Efficient Horizontal-Plane DOA Estimation via Pairwise Capon and Recursive Steering-Vector Generation

Broadband Capon direction-of-arrival estimation is computationally demanding because covariance processing, spatial spectrum evaluation, and steering-vector construction are repeatedly performed over multiple frequency bins and candidate directions. This study presents an efficient framework for horizontal-plane sound source azimuth estimation by combining pairwise Capon processing with recursive steering-vector generation. The array is partitioned into ordered two-microphone pairs, enabling independent 2×2 covariance processing. Each pair estimates a local angle relative to its directed baseline, and the resulting constraints are fused according to the array geometry. In the implemented orthogonal cross array, both pairs lie in the horizontal plane and provide complementary components of the planar source direction. A general fusion formulation is also provided for non-orthogonal baselines and non-coincident pair midpoints. The frequency-linear phase structure of the pairwise steering vector is exploited to replace repeated trigonometric evaluations across DFT bins with recursive complex rotations. Across 80 single-source trials, the proposed method achieved an MAE of 1.88°, an RMSE of 3.54°, and 100% of estimates within ±10°. The steering-vector generation time decreased from 165.69 ms to 66.77 ms, while the total measured component time decreased from 172.14 ms to 70.92 ms. Additional evaluations of multi-source resolution, reverberation, moving sources, numerical stability, and irregular arrays demonstrate a practical trade-off between computational efficiency and localization robustness.