An Off-Grid DOA Estimation Algorithm Based on the Log-Marginal Likelihood Function and the Second-Order Taylor Expansion

Existing methods for solving grid mismatch problems are often based on first-order Taylor expansion, polynomial root-finding, or exhaustive search over a given angular range. However, these methods either approximate the original model inaccurately enough or are constrained by the search grid size, which leads to unsatisfactory DOA estimation accuracy. To address these issues, this paper proposes a high-accuracy off-grid DOA estimation algorithm based on the log-marginal likelihood function and the second-order Taylor expansion. The proposed algorithm derives the first- and second-order derivatives of the log-marginal likelihood function with respect to the target DOA and gets the numerical solution of the grid mismatch based on these derivatives. After obtaining the grid mismatch, the array manifold matrix as well as the signal and noise powers are updated iteratively, ultimately achieving off-grid DOA estimation. Simulation results demonstrate the superior DOA estimation performance of the proposed algorithm.