Low Cost Quasi Gauss-Newton Algorithm Implementation for 2D ML-DoA Estimation Using a Sparse Representation of Array Covariance

Maximum Likelihood (ML) Direction-of-Arrival (DoA) estimation under the Vectorized Covariance Matrix Model (VCMM) provides improved performance. However, the associated optimization problem remains computationally intractable due to its highly non-convex and multi-dimensional nature. To alleviate this issue, a sparse estimation strategy has been proposed, shown to be equivalent to the ML after a pre-whitening noise transformation when the regularization parameter is properly chosen. Yet, the resulting cost function remains challenging, with optimization limited to first-order methods such as the Proximal Gradient Algorithm (PGA), which suffers from slow convergence due to strong correlations in the dictionary matrix. This work exploits the decorrelation induced by the prewhitening transform to enable acceleration via a variable stepsize strategy. The transform increases the allowable stepsize by reducing the correlation of the dictionary near source directions, thus significantly improving convergence speed. Furthermore, the final iterations are shown to be equivalent with a more computationally demanding second-order algorithm, yielding an efficient approximation with reduced complexity. Numerical simulations confirm the predicted speed improvements in the case of 2D DoA estimation.