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 on the Vectorized Covariance Matrix Model (VCMM) exhibits enhanced performances. However, its implementation remains challenging as highly non-convex multidimensional optimization is required. To mitigates this, we recently propose to employ a sparse estimator for which we shown equivalence with the ML after a pre-whitening transform. Nevertheless, the sparse estimator yields an intricate objective function whose optimization is restricted to first-order methods such as the Forward-Backward Splitting (FBS) algorithm. The high correlation between the dictionary matrix vectors leads to slow convergence and thereby refrains the estimator practical use. To tackle this issue, the pre-whitening transform benefits are leveraged using a variable stepsize algorithm. The transform is shown to significantly improve the stepsize by decorrelating the dictionary matrix vectors in the sources directions and thus, yielding consequent acceleration. Furthermore, the last iterations of the algorithm are shown to be equivalent with a more computationally demanding second-order algorithm. Numerical simulations confirm the predicted speed improvements in the case of 2D DoA estimation.