In the last decade, the signal processing (SP) community has witnessed a paradigm shift from model-based to data-driven methods. Machine learning (ML) - more specifically, deep learning - methodologies are nowadays widely used in all SP fields, e.g., audio, speech, image, video, multimedia, and multimodal/multisensor processing, to name a few. Many data-driven methods also incorporate domain knowledge to improve problem modeling, especially when computational burden, training data scarceness, and memory size are important constraints.

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In this paper, we present a localization algorithm which simultaneously estimates the locations of the target sound sources and dual-microphone sub-arrays using time-of-flight (TOF) measurements of the target signals. The proposed solution is mainly developed for a binaural hearing aid system (HAS) which consists of two hearing aids (HAs) mounted on the ears of a user. Each HA has two microphones at a known distance from each other, but the relative locations of the HAs are unknown. In this paper, we aim to find the relative locations of the HAs and the locations of the target sources. The main contribution of this paper is in modeling the localization problem as a simple linear system of equations, which markedly decreases the computation overhead in contrast to most state-of-the-art localization algorithms, which model the problem as a non-linear problem resulting in higher computational complexity. The proposed algorithm requires at least two sound sources with different locations to solve the localization problem in 2D.@en