标题： 一种通用的四元数值梯度算子及其在计算流体力学和自适应波束成形中的应用 显示英文标题

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

摘要： 四元数值信号处理近年来受到了越来越多的关注。 涉及各种自适应算法推导的关键操作是梯度算子。 尽管在文献中已经有一些关于该算子的不同详细程度的推导，但目前仍不完全清楚如何在最一般的情况下推导该算子，以及如何将其应用于各种信号处理问题。 在本工作中，我们将给出四元数值梯度算子的一般推导，然后将其应用到两个不同的领域。 一个是将它与风廓线预测中的经典计算流体力学（CFD）方法相结合，另一个是将结果应用于矢量传感器阵列的自适应波束成形问题。 显示英文摘要

摘要： 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.