A 3D multi-source radiation localization method based on wave arrival direction and two-step clustering in multipath environments

A localization method based on noise subspace reconstruction for direction of arrival (DOA) and two-step clustering is proposed to address the problems of difficult estimation of the number of radiation sources and insufficient localization accuracy in three-dimensional multiple radiation source localization under multipath environments. The method estimates the azimuth and elevation angles of the main paths of each radiation source signal using an improved noise subspace reconstruction algorithm. Subsequently, the number of radiation sources is estimated by applying a combined analysis method of silhouette coefficient and elbow method to the spatial intersection points obtained from DOA association. On this basis, a multi-region cooperation strategy is adopted, and a two-step clustering method combining density-based spatial clustering of applications with noise (DBSCAN) and K-means clustering (K-means) is used to estimate the planar coordinates of each radiation source. Then, the spatial point sets adjacent to the estimated planar coordinates are screened, and the densest height region is selected for averaging to determine the height coordinate, thereby achieving three-dimensional localization. Simulation results show that when the main-to-multipath amplitude ratio is 5  dB, the proposed DOA estimation method reduces the root mean square error (RMSE) by about 47% compared with the existing improved reconstructed noise-subspace multiple signal classification (IRNSMUSIC) method. Furthermore, the proposed two-step clustering localization method reduces the average localization error of three sources by about 54% compared with the existing mean shift localization method.