It is challenging to ensure both high accuracy and low complexity when localizing radiation sources. To address this challenge, we propose two novel methods leveraging time difference of arrival (TDOA) measurements. Specifically, we introduce a TDOA estimation method and a direct position determination (DPD) method based on parallel factor (PARAFAC) analysis in the cross-correlation domain. Initially, multiple sensors synchronously capture the source signal, and the cross-correlation function between signals received from a reference sensor and other sensors is calculated. Then, the primary cross-spectrum data undergoes an expansion and integration process to establish the PARAFAC model. Through cross-spectrum expansion, virtual nodes are formed, which further improves the estimation performance. The TDOA estimates for each sensor are obtained by normalizing and extracting the phase from this matrix. Additionally, we introduce a novel DPD method tailored for multipath propagation scenarios. Simulations and real-world measurements demonstrate the superiority and effectiveness of our proposed methods compared with cutting-edge methods.

In this article, source localization exploiting time difference of arrival (TDOA) information is discussed, and a parallel factor (PARAFAC) analysis-based method for multi-TDOA estimation and direct position determination (DPD) is proposed. First, signals from the radiation source are received by multiple antennas through synchronous sensing. Then, the data from multiple antennas is fused by extracting the time-delay matrix to construct a PARAFAC model. Thereafter, the time-delay matrix is obtained by fast iterative decomposition using the trilinear alternating least square (TALS) algorithm. In the case of no multipath or weak multipath, where the typical scenario is the antennas being deployed on the airborne platform, the multi-TDOA estimation can be obtained simultaneously according to the time-delay matrix to improve the processing speed. In the case of multipath, such as the antennas being located on the ground, the DPD cost function directly related to the source position can be established based on the time-delay matrix, and the source position estimation can be achieved through grid search. Compared with the other DPD methods, the proposed DPD method has better positioning performance and lower complexity. The effectiveness and superiority of the proposed methods are verified by both simulations and actual scenario tests.