皮尔逊相关系数时延估计在声学定向上的应用

doi:10.11947/j.AGCS.2025.20240406

测绘学报 ›› 2025, Vol. 54 ›› Issue (7): 1206-1214.doi: 10.11947/j.AGCS.2025.20240406

皮尔逊相关系数时延估计在声学定向上的应用

胡辉雯¹^,²(), 沈聪¹^,², 柳林涛¹(), 王国成¹

^1.中国科学院精密测量科学与技术创新研究院精密大地测量与定位全国重点实验室，湖北　武汉　430077
^2.中国科学院大学，北京　101408

收稿日期:2024-10-11 修回日期:2025-06-20 出版日期:2025-08-18 发布日期:2025-08-18
通讯作者: 柳林涛 E-mail:huhuiwen@apm.ac.cn;llt@asch.whigg.ac.cn
作者简介:胡辉雯（1997—），男，博士，研究方向为时延估计、阵列信号处理、麦克风阵列定向。E-mail：huhuiwen@apm.ac.cn
基金资助:
国家自然科学基金(42074011);中国科学院重大科技任务局重点部署项目(T24Y6303)

Pearson correlation coefficient time delay estimation applied in acoustic orientation

Huiwen HU¹^,²(), Cong SHEN¹^,², Lintao LIU¹(), Guocheng WANG¹

^1.State Key Laboratory of Precision Geodesy, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China
^2.University of Chinese Academy of Sciences, Beijing 101408, China

Received:2024-10-11 Revised:2025-06-20 Online:2025-08-18 Published:2025-08-18
Contact: Lintao LIU E-mail:huhuiwen@apm.ac.cn;llt@asch.whigg.ac.cn
About author:HU Huiwen (1997—), male, PhD, majors in time delay estimation, array signal processing, and microphone array orientation. E-mail: huhuiwen@apm.ac.cn
Supported by:
The National Natural Science Foundation of China(42074011);Key Projects Deployed by the Major Scientific and Technological Mission Bureau of the Chinese Academy of Sciences(T24Y6303)

摘要/Abstract

摘要：

针对广义互相关-PHAT（generalized cross correlation-PHAT，GCC-PHAT）中不能合理反映两信号的相关性、存在边缘效应问题，导致在目标被动定向中时延估计扭曲、精度低、有时无法定向目标等现象，本文提出了一种基于皮尔逊相关系数的时延估计方法。该方法利用皮尔逊相关系数合理地、精确地测量两个信号的相关性，并利用平移观测信号与参考信号求滑动皮尔逊相关系数，通过绝对值的峰值所在位置来估计时延。仿真试验表明，与GCC-PHAT相比，本文方法在时延估计的有效值比例上提高了14.67个百分点，在时延估计的精度上提高了92.67个百分点，在目标定向的精度上提高了88.24个百分点。将本文方法应用于麦克风阵列定向无人机试验，试验结果进一步验证了本文方法在时延估计和目标定向上的高稳健性和高精确性，并且在目标方向的稳定点比例上较GCC-PHAT提高了28.66个百分点。

Abstract:

To address the problems of unreasonably reflecting the correlation between two signals and edge effects in the generalized cross correlation-PHAT (GCC-PHAT), which lead to inaccurate time delay estimation (TDE), low-precision TDE, in-ability to orientate targets, et al, a method for the TDE based on the Pearson correlation coefficient (PCC) was proposed in this paper. The method uses the PCC to measure the correlation between two signals in a reasonable, accurate, and absolute manner. It shifts the observation signal, calculates the sliding PCC with the reference signal, and finds the position of the peak of absolute values to estimate the time delay. Simulation experiments show that compared to the GCC-PHAT, the proposed method improves the effective value ratio of the TDE by 14.67%, the precision of the TDE by 92.67%, and the precision of target orientation by 88.24%. Applying the method in a microphone array directional drone experiment, results further verify the high robustness and precision of the proposed method in the TDE; and compared to the GCC-PHAT, the proposed method improves the stable points ratio of target direction by 28.66%.

Key words: time delay estimation, generalized cross correlation-PHAT, Pearson correlation coefficient, microphone array, target orientation

中图分类号:

P228

胡辉雯, 沈聪, 柳林涛, 王国成. 皮尔逊相关系数时延估计在声学定向上的应用[J]. 测绘学报, 2025, 54(7): 1206-1214.

Huiwen HU, Cong SHEN, Lintao LIU, Guocheng WANG. Pearson correlation coefficient time delay estimation applied in acoustic orientation[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(7): 1206-1214.

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链接本文: http://xb.chinasmp.com/CN/10.11947/j.AGCS.2025.20240406

http://xb.chinasmp.com/CN/Y2025/V54/I7/1206

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阵元序号	异常值个数的比例/（%）		去异常值后均方根误差/（°）
阵元序号	GCC-PHAT	本文方法	GCC-PHAT	本文方法
1、2	14.00	0.00	1.5×10^－4	1.1×10^－5
1、3	48.00	0.00	2.2×10^－4	2.9×10^－4
1、4	0.00	0.00	2.1×10^－5	1.5×10^－5
2、3	3.00	0.00	1.6×10^－5	1.3×10^－5
2、4	8.00	0.00	7.7×10^－5	7.8×10^－6
3、4	15.00	0.00	1.0×10^－5	1.0×10^－5

目标方向	方法	定向方程组有解的比例/（%）	异常值个数的比例/（%）	去异常值后均方根误差/（°）
俯仰角	GCC-PHAT	71.00	28.17	0.54
俯仰角	本文方法	100.00	0.00	0.13
方位角	GCC-PHAT	71.00	21.13	0.85
方位角	本文方法	100.00	0.00	0.10

方法	定向方程组有解的比例	在俯仰角稳定性上占优比例	在方位角稳定性上占优比例
GCC-PHAT	98.22	35.67	39.89
本文方法	100.00	64.33	60.11

皮尔逊相关系数时延估计在声学定向上的应用

Pearson correlation coefficient time delay estimation applied in acoustic orientation

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