An adaptive diffusion quaternion LMS algorithm for distributed networks of 3D and 4D vector sensors

A diffusion widely linear quaternion least mean square (D-WLIQLMS) algorithm for the collaborative processing of quaternion signals over distributed networks is proposed. We show that the underlying quaternion division algebra and the widely linear model allow for a unified processing of 3D and 4D data, which can exhibit both circular and noncircular distributions. The analysis shows that the D-WLIQLMS provides a solution that is robust to link and node failures in sensor networks. Simulations on benchmark 4D signals illustrate the advantages offered by the D-WLIQLMS.