Refinement of Direction of Arrival Estimators by Majorization-Minimization Optimization on the Array Manifold

We propose a generalized formulation of direction of arrival estimation that includes many existing methods such as steered response power, subspace, coherent and incoherent, as well as speech sparsity-based methods. Unlike most conventional methods that rely exclusively on grid search, we introduce a continuous optimization algorithm to refine DOA estimates beyond the resolution of the initial grid. The algorithm is derived from the majorization-minimization (MM) technique. We derive two surrogate functions, one quadratic and one linear. Both lead to efficient iterative algorithms that do not require hyperparameters, such as step size, and ensure that the DOA estimates never leave the array manifold, without the need for a projection step. In numerical experiments, we show that the accuracy after a few iterations of the MM algorithm nearly removes dependency on the resolution of the initial grid used. We find that the quadratic surrogate function leads to very fast convergence, but the simplicity of the linear algorithm is very attractive, and the performance gap small.