Off-grid hydroacoustic signal orientation estimation based on interpolation and subspace fitting in coprime arrays

This letter presents a novel approach to sparse Bayesian underwater acoustic signal direction estimation. The proposed method incorporates interpolation of the coprime array and signal subspace fitting. It addresses the limitations of the hydrophone coprime array in utilizing all array elements’ information and mitigates the interference of ocean noise in shallow waters, which impairs the accuracy and resolution of target direction estimation. Firstly, the hydroacoustic signals are received using a coprime array, then the missing information is filled by interpolating the virtual array elements in the virtual domain, and by optimizing the design of the atomic norm and reconstructing the covariance matrix, the direction-of-arrival (DOA) estimation is performed using all the information of the received signal. Then, the received signal is reconstructed in conjunction with the reconstructed covariance signal subspace, which effectively reduces the impact of background noise. Finally, we derive an off-grid sparse model for the reconstructed signal by exploiting sparsity in the null domain and use Bayesian learning to compute the maximum a posteriori probability of the source signal, thus achieving DOA estimation. The results of numerical simulations and sea trial experimental data indicate that the use of subarrays comprising 5 and 3 array elements, respectively, is sufficient to effectively estimate 12 source angles. Furthermore, the estimation of the DOA can be accurately carried out under low signal-to-noise ratio conditions. This method effectively utilizes the degrees of freedom provided by the virtual array, reducing noise interference, and exhibiting better performance in terms of positioning accuracy and algorithm stability.