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.

图/表 9

图1

图2

图3

表1

表2

图4

图5

表3

图6

参考文献 27

[1]	LI Fu, VACCARO R J. Unified analysis for DOA estimation algorithms in array signal processing[J]. Signal Processing, 1991, 25(2): 147-169.
[2]	LIAO Bin, MADANAYAKE A, AGATHOKLIS P. Array signal processing and systems[J]. Multidimensional Systems and Signal Processing, 2018, 29(2): 467-473.
[3]	蒋德军, 胡涛. 时延估计技术及其在多途环境中的应用[J]. 声学学报, 2001, 26(1): 34-40.
	JIANG Dejun, HU Tao. Time-delay estimation and its application in multipath environment[J]. Acta Acustica, 2001, 26(1): 34-40.
[4]	DA ROSA ZANATTA M, LÓPES DE MENDONÇA F L, ANTREICH F, et al. Tensor-based time-delay estimation for second and third generation global positioning system[J]. Digital Signal Processing, 2019, 92: 1-19.
[5]	AZARIA M, HERTZ D. Time delay estimation by generalized cross correlation methods[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984, 32(2): 280-285.
[6]	张传义, 卢晓. 基于广义互功率谱相位法的声源定位技术[J]. 东北大学学报(自然科学版), 2018, 39(8): 1075-1079.
	ZHANG Chuanyi, LU Xiao. Sound source localization technology based on generalized cross-power spectrum phase[J]. Journal of Northeastern University (Natural Science), 2018, 39(8): 1075-1079.
[7]	GAO Y, BRENNAN M J, JOSEPH P F. A comparison of time delay estimators for the detection of leak noise signals in plastic water distribution pipes[J]. Journal of Sound and Vibration, 2006, 292(3-5): 552-570.
[8]	ZHANG Cheng, SHEN Shihui, HUANG Hai, et al. Estimation of the vehicle speed using cross-correlation algorithms and MEMS wireless sensors[J]. Sensors, 2021, 21(5): 1721.
[9]	COBOS M, ANTONACCI F, COMANDUCCI L, et al. Frequency-sliding generalized cross-correlation: a sub-band time delay estimation approach[J]. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 2020, 28: 1270-1281.
[10]	李皖婷, 李登峰, 张修靖, 等. 指数形式的二次相关GCC-PHAT-β时延估计算法[J]. 科学技术与工程, 2022, 22(33): 14779-14785.
	LI Wanting, LI Dengfeng, ZHANG Xiujing, et al. Exponential quadratic correlation GCC-PHAT-β delay estimation algorithm[J]. Science Technology and Engineering, 2022, 22(33): 14779-14785.
[11]	梁宇, 马良, 纳霞, 等. 基于广义互相关算法的时延估计[J]. 计算机科学, 2011, 38(): 454-456.
	LIANG Yu, MA Liang, NA Xia, et al. Research of time delay estimation based on GCC algorithm[J]. Computer Science, 2011, 38(): 454-456.
[12]	邢毓华, 郑琦. 广义互相关在混沌扩频时延估计中的研究与应用[J]. 激光与光电子学进展, 2021, 58(23): 1907001.
	XING Yuhua, ZHENG Qi. Research and application of generalized cross correlation in chaotic spread spectrum time delay estimation[J]. Laser & Optoelectronics Progress, 2021, 58(23): 1907001.
[13]	NIKIAS C L, PAN R. Time delay estimation in unknown Gaussian spatially correlated noise[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1988, 36(11): 1706-1714.
[14]	TUGNAIT J K. Time delay estimation with unknown spatially correlated Gaussian noise[C]//Proceedings of 1991 International Conference on Acoustics, Speech, and Signal Processing. Toronto: IEEE, 1991: 1265-1268.
[15]	LIU Qing, HAN Shuangwang, MA Xiaoshu. Research of time delay estimation based on higher order statistics[J]. Applied Mechanics and Materials, 2014, 530-531.
[16]	ARULAMPALAM M S, MASKELL S, GORDON N, et al. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188.
[17]	HAYES E E, THORP S, MANDEL K S, et al. Gaussn: Bayesian time-delay estimation for strongly lensed supernovae[J]. Monthly Notices of the Royal Astronomical Society, 2024, 530(4): 3942-3963.
[18]	CHAN K L, WANG Zhuoru, DING Aijun, et al. MAX-DOAS and OMI measurements of tropospheric NO2 and HCHO over Eastern China[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(4): 1-13.
[19]	REN Dong, WANG Yong, WANG Guocheng, et al. Rising trends of global precipitable water vapor and its correlation with flood frequency[J]. Geodesy and Geodynamics, 2023, 14(4): 355-367.
[20]	RUSAKOV D A. A misadventure of the correlation coefficient[J]. Trends in Neurosciences, 2023, 46(2): 94-96.
[21]	CHEN Kai, CHEN Li, XIAO Jiaqi, et al. Speckle reduction in digital holography with non-local means filter based on the Pearson correlation coefficient and Butterworth filter[J]. Optics Letters, 2022, 47(2): 397-400.
[22]	路晓妹, 寇文珍, 段渭军. 基于EMD分解重构的互相关时延估计方法[J]. 测控技术, 2013, 32(7): 45-48, 56.
	LU Xiaomei, KOU Wenzhen, DUAN Weijun. Cross-correlation delay estimation method based on EMD decomposition and reconstruction algorithm[J]. Measurement & Control Technology, 2013, 32(7): 45-48, 56.
[23]	CHEN Lai, KANG Chaogui, YANG Chao. Understanding citizens' emotion states under the urban livability environment through social media data: a case study of Wuhan[J]. Journal of Geodesy and Geoinformation Science, 2022, 5(2): 49-59.
[24]	张春森, 张萌萌, 郭丙轩. 影像信息驱动的三角网格模型优化方法[J]. 测绘学报, 2018, 47(7): 959-967. DOI: . doi: 10.11947/j.AGCS.2018.20170733
	ZHANG Chunsen, ZHANG Mengmeng, GUO Bingxuan. Refinement of the 3D mesh model driven by the image information[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(7): 959-967. DOI: . doi: 10.11947/j.AGCS.2018.20170733
[25]	王兆瑞, 张杰. 一种基于小波变换的波达方向估计方法[J]. 测绘学报, 2011, 40(): 111-114.
	WANG Zhaorui, ZHANG Jie. A method of DOA estimation based on wavelet transform[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(): 111-114.
[26]	YANG Xu, XING Hongyan, YAN Yan. A data complementary method for sound source localization based on four-element microphone array groups[J]. Measurement Science and Technology, 2021, 32(9): 095015.
[27]	LI Yang, ZOU Xihua, LIU Puyu, et al. Four-element array for GNSS attitude determination using IRLS: an improved rounding of long-short baseline approach[J]. IEEE Transactions on Vehicular Technology, 2020, 69(5): 4920-4934.

