We develop a closed-form framework for three-dimensional sound source localization that incorporates the motion of acoustic arrays. Previous closed-form methods for TDOA–AOA localization assume that sensor stations are located at fixed positions; here, the formulation is extended to arrays whose positions and orientations vary over time. Quaternion-based transformations are used to represent array orientation and map measurements into the global frame, thereby avoiding the singularities associated with angle-based representations and enabling the accurate handling of arbitrary rotations. The method fuses Time Difference of Arrival (TDOA) and Angle of Arrival (AOA) observations from three arrays through a weighted least squares solution, providing an analytical estimate of source position that remains stable in the presence of measurement noise. Accounting for array motion eliminates the need for iterative search and ensures that localization accuracy is maintained as the observation geometry changes. This framework supports applications where static sensors are impractical, including underwater environments where visual sensing is limited and positioning systems such as GPS are unavailable. By enabling sound source localization with moving arrays, the method provides a foundation for reliable mapping and navigation in conditions where traditional sensing approaches are ineffective.
Abualsaud et al. (2025) studied this question.