Joint DOA-delay estimation approach based on atomic norm

To address the difficult problem of localizing autonomous underwater vehicle in underwater acoustic communication environments, a joint DOA-delay estimation approach based on atomic norm was proposed. Firstly, a channel impulse response formula was established based on the characteristics of underwater acoustic multipath and Doppler effects, and the received signal was represented in a matrix form with normalized parameters. After that, a new set of atoms was established based on the geometric structure of the hydrophone array and the phase error caused by the Doppler effects. Considering the sparsity of the underwater acoustic signal in the spatial domain, the corresponding atoms were solved using atomic norm minimization. Finally, in order to solve the problem that the sub-matrix in the positive semi-definite matrix caused by arbitrary linear arrays was a non-Toeplitz matrix structure and could not be decomposed by Vandermonde, a Hermitian set about the geometric structure of the hydrophone was defined, and the prolate spheroidal wave functions were used to solve the semi-definite programming problem to obtain a joint estimate of DOA and delay. The experimental results show that the root mean square error (RMSE) of the proposed approach is as low as 0.2° when the signal-to-noise ratio (SNR) is 20 dB, and there is still a 77.98% estimation success probability when the DOA interval is as low as 3°. The error between the estimation delay and the actual delay can reach the microsecond level.