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 9

参考文献 27

相关文章 15

编辑推荐

Metrics

本文评价

[1]	李鹏, 白建博, 李振洪, 王厚杰. 融合多轨道TS-InSAR的广域海岸带地面沉降监测及成因解析——以山东省为例[J]. 测绘学报, 2025, 54(7): 1178-1191.
[2]	赵庆志, 常璐璐, 姚宜斌, 李浩杰. 一种联合GNSS和气象数据的水文干旱指数构建方法[J]. 测绘学报, 2025, 54(7): 1192-1205.
[3]	邓敏, 彭翀, 谌恺祺. 顾及地理空间特性的空间面板数据可预测性评估理论与方法[J]. 测绘学报, 2025, 54(7): 1305-1317.
[4]	王潜心, 胡超, 程彤. 基于GNSS钟差参数先验信息的超快速轨道钟差估计方法[J]. 测绘学报, 2025, 54(6): 982-994.
[5]	沈洋, 李广云, 陈明剑, 李林阳, 施星宇, 蔡巍, 郝卫峰. 基于风云三号TEC的极区GNSS电离层模型精度评估[J]. 测绘学报, 2025, 54(6): 995-1008.
[6]	邹晨曦, 石震, 刘迪, 杨子毅. 基于BP神经网络模型的光纤陀螺全站仪温度补偿算法[J]. 测绘学报, 2025, 54(6): 1021-1030.
[7]	李德伟. 面向固体地球宏观运动现象的月基SAR系统仿真与形变相位模拟[J]. 测绘学报, 2025, 54(6): 1152-1152.
[8]	郭仕伟. 融合GNSS/ISL/SLR/LEO技术的地心运动估计理论方法研究[J]. 测绘学报, 2025, 54(6): 1154-1154.
[9]	李晨辉. BDS/蓝牙阵列/PDR融合的智能手机定位方法研究[J]. 测绘学报, 2025, 54(6): 1156-1156.
[10]	范昊鹏, 张博骄, 孙中苗, 冯进凯. 基于ConvLSTM网络的区域对流层湿延迟预报方法[J]. 测绘学报, 2025, 54(5): 795-804.
[11]	胡顺强, 陈克杰, 贺小星, 朱海, 王坦. 环境负载对川滇地区GNSS观测站三维坐标时间序列非线性变化的影响[J]. 测绘学报, 2025, 54(5): 805-818.
[12]	王瑞. 开采沉陷监测多源数据融合技术及应用研究[J]. 测绘学报, 2025, 54(5): 964-964.
[13]	沈祎凡. 基于深度学习算法融合GNSS和GRACE数据的陆地水储量异常反演[J]. 测绘学报, 2025, 54(5): 965-965.
[14]	王强. 基于深度学习的GNSS-R海面高度反演模型研究[J]. 测绘学报, 2025, 54(5): 966-966.
[15]	卢一鹏, 李雨昊, 王海平, 刘缘, 董震, 杨必胜. 基于CVT空间变换的大场景多尺度隐式三维重建[J]. 测绘学报, 2025, 54(4): 702-713.