A General Quaternion-valued Gradient Operator and Its Applications to Computational Fluid Dynamics and Adaptive Beamforming

TL;DR

This paper introduces a comprehensive quaternion-valued gradient operator, deriving it in the most general form and demonstrating its applications in computational fluid dynamics and adaptive beamforming.

Contribution

It provides the first general derivation of the quaternion gradient operator and applies it to CFD wind prediction and adaptive beamforming tasks.

Findings

Enhanced wind profile prediction accuracy

Improved adaptive beamforming performance

Unified quaternion gradient framework

Abstract

Quaternion-valued signal processing has received increasing attention recently. One key operation involved in derivation of all kinds of adaptive algorithms is the gradient operator. Although there have been some derivations of this operator in literature with different level of details, it is still not fully clear how this operator can be derived in the most general case and how it can be applied to various signal processing problems. In this work, we will give a general derivation of the quaternion-valued gradient operator and then apply it to two different areas. One is to combine with the classic computational fluid dynamics (CFD) approach in wind profile prediction and the other one is to apply the result to the adaptive beamforming problem for vector sensor arrays.