Six-Degrees-of-Freedom Compensation for Microphone Array Installation Uncertainty in Rotating Sound Source Localization

Accurate rotating sound source localization requires precise knowledge of the relative pose between the microphone array and the rotating object. In practice, six-degrees-of-freedom (6-DOF) installation uncertainties often arise, degrading beamforming performance. This paper presents a 6-DOF compensation method formulated as an optimization problem. The method treats the array as a rigid body and estimates its translational and rotational offsets by minimizing the sum of Euclidean distances between beamforming peaks and a small set of stationary single-frequency reference sources. A novel cascaded local-Bayesian optimization (CLBO) algorithm is proposed, initialized via coordinate descent local search followed by Bayesian optimization refinement. Our simulations show that CLBO yields the lowest residual error and requires the fewest evaluations, outperforming Bayesian optimization, simulated annealing, and local search. Mode composition beamforming (MCB) maps confirm that 6-DOF compensation restores spatial resolution and dynamic range to near-ideal levels, even under perturbed reference-source positions. Our experimental validation on a UAV rotor confirms practical feasibility, restoring focal peaks at blade tips. The proposed approach requires no external metrology, it is robust in practice, and it offers an efficient solution to array installation uncertainty.