Ensemble deep random vector functional link for self-supervised direction-of-arrival estimation

Direction-of-arrival (DOA) estimation is a key step in the passive target location. The primary issues with traditional DOA estimation methods are the huge computation and weak noise immunity in extreme noise environments. Random vector functional link (RVFL) and its variants (RVFL without direct links, RVFLv) have demonstrated high learning efficiency and strong generalization ability in previous studies. However, due to the shallow network structure, they may not be effective for underwater acoustic array signals with complex features. Therefore, we propose a model-embedded self-supervised ensemble deep RVFL (ME-SedRVFL) network to estimate the DOA of underwater acoustic array signals. To prove the efficiency and generalization ability, ME-SedRVFL is compared with its variants (ME-SRVFLv), as well as other well-known randomization-based networks. The results testify the noise immunity of ME-SedRVFL and ME-SRVFLv is 9.62% and 9.34% better than traditional signal model-based methods, 1.68% and 1.40% better than randomization-based parameter estimation methods (Signal-to-noise ratio is −20 dB, frequency is 200 Hz). The statistical box diagrams and statistical comparisons are performed to evaluate different methods, which indicate that the ME-SedRVFL obtains superior DOA estimation performance to ME-SRVFLv in most cases, due to direct input–output connections helping regularize the randomization. Hence, ME-SedRVFL is identified as the best-performing DOA estimation method through a comprehensive evaluation of real-world and simulated datasets. [Display omitted] •We design a signal model-embedded loss function, which is a closed-form solution.•We introduce an L1 auxiliary loss term to obtain the signal sparse solution.•The proposed models are instantiated and have excellent generalization ability.•We compare with the RVFL variants, the results manifested competitive performance.