the data fusion processing method of target coordinates on multi-acoustic basic arrays.  
In acoustic signal processing, we employ VMD to decompose the target signal into modal components with distinct center frequencies. Subsequently, wavelet threshold processing is applied to the low-frequency segment of the signal. After recognizing the remaining signal components and establishing the low-frequency part threshold, it undergoes filtering and removal, and the components that persist are then reconstructed. The five acoustic sensor signals in each basic array of the multiple five-element acoustic positioning system are correlated to obtain the target information time extraction by using cross-correlation function. Finally the target positioning value is determined by the data fusion processing method, and the positioning test of the drone target is verified.  
Simultaneously, we conducted a comparative verification with the high-speed camera method, and the results indicated that the average error in a test area of 100 \(\times\) 100 m was less than 1 m. The fundamental principles of the high-speed camera method suggest that it is relatively ideal, being unaffected by external factors such as environmental temperature and wind speed, and possesses relatively high test accuracy. However, for UAV target positioning, the test area range of the high-speed camera method is relatively limited, making it prone to missed captures. In contrast, the method based on multiple acoustic sensor arrays, serving as the test principle, can expand the test range by increasing the number of arrays, making it a crucial means for future low, slow, and small target positioning tests.  
Due to the sensitivity of acoustic sensors to environmental conditions, there exists an inherent uncertain time delay error, resulting in relatively lower test accuracy. However, this paper introduces the VMD method for acoustic information processing and a time calculation method based on correlation functions for multiple acoustic sensors, successfully mitigating the impact of environmental factors on acoustic sensors and effectively reducing errors. This innovative achievement is the core highlight of this paper. Through observation of comparative experimental results, it is evident that the proposed method in this paper approaches the test accuracy of the high-speed camera method. An acoustic array sensor signal recognition algorithm of low-altitude targets in multiple five-element acoustic positioning systems with VMD not only addresses the positioning issue of low, slow, and small targets in a large area but is also applicable to spatial positioning tests of projectile impact points in the current weapon equipment system. This provides new insights for future intelligent fuze projectile impact position tests, high-speed small target spatial positioning, and the positioning of other novel aerial targets, showcasing broad application prospects.  
Conceptualization and methodology and validation, writing--original draft, C.S.; methodology, software and validation, writing--original draft, H.L. All authors have read and agreed to the published version of the manuscript. This research was funded by Shaanxi Provincial Science and Technology Department fund (No. 2023-YBGY-342) and National Natural Science Foundation of China (No. 62073256).  
Not applicable.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.