Real-valued off-grid DOA estimation via iterative optimisation based on covariance differencing method with spatial coloured noise

In this study, a real-valued off-grid direction-of-arrival (DOA) estimation algorithm is presented based on covariance differencing technique in the presence of unknown spatial coloured noise. The noise component is eliminated by forming the difference between the original and the transformed covariance matrices. A new observation model is constructed based on the eigenvectors corresponding to the positive eigenvalues of the difference matrix, which can solve the pseudo peaks problem caused by the covariance differencing process. To reduce the computational cost and improve the estimation accuracy, the observation model is transformed into a real-valued one via a unitary transformation. Then, a real-valued off-grid DOA estimation model is established by incorporating the bias parameter into the observation model. The off-grid DOA estimation problem is solved via iterative optimisation. Numerical simulations verify the superiority of the authors’ scheme including increased accuracy, reduced complexity and improved robustness to coloured noise.