Joint 3D coordinate and wave-speed estimation with nonuniform planar array: Multi-leak localization in gas pipe buried in sandy soil

Abstract

The acoustic-based methods enable remote detection of gas pipeline leaks and provide the leak area. However, accurate localization of buried leaks within the leak area requires further investigation. In this scenario, the unknown wave speed in soils and the computational complexity associated with three-dimensional (3D) localization in underground spaces pose challenges. Therefore, a joint estimation method based on a specially-designed nonuniform planar array is proposed to determine both the leak position and wave-speed. Specifically, a small-aperture uniform subarray is embedded into the large-aperture nonuniform array. By utilizing the small-aperture subarray, we can solve for the relationship between wave-speed and direction of arrival (DOA) of far-field waves. Subsequently, two-dimensional spectrum estimation is performed using the large-aperture array to obtain estimates for both wave-speed and near-field source distance. Finally, without resorting to 3D spectrum estimation, the 3D coordinates of the leak are determined. Experimental results conducted on buried pipes demonstrate that the proposed method effectively works across three soil types at varying burial depths. Notably high accuracy is achieved using a large-aperture array expended from the uniform L-shaped array with RMSE less than 0.1 m at SNR of 15 dB. Both experimental validations and simulations confirm that the novel approach can be successfully applied in various scenarios.