optimizing hydrophone array configurations for 6-dof motion-induced phase error correction in synthetic aperture sonar imaging

Synthetic aperture sonar (sas) achieves high-resolution imaging by coherently integrating echoes along the platform trajectory, making it inherently sensitive to six-degree-of-freedom (6-dof) motion. sub-wavelength perturbations distort phase, broaden the main lobe, and raise sidelobes. this paper introduces a geometry-centric array optimization framework that: (i) operationalizes a phase sensitivity index (psi) with translational and rotational components to quantify array-dependent motion sensitivity; and (ii) calibrates pslr/islr to image signatures (main-lobe width and sidelobe proximity) against a back-projection (bp) reference, ensuring physics-consistent visual interpretation. three receiver arrays—2d planar, 3d cubic, and 3d hemispherical (36 elements each)—are evaluated under six motions (surge, sway, heave, roll, pitch, yaw) and three imaging states (ideal, motion-degraded, corrected), yielding 54 scenarios. motion parameters reflect realistic autonomous underwater vehicle conditions: translational rms 2.0–3.2 mm, rotational rms 0.25°–0.35°, platform speed 2.5 m/s, and dominant 0.2–2 hz content. the hemispherical array attains the lowest normalized psi and consistently superior sidelobe metrics, outperforming the planar array by approximately 6.5 db in pslr and 5.6 db in islr on updated corrected global means, and the cubic array by approximately 2.9 db in both pslr and islr. yaw and heave cause the greatest degradation; roll is least harmful. motion correction improves pslr by ≥4 db and islr by ≥3 db relative to degraded images, while the residual gap to ideal remains ≤4 db, by design. the proposed framework enables quantitative array selection and supports robust sas imaging in embedded auvs without external navigation sensors.