Pearson correlation coefficient time delay estimation applied in acoustic orientation

doi:10.11947/j.AGCS.2025.20240406

Abstract

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

CLC Number:

P228

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.

Figures/Tables 9

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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