Grid-less coherent DOA estimation based on fourth-order cumulants with Gaussian coloured noise

This study investigates the continuous coherent direction-of-arrival (DOA) estimation, and concentrated on developing grid-less sparsity-based methods to Gaussian coloured noise environment. The noise component is greatly suppressed by applying fourth-order cumulants (FOC) due to its blind property to additive Gaussian noise. Two grid-less sparse models are designed separately. The first sparse representation model is built based on the simplified FOC vector, which would effectively reduce the computational complexity. Then the dual atomic norm minimisation algorithms are applied to solve the basis mismatch problem and improve the estimation accuracy. Additionally, a Toeplitz matrix based on FOC vector is constructed. The second sparse model based on this Toeplitz FOC matrix is proposed to implement array aperture extension, which can break through the restriction of maximum signal number and improve resolution. The proposed methods can handle the coherent signals and do not require the signal number as a prior. Numerical simulations demonstrate the outperformance of the proposed methods in estimation precision, computational cost and robustness to coloured noise.