Detecting the direction of arrival and time of arrival of impulsive transient signals

The ability to detect the direction of arrival and time of arrival (DoA-ToA) of propagating signals generated by underwater sources using array of sensors is crucial for passive sensing. This is a challenging task especially for transient and impulsive signals which have similar acoustic signature. We consider these signals, received by each sensor in a sensor array over an observation period. We assume that only a small number of these signals exist in the observation window, and that they have distinct direction of arrival (DoA) and time of arrival (DoA). The sensor array data of these signals can be transformed into a DoA-ToA space and we should expect this to be sparse. We show that this transformation can be written as an underdetermined linear system. We suggest robust methods to recover the DoA-ToA of the signals by enforcing sparsity in the DoA-ToA space. Through receiver operating characteristic (ROC) analysis, we show in numerical simulations that our methods outperform conventional practices such as cross-correlation-based time difference of arrival (TDoA) and beamforming. We present a scatter plot of the detected DoA-ToA based on the acoustic pressure sensor array recording in Singapore waters to show that the sparse DoA-ToA technique is robust and produces imaging results that match the known underwater man-made structures at the experimental site